AGE of the UNIVERSE

NASA's Wilkinson Microwave Anisotropy Probe (WMAP) has taken the best measurement of the age of the Universe to date. According to highly precise observations of microwave radiation observed all over the cosmos, WMAP scientists now have the best estimate yet on the age of the Universe: 13.73 billion years, plus or minus 120 million years (that's an error margin of only 0.87%… not bad really…).

The WMAP mission was sent to the Sun-Earth second Lagrangian point (L2), located approximately 1.5 million km from the surface of the Earth on the night-side (i.e. WMAP is constantly in the shadow of the Earth) in 2001. The reason for this location is the nature of the gravitational stability in the region and the lack of electromagnetic interference from the Sun. Constantly looking out into space, WMAP scans the cosmos with its ultra sensitive microwave receiver, mapping any small variations in the background "temperature" (anisotropy) of the universe. It can detect microwave radiation in the wavelength range of 3.3-13.6 mm (with a corresponding frequency of 90-22 GHz). Warm and cool regions of space are therefore mapped, including the radiation polarity.

This microwave background radiation originates from a very early universe, just 400,000 years after the Big Bang, when the ambient temperature of the universe was about 3,000 K. At this temperature, neutral hydrogen atoms were possible, scattering photons. It is these photons WMAP observes today, only much cooler at 2.7 Kelvin (that's only 2.7 degrees higher than absolute zero, -273.15°C). WMAP constantly observes this cosmic radiation, measuring tiny alterations in temperature and polarity. These measurements refine our understanding about the structure of our universe around the time of the Big Bang and also help us understand the nature of the period of "inflation", in the very beginning of the expansion of the Universe.

It is a matter of exposure for the WMAP mission, the longer it observes the better refined the measurements. After seven years of results-taking, the WMAP mission has tightened the estimate on the age of the Universe down to an error margin of only 120 million years, that's 0.87% of the 13.73 billion years since the Big Bang.

"Everything is tightening up and giving us better and better precision all the time [...] It's actually significantly better than previous results. There is all kinds of richness in the data." – Charles L. Bennett, Professor of Physics and Astronomy at Johns Hopkins University.

This will be exciting news to cosmologists as theories on the very beginning of the Universe are developed even further.

Source: New York Times

Filed under: Cosmology, Observing

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From Wikipedia.com

The AGE of the UNIVERSE is the time elapsed between the Big Bang and the present day. Current theory and observations suggest that the universe is between 13.5 and 14 billion years old.[1] The uncertainty range has been obtained by the agreement of a number of scientific research projects. These projects included background radiation measurements and more ways to measure the expansion of the universe. Background radiation measurements give the cooling time of the universe since the Big Bang. Expansion of the universe measurements give accurate data to calculate the age of the universe.

Explanation

The Lambda-CDM concordance model describes the evolution of the universe from a very uniform, hot, dense primordial state to its present state over a span of about 13.73 billion years of cosmological time. This model is well understood theoretically and strongly supported by recent high-precision astronomical observations such as WMAP. In contrast, theories of the origin of the primordial state remain very speculative. If one extrapolates the Lambda-CDM model backward from the earliest well-understood state, it quickly (within a small fraction of a second) reaches a singularity called the "Big Bang singularity." This singularity is not considered to have any physical significance, but it is convenient to quote times measured "since the Big Bang," even though they do not correspond to a physically measurable time. For example, "10−6 second after the Big Bang" is a well-defined era in the universe's evolution. In one sense it would be more meaningful to refer to the same era as "13.7 billion years minus 10−6 seconds ago," but this is unworkable since the latter time interval is swamped by uncertainty in the former.

Though the universe might in theory have a longer history, cosmologists presently use "age of the universe" to mean the duration of the Lambda-CDM expansion, or equivalently the elapsed time since the Big Bang.

Observational limits

Since the universe must be at least as old as the oldest thing in it, there are a number of observations which put a lower limit on the age of the universe; these include the temperature of the coolest white dwarfs, which gradually cool as they age, and the dimmest turnoff point of main sequence stars in clusters (lower-mass stars spend a greater amount of time on the main sequence, so the lowest-mass stars that have evolved off of the main sequence set a minimum age). On April 23, 2009 a gamma-ray burst was detected which was later confirmed at being over 13 billion years old.[2]

Cosmological parameters

The age of the universe can be determined by measuring the Hubble constant today and extrapolating back in time with the observed value of density parameters (Ω). Before the discovery of dark energy, it was believed that the universe was matter-dominated, and so Ω on this graph corresponds to Ωm. Note that the accelerating universe has the greatest age, while the Big Crunch universe has the smallest age.

The value of the age correction factor F is shown as a function of two cosmological parameters: the current fractional matter density and cosmological constant density ΩmΩΛ. The best-fit values of these parameters are shown by the box in the upper left; the matter-dominated universe is shown by the star in the lower right.

The problem of determining the age of the universe is closely tied to the problem of determining the values of the cosmological parameters. Today this is largely carried out in the context of the ΛCDM model, where the Universe is assumed to contain normal (baryonic) matter, cold dark matter, radiation (including both photons and neutrinos), and a cosmological constant. The fractional contribution of each to the current energy density of the Universe is given by the density parameters Ωm, Ωr, and ΩΛ. The full ΛCDM model is described by a number of other parameters, but for the purpose of computing its age these three, along with the Hubble parameter H0 are the most important.

If one has accurate measurements of these parameters, then the age of the universe can be determined by using the Friedmann equation. This equation relates the rate of change in the scale factor a(t) to the matter content of the Universe. Turning this relation around, we can calculate the change in time per change in scale factor and thus calculate the total age of the universe by integrating this formula. The age t0 is then given by an expression of the form

where the function F depends only on the fractional contribution to the universe's energy content that comes from various components. The first observation that one can make from this formula is that it is the Hubble parameter that controls that age of the universe, with a correction arising from the matter and energy content. So a rough estimate of the age of the universe comes from the inverse of the Hubble parameter,

To get a more accurate number, the correction factor F must be computed. In general this must be done numerically, and the results for a range of cosmological parameter values are shown in the figure. For the WMAP values (Ωm, ΩΛ) = (0.266, 0.732), shown by the box in the upper left corner of the figure, this correction factor is nearly one: F = 0.996. For a flat universe without any cosmological constant, shown by the star in the lower right corner, F = 2/3 is much smaller and thus the universe is younger for a fixed value of the Hubble parameter. To make this figure, Ωr is held constant (roughly equivalent to holding the CMB temperature constant) and the curvature density parameter is fixed by the value of the other three.

The Wilkinson Microwave Anisotropy Probe (WMAP) was instrumental in establishing an accurate age of the universe, though other measurements must be folded in to gain an accurate number. CMB measurements are very good at constraining the matter content Ωm[3] and curvature parameter Ωk.[4] It is not as sensitive to ΩΛ directly,[4] partly because the cosmological constant only becomes important at low redshift. The most accurate determinations of the Hubble parameter H0 come from Type Ia supernovae. Combining these measurements leads to the generally accepted value for the age of the universe quoted above.

The cosmological constant makes the universe "older" for fixed values of the other parameters. This is significant, since before the cosmological constant became generally accepted, the Big Bang model had difficulty explaining why globular clusters in the Milky Way appeared to be far older than the age of the universe as calculated from the Hubble parameter and a matter-only universe.[5][6] Introducing the cosmological constant allows the universe to be older than these clusters, as well as explaining other features that the matter-only cosmological model could not.[7]

WMAP

NASA's Wilkinson Microwave Anisotropy Probe (WMAP) project estimates the age of the universe to be:

(1.373 ± 0.012) × 1010 years.

That is, the universe is about 13.73 billion years old,[1] with an uncertainty of 120 million years. However, this age is based on the assumption that the project's underlying model is correct; other methods of estimating the age of the universe could give different ages. Assuming an extra background of relativistic particles, for example, can enlarge the error bars of the WMAP constraint by one order of magnitude.[8]

This measurement is made by using the location of the first acoustic peak in the microwave background power spectrum to determine the size of the decoupling surface (size of universe at the time of recombination). The light travel time to this surface (depending on the geometry used) yields a reliable age for the universe. Assuming the validity of the models used to determine this age, the residual accuracy yields a margin of error near one percent.[9]

This is the value currently most quoted by astronomers.

Assumption of strong priors

Calculating the age of the universe is only accurate if the assumptions built into the models being used to estimate it are also accurate. This is referred to as strong priors and essentially involves stripping the potential errors in other parts of the model to render the accuracy of actual observational data directly into the concluded result. Although this is not a valid procedure in all contexts (as noted in the accompanying caveat: "based on the fact we have assumed the underlying model we used is correct"), the age given is thus accurate to the specified error (since this error represents the error in the instrument used to gather the raw data input into the model).

The age of the universe based on the "best fit" to WMAP data "only" is 13.69±0.13 Gyr[1] (the slightly higher number of 13.73 includes some other data mixed in). This number represents the first accurate "direct" measurement of the age of the universe (other methods typically involve Hubble's law and age of the oldest stars in globular clusters, etc). It is possible to use different methods for determining the same parameter (in this case – the age of the universe) and arrive at different answers with no overlap in the "errors". To best avoid the problem, it is common to show two sets of uncertainties; one related to the actual measurement and the other related to the systematic errors of the model being used.

An important component to the analysis of data used to determine the age of the universe (e.g. from WMAP) therefore is to use a Bayesian Statistical analysis, which normalizes the results based upon the priors (i.e. the model).[9] This quantifies any uncertainty in the accuracy of a measurement due to a particular model used.[10][11]

See also

References

External links

Retrieved from "http://en.wikipedia.org/wiki/Age_of_the_universe"

Categories: Universe | Physical cosmology

WMAP

Wilkinson Microwave Anisotropy Probe (WMAP) — also known as the Microwave Anisotropy Probe (MAP), and Explorer 80 — is a spacecraft which measures differences in the temperature of the Big Bang's remnant radiant heat — the Cosmic Microwave Background Radiation — across the full sky.[4][5] Headed by Professor Charles L. Bennett, Johns Hopkins University, the mission was developed in a joint partnership between the NASA Goddard Space Flight Center and Princeton University.[6] The WMAP spacecraft was launched on 30 June 2001, at 19:46:46 GDT, from Florida. The WMAP mission succeeds the COBE space mission and was the second medium-class (MIDEX) spacecraft of the Explorer program. In 2003, MAP was renamed WMAP in honor of David Todd Wilkinson[6], (1935-2002) who had been a member of the mission's science team.

WMAP's measurements played the key role in establishing the current Standard Model of Cosmology. WMAP data are very well fit by a universe that is dominated by dark energy in the form of a cosmological constant. Other cosmological data are also consistent, and together tightly constrain the Model. In this Lambda-CDM model of the universe, the age of the universe is 13.73 ± 0.12 billion years. The WMAP mission's determination of the age of the universe to better than 1% precision was recognized by the Guinness Book of World Records. The current expansion rate of the universe is (see Hubble constant) of 70.5 ± 1.3 km·s−1·Mpc−1. The content of the universe presently consists of 4.56% ± 0.15% ordinary baryonic matter; 22.8% ± 1.3% Cold Dark Matter (CDM) that neither emits nor absorbs light; and 72.6% ± 1.5% of dark energy in the form of a cosmological constant that accelerates the expansion of the universe. Less than 1% of the current contents of the universe is in neutrinos, however WMAP's measurements have found, for the first time in 2008, that the data prefers the existence of a cosmic neutrino background [7] with an effective number of neutrino flavors of 4.4 ± 1.5, consistent with the expectation of 3.06. The contents point to a ``flat" Euclidean flat geometry, with the ratio of the energy density in curvature to the critical density 0.0179 < Ωk <0.0081 (95%CL). The WMAP measurements also support the cosmic inflation paradigm in several ways, including the flatness measurement.

Per Science magazine, the WMAP was the Breakthrough of the Year for 2003.[8] This mission's results papers were first and second in the "Super Hot Papers in Science Since 2003" list.[9] Of the all-time most referenced refereed papers in physics and astronomy in the SPIRES database, only three have been published since 2000, and all three are WMAP publications.

As of 2009, the WMAP spacecraft continues to take data in perfect working order, approaching 8 years of operations. The Astronomy and Physics Senior Review panel at NASA Headquarters has endorsed a total of 9 years of WMAP operations, through September 2010.[3] All WMAP data are released to the public and have been subject to careful scrutiny.

Some aspects of the data are statistically unusual for the Standard Model of Cosmology. For example, the greatest angular-scale measurements, the quadrupole moment, is somewhat smaller than the Model would predict, but this discrepancy is not highly significant. A large cold spot and other features of the data are more statistically significant, and research continues into these.

Objectives

Universe's Timeline from Inflation to the WMAP.

The WMAP is to measure the temperature differences in the Cosmic Microwave Background (CMB) radiation. The anisotropies then are used to measure the universe's geometry, content, and evolution; and to test the Big Bang model, and the cosmic inflation theory.[1] For that, the mission is creating a full-sky map of the CMB, with a 13 arcminute resolution via multi-frequency observation. The map requires the fewest systematic errors, no correlated pixel noise, and accurate calibration, to ensure angular-scale accuracy greater than its resolution.[1] The map contains 3,145,728 pixels, and uses the HEALPix scheme to pixelize the sphere.[10] The telescope also measures the CMB's E-mode polarization,[1] and foreground polarization; [7] its life is 27 months; 3 to reach the L2 position, 2 years of observation.[1]

Development

A comparison of the sensitivity of WMAP with COBE and Penzias and Wilson's telescope. Simulated data.

The MAP mission was proposed to NASA in 1995, selected for definition study in 1996, and approved for development in 1997.[3][11]

The WMAP was preceded by two missions to observe the CMB; (i) the Soviet RELIKT-1 that reported the upper-limit measurements of CMB anisotropies, and (ii) the U.S. COBE satellite that reported large-scale CMB fluctuations, and the ground-based and balloon experiments measuring the small-scale fluctuations in patches of sky: the Boomerang, the Cosmic Background Imager, and the Very Small Array. The WMAP is 45 times more sensitive, with 33 times the angular resolution of its COBE satellite predecessor.[2]

The Spacecraft

WMAP Spacecraft Diagram

The telescope's primary reflecting mirrors are a pair of Gregorian 1.4m x 1.6m dishes (facing opposite directions), that focus the signal onto a pair of 0.9m x 1.0m secondary reflecting mirrors. They are shaped for optimal performance: a carbon fibre shell upon a Korex core, thinly-coated with aluminium and silicon oxide. The secondary reflectors transmit the signals to the corrugated feedhorns that sit on a focal plane array box beneath the primary reflectors.[1]

Illustration of WMAP's receivers

The receivers are polarization-sensitive differential radiometers measuring the difference between two telescope beams. The signal is amplified with HEMT low-noise amplifiers. There are 20 feeds, 10 in each direction, from which a radiometer collects a signal; the measure is the difference in the sky signal from opposite directions. The directional separation azimuth is 180 degrees; the total angle is 141 degrees.[1] To avoid collecting Milky Way galaxy foreground signals, the WMAP uses five discrete radio frequency bands, from 23GHz to 94GHz.[1]

The WMAP's base is a 5.0m-diameter solar panel array that keeps the instruments in shadow during CMB observations, (by keeping the craft constantly angled at 22 degrees, relative to the sun). Upon the array sit a bottom deck (supporting the warm components) and a top deck. The telescope's cold components: the focal-plane array and the mirrors, are separated from the warm components with a cylindrical, 33 cm-long thermal isolation shell atop the deck.[1]

Passive thermal radiators cool the WMAP to ca. 90 degrees K; they are connected to the low-noise amplifiers. The telescope consumes 419 W of power. The available telescope heaters are emergency-survival heaters, and there is a transmitter heater, used to warm them when off. The WMAP spacecraft's temperature is monitored with platinum resistance thermometers.[1]

The WMAP's calibration is effected with the CMB dipole and measurements of Jupiter; the beam patterns are measured against Jupiter. The telescope's data are relayed daily via a 2GHz transponder providing a 667kbit/s downlink to a 70m Deep Space Network telescope. The spacecraft has two transponders, one a redundant back-up; they are minimally active — ca. 40 minutes daily — to minimize radio frequency interference. The telescope's position is maintained, in its three axes, with three reaction wheels, gyroscopes, two star trackers and sun sensors, and is steered with eight hydrazine thrusters.[1]

Launch, Trajectory, and Orbit

The WMAP's Trajectory and Orbit.

The WMAP spacecraft arrived at the Kennedy Space Center on 20 April 2001. After being tested for two months, it was launched via Delta II 7425 rocket on 30 June 2001.[2][3] It began operating on its internal power five minutes before its launching, and so continued operating until the solar panel array deployed. The WMAP was activated and monitored while it cooled. On 2 July, it began working, first with in-flight testing (from launching 'til 17 August), then began constant, formal work.[2] Afterwards, it effected three Earth-Moon phase loops, measuring its sidelobes, then flew by the Moon on 30 July, enroute to the Sun-Earth L2 Lagrangian point, arriving there on 1 October 2001, becoming, thereby, the first CMB observation mission permanently posted there.[3]

WMAP's Orbit and Sky Scan Strategy

The spacecraft's location at Lagrange 2, (1.5 million kilometers from Earth) minimizes the amount of contaminating solar, terrestrial, and lunar emissions registered, and thermally stabilizes it. To view the entire sky, without looking to the sun, the WMAP traces a path around L2 in a Lissajous orbit ca. 1.0 degree to 10 degrees,[1] with a 6-month period.[3] The telescope rotates once every 2 minutes, 9 seconds" (0.464 rpm) and processes at the rate of 1 revolution per hour.[1] WMAP measures the entire sky every six months, and completed its first, full-sky observation in April 2002.[11]

Foreground Radiation Subtraction

The WMAP observes in five frequencies, permitting the measurement and subtraction of foreground contamination (from the Milky Way and extra-galactic sources) of the CMB. The main emission mechanisms are synchrotron radiation and free-free emission (dominating the lower frequencies), and astrophysical dust emissions (dominating the higher frequencies). The spectral properties of these emissions contribute different amounts to the five frequencies, thus permitting their identification and subtraction.[1]

Foreground contamination is removed in several ways. First, subtract extant emission maps from the WMAP's measurements; second, use the components' known, spectral values to identify them; third, simultaneously fit the position and spectra data of the foreground emission, using extra data sets. Foreground contamination also is reduced by using only the full-sky map portions with the least foreground contamination, whilst masking the remaining map portions.[1]

The five-year models of foreground emission, at different frequencies. Red = Synchrotron; Green = free-free; Blue = thermal dust.

23 GHz

33 GHz

41 GHz

61 GHz

94 GHz

Wilkinson Microwave Anisotropy Probe

General information

NSSDC ID

Organization

Launch date

Launched from

Launch vehicle

Mission length

Mass

Type of orbit

Location

2001-027A

NASA

30 June 2001, 19:46 UTC

Cape Canaveral Air Force Station

Delta II 7425-10

8 years, 4 months, and 6 days elapsed

840 kg

Lissajous orbit

L2

Instruments

K-band 23 GHz

Ka-band 33 GHz

Q-band 41 GHz

V-band 61 GHz

W-band 94 GHz

Website

52.8 MOA beam

39.6 MOA beam

30.6 MOA beam

21 MOA beam

13.2 MOA beam

http://map.gsfc.nasa.gov

References: [1][2][3]

Measurements and Discoveries

One-year data release

The first-year map of the CMB.

On 11 February 2003, based upon one year's worth of WMAP data, NASA published the latest calculated age, composition, and image of the universe to date, that "contains such stunning detail, that it may be one of the most important scientific results of recent years"; the data surpass previous CMB measurements.[6]

Based upon the Lambda-CDM model, the WMAP team produced cosmological parameters from the WMAP's first-year results. Three sets are given below; the first and second sets are WMAP data; the difference is the addition of spectral indices, predictions of some inflationary models. The third data set combines the WMAP constraints with those from other CMB experiments (ACBAR and CBI), and constraints from the 2dF Galaxy Redshift Survey and Lyman alpha forest measurements. Note that there are degenerations among the parameters, the most significant is between ns and τ; the errors given are at 68% confidence.[12]

Using the best-fit data and theoretical models, the WMAP team determined the times of important universal events, including the redshift of reionization, 17±4; the redshift of decoupling, 1,089±1 (and the universe's age at decoupling, 379

+8

−7

ka; and the redshift of matter/radiation equality, 3,233

+194

−210

. They determined the thickness of the surface of last scattering to be 195±2 in redshift, or 118

+3

−2

ka. They determined the current density of baryons, 2.5±0.1×10−7 cm−1, and the ratio of baryons to photons, 6.1

+0.3

−0.2

×10−10. The WMAP's detection of an early reionization excluded warm dark matter.[12]

The team also examined Milky Way emissions at the WMAP frequencies, producing a 208-point source catalogue. Also, they observed the Sunyaev-Zel'dovich effect at 2.5 σ the strongest source is the Coma cluster.[10]

Three-year data release

A map of the polarization from the 3rd year results

The three-year WMAP data were released on 17 March 2006. The data included temperature and polarization measurements of the CMB, which provided further confirmation of the standard flat Lambda-CDM model and new evidence in support of inflation.

The 3-year WMAP data alone shows that the universe must have dark matter. Results were computed both only using WMAP data, and also with a mix of parameter constraints from other instruments, including other CMB experiments (ACBAR, CBI and BOOMERANG), SDSS, the 2dF Galaxy Redshift Survey, the Supernova Legacy Survey and constraints on the Hubble constant from the Hubble Space Telescope.[13]

[a] ^ Optical depth to reionization improved due to polarization measurements.[14]

[b] ^ < 0.30 when combined with SDSS data. No indication of non-gaussianity.[13]

Five-year data release

5 year WMAP image of background cosmic radiation (2008)

The five-year WMAP data were released on 28 February 2008. The data included new evidence for the cosmic neutrino background, evidence that it took over half a billion years for the first stars to reionize the universe, and new constraints on cosmic inflation.[15]

The improvement in the results came from both having an extra 2 years of measurements (the data set runs between midnight on 10 August 2001 to midnight of 9 August 2006), as well as using improved data processing techniques and a better characterization of the instrument, most notably of the beam shapes. They also make use of the 33 GHz observations for estimating cosmological parameters; previously only the 41 GHz and 61 GHz channels had been used. Finally, improved masks were used to remove foregrounds.[7]

The five-year total-intensity and polarization spectra from WMAP

Improvements to the spectra were in the 3rd acoustic peak, and the polarization spectra.[7]

The measurements put constraints on the content of the universe at the time that the CMB was emitted; at the time 10% of the universe was made up of neutrinos, 12% of atoms, 15% of photons and 63% dark matter. The contribution of dark energy at the time was negligible.[15]

The WMAP five-year data was combined with measurements from Type Ia supernova (SNe) and Baryon acoustic oscillations (BAO).[7]

The elliptical shape of the WMAP skymap is the result of a Mollweide projection[16].

Matter content in the current universe

The data puts a limits on the value of the tensor-to-scalar ratio, r < 0.22 (95% certainty), which determines the level at which gravitational waves affect the polarization of the CMB, and also puts limits on the amount of primordial non-gaussianity. Improved constraints were put on the redshift of reionization, which is 10.9±1.4, the redshift of decoupling, 1,090.88±0.72 (as well as age of universe at decoupling, 376.971

+3.162

−3.167

ka) and the redshift of matter/radiation equality, 3,253

+89

−87

.[7]

The extragalactic source catalogue was expanded to include 390 sources, and variability was detected in the emission from Mars and Saturn.[7]

The five-year maps at different frequencies from WMAP with foregrounds (the red band)

23 GHz

33 GHz

41 GHz

61 GHz

94 GHz

Future Measurements

Artist's impression of the Planck spacecraft

The original timeline for WMAP gave it two years of observations; these were completed by September 2003. Mission extensions were granted in both 2002 and 2004, giving the spacecraft a total of 8 observing years (the originally proposed duration), which end in September 2009.[3]

WMAP's results will be built upon by several other instruments that are currently under construction. These will either be focusing on higher sensitivity total intensity measurements or measuring the polarization more accurately in the search of B-mode polarization indicative of primordial gravitational waves.

The next space-based instrument will be the Planck spacecraft, which launched on 14 May 2009. This instrument aims to measure the CMB more accurately than WMAP at all angular scales, both in total intensity and polarization. Various ground- and balloon-based instruments are being constructed to look for B-mode polarization, including Clover and EBEX.

See also

References

Technical Pages

External links

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Full-sky temperature map taken by NASA's Wilkinson Microwave Anisotropy Probe (WMAP)

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Absorption lines in the optical spectrum of a supercluster of distant galaxies (right), as compared to absorption lines in the optical spectrum of the Sun (left). Arrows indicate redshift. Wavelength increases up towards the red and beyond (frequency decreases).

Redshift and blue shift

In physics and astronomy, redshift occurs when electromagnetic radiation—usually visible light—emitted or reflected by an object is shifted towards the (less energetic) red end of the electromagnetic spectrum due to the Doppler effect or other gravitationally-induced effects. More generally, redshift is defined as an increase in the wavelength of electromagnetic radiation received by a detector compared with the wavelength emitted by the source. This increase in wavelength corresponds to a drop in the frequency of the electromagnetic radiation. Conversely, a decrease in wavelength is called blue shift.

Any increase in wavelength is called "redshift", even if it occurs in electromagnetic radiation of non-optical wavelengths, such as gamma rays, x-rays and ultraviolet. This nomenclature might be confusing since, at wavelengths longer than red (e.g., infrared, microwaves, and radio waves), redshifts shift the radiation away from the red wavelengths.

An observed redshift due to the Doppler effect occurs whenever a light source moves away from the observer, corresponding to the Doppler shift that changes the perceived frequency of sound waves. Although observing such redshifts, or complementary blue shifts, has several terrestrial applications (e.g., Doppler radar and radar guns),[1] spectroscopic astrophysics uses Doppler redshifts to determine the movement of distant astronomical objects.[2]

A special relativistic redshift formula (and its Newtonian approximation) is used when spacetime is flat. Where gravitational effects are important, redshift must be calculated using general relativity. Two important special-case formulae are the so-called gravitational redshift formula which applies to any stationary (that is, unchanging with time) gravitational field, and the cosmological redshift formula which applies to the expanding universe of Big Bang cosmology.[3]

Special relativistic, gravitational, and cosmological redshifts can be understood under the umbrella of frame transformation laws. There exist other physical processes that can lead to a shift in the frequency of electromagnetic radiation that are not generally referred to as "redshifts", including scattering and optical effects (for more see section on physical optics and radiative transfer).

History

The history of the subject began with the development in the 19th century of wave mechanics and the exploration of phenomena associated with the Doppler effect. The effect is named after Christian Andreas Doppler, who offered the first known physical explanation for the phenomenon in 1842.[4] The hypothesis was tested and confirmed for sound waves by the Dutch scientist Christoph Hendrik Diederik Buys Ballot in 1845.[5] Doppler correctly predicted that the phenomenon should apply to all waves, and in particular suggested that the varying colors of stars could be attributed to their motion with respect to the Earth.[6] While this attribution turned out to be incorrect (stellar colors are indicators of a star's temperature, not motion), Doppler would later be vindicated by verified redshift observations.

The first Doppler redshift was described in 1848 by French physicist Armand-Hippolyte-Louis Fizeau, who pointed to the shift in spectral lines seen in stars as being due to the Doppler effect. The effect is sometimes called the "Doppler-Fizeau effect". In 1868, British astronomer William Huggins was the first to determine the velocity of a star moving away from the Earth by this method.[7]

In 1871, optical redshift was confirmed when the phenomenon was observed in Fraunhofer lines using solar rotation, about 0.1 Å in the red.[8] In 1901 Aristarkh Belopolsky verified optical redshift in the laboratory using a system of rotating mirrors.[9]

The earliest occurrence of the term "red-shift" in print (in this hyphenated form), appears to be by American astronomer Walter S. Adams in 1908, where he mentions "Two methods of investigating that nature of the nebular red-shift".[10] The word doesn't appear unhyphenated, perhaps indicating a more common usage of its German equivalent, Rotverschiebung, until about 1934 by Willem de Sitter.[11]

Beginning with observations in 1912, Vesto Slipher discovered that most spiral nebulae had considerable redshifts.[12] Subsequently, Edwin Hubble discovered an approximate relationship between the redshift of such "nebulae" (now known to be galaxies in their own right) and the distance to them with the formulation of his eponymous Hubble's law.[13] These observations corroborated Alexander Friedman's 1922 work, in which he derived the famous Friedmann equations.[14] They are today considered strong evidence for an expanding universe and the Big Bang theory.[15]

Measurement, characterization, and interpretation

The spectrum of light that comes from a single source (see idealized spectrum illustration top-right) can be measured. To determine the redshift, features in the spectrum such as absorption lines, emission lines, or other variations in light intensity, are searched for. If found, these features can be compared with known features in the spectrum of various chemical compounds found in experiments where that compound is located on earth. A very common atomic element in space is hydrogen. The spectrum of originally featureless light shined through hydrogen will show a signature spectrum specific to hydrogen that has features at regular intervals. If restricted to absorption lines it would look similar to the illustration (top right). If the same pattern of intervals is seen in an observed spectrum from a distant source but occurring at shifted wavelengths, it can be identified as hydrogen too. If the same spectral line is identified in both spectra but at different wavelengths then the redshift can be calculated using the table below. Determining the redshift of an object in this way requires a frequency- or wavelength-range. In order to calculate the redshift one has to know the wavelength of the emitted light in the rest frame of the source, in other words, the wavelength that would be measured by an observer located adjacent to and comoving with the source. Since in astronomical applications this measurement cannot be done directly, because that would require travelling to the distant star of interest, the method using spectral lines described here is used instead. Redshifts cannot be calculated by looking at unidentified features whose rest-frame frequency is unknown, or with a spectrum that is featureless or white noise (random fluctuations in a spectrum).[16]

Redshift (and blue shift) may be characterized by the relative difference between the observed and emitted wavelengths (or frequency) of an object. In astronomy, it is customary to refer to this change using a dimensionless quantity called z. If λ represents wavelength and f represents frequency (note, λf = c where c is the speed of light), then z is defined by the equations:

Calculation of redshift, z

Based on wavelength

Based on frequency

After z is measured, the distinction between redshift and blue shift is simply a matter of whether z is positive or negative. See the formulae section below for some basic interpretations that follow when either a redshift or blue shift is observed. For example, Doppler effect blue shifts (z < 0) are associated with objects approaching (moving closer to) the observer with the light shifting to greater energies. Conversely, Doppler effect redshifts (z > 0) are associated with objects receding (moving away) from the observer with the light shifting to lower energies. Likewise, gravitational blue shifts are associated with light emitted from a source residing within a weaker gravitational field observed within a stronger gravitational field, while gravitational redshifting implies the opposite conditions.

Redshift formulae

In general relativity one can derive several important special-case formulae for redshift in certain special spacetime geometries, as summarized in the following table. In all cases the magnitude of the shift (the value of z) is independent of the wavelength.[2]

Doppler effect, yellow (~575 nm wavelength) ball appears greenish (blueshift to ~565 nm wavelength) approaching observer, turns orange (redshift to ~585 nm wavelength) as it passes, and returns to yellow when motion stops. To observe such a change in color, the object would have to be traveling at approximately 5200 km/s, or about 75 times faster than the speed record for the fastest manmade space probe.

Redshift Summary

Redshift type

Relativistic Doppler

Cosmological redshift

Gravitational redshift

Geometry

Minkowski space (flat spacetime)

FLRW spacetime (expanding Big Bang universe)

any stationary spacetime (e.g. the Schwarzschild geometry)

Formula[17]

( for small v)

(for the Schwarzschild geometry, )

Doppler effect

Main article: Doppler effect

If a source of the light is moving away from an observer, then redshift (z > 0) occurs; if the source moves towards the observer, then blue shift (z < 0) occurs. This is true for all electromagnetic waves and is explained by the Doppler effect. Consequently, this type of redshift is called the Doppler redshift. If the source moves away from the observer with velocity v, then, ignoring relativistic effects, the redshift is given by

(Since , see below)

where c is the speed of light. In the classical Doppler effect, the frequency of the source is not modified, but the recessional motion causes the illusion of a lower frequency.

Relativistic Doppler effect

Main article: Relativistic Doppler effect

A more complete treatment of the Doppler redshift requires considering relativistic effects associated with motion of sources close to the speed of light. A complete derivation of the effect can be found in the article on the relativistic Doppler effect. In brief, objects moving close to the speed of light will experience deviations from the above formula due to the time dilation of special relativity which can be corrected for by introducing the Lorentz factor γ into the classical Doppler formula as follows:

This phenomenon was first observed in a 1938 experiment performed by Herbert E. Ives and G.R. Stilwell, called the Ives-Stilwell experiment.[18]

Since the Lorentz factor is dependent only on the magnitude of the velocity, this causes the redshift associated with the relativistic correction to be independent of the orientation of the source movement. In contrast, the classical part of the formula is dependent on the projection of the movement of the source into the line-of-sight which yields different results for different orientations. Consequently, for an object moving at an angle θ to the observer (zero angle is directly away from the observer), the full form for the relativistic Doppler effect becomes:

and for motion solely in the line of sight (θ = 0°), this equation reduces to:

For the special case that the source is moving at right angles (θ = 90°) to the detector, the relativistic redshift is known as the transverse redshift, and a redshift:

is measured, even though the object is not moving away from the observer. Even if the source is moving towards the observer, if there is a transverse component to the motion then there is some speed at which the dilation just cancels the expected blue shift and at higher speed the approaching source will be redshifted.[19]

A variety of possible recession velocity vs. redshift functions including the simple linear relation v = cz; a variety of possible shapes from theories of cosmological expansion related to general relativity; and a curve that does not permit speeds faster than light in accordance with special relativity. All curves are linear at low redshifts. See Davis and Lineweaver.[20]

Expansion of space

Main article: Metric expansion of space

In the early part of the twentieth century, Slipher, Hubble and others made the first measurements of the redshifts and blue shifts of galaxies beyond the Milky Way. They initially interpreted these redshifts and blue shifts as due solely to the Doppler effect, but later Hubble discovered a rough correlation between the increasing redshifts and the increasing distance of galaxies. Theorists almost immediately realized that these observations could be explained by a different mechanism for producing redshifts. Hubble's law of the correlation between redshifts and distances is required by models of cosmology derived from general relativity that have a metric expansion of space.[15] As a result, photons propagating through the expanding space are stretched, creating the cosmological redshift. This differs from the Doppler effect redshifts described above because the velocity boost (i.e. the Lorentz transformation) between the source and observer is not due to classical momentum and energy transfer, but instead the photons increase in wavelength and redshift as the space through which they are traveling expands.[21] The observational consequences of this effect can be derived using the equations from general relativity that describe a homogeneous and isotropic universe.

To derive the redshift effect, use the geodesic equation for a light wave, which is

where

For an observer observing the crest of a light wave at a position r = 0 and time t = tnow, the crest of the light wave was emitted at a time t = tthen in the past and a distant position r = R. Integrating over the path in both space and time that the light wave travels yields:

In general, the wavelength of light is not the same for the two positions and times considered due to the changing properties of the metric. When the wave was emitted, it had a wavelength λthen. The next crest of the light wave was emitted at a time

The observer sees the next crest of the observed light wave with a wavelength λnow to arrive at a time

Since the subsequent crest is again emitted from r = R and is observed at r = 0, the following equation can be written:

The right-hand side of the two integral equations above are identical which means

or, alternatively,

For very small variations in time (over the period of one cycle of a light wave) the scale factor is essentially a constant (a = anow today and a = athen previously). This yields

which can be rewritten as

Using the definition of redshift provided above, the equation

is obtained. In an expanding universe such as the one we inhabit, the scale factor is monotonically increasing as time passes, thus, z is positive and distant galaxies appear redshifted. This type of redshift is called the cosmological redshift or Hubble redshift. If the universe were contracting instead of expanding, we would see distant galaxies blue shifted by an amount proportional to their distance instead of redshifted.[22]

These galaxies are not receding simply by means of a physical velocity in the direction away from the observer; instead, the intervening space is stretching, which accounts for the large-scale isotropy of the effect demanded by the cosmological principle.[23] For cosmological redshifts of z < 0.01 the effects of spacetime expansion are minimal and cosmological redshifts can be dominated by additional Doppler redshifts and blue shifts caused by the peculiar motions of the galaxies relative to one another.[24] The difference between physical velocity and space expansion can be illustrated by the Expanding Rubber Sheet Universe, a common cosmological analogy used to describe the expansion of space. If two objects are represented by ball bearings and spacetime by a stretching rubber sheet, the Doppler effect is caused by rolling the balls across the sheet to create peculiar motion. The cosmological redshift occurs when the ball bearings are stuck to the sheet and the sheet is stretched. (Obviously, there are dimensional problems with the model, as the ball bearings should be in the sheet, and cosmological redshift produces higher velocities than Doppler does if the distance between two objects is large enough.)

Using a model of the expansion of the universe, redshift can be related to the age of an observed object, the so-called cosmic time–redshift relation. Denote a density ratio as Ω0:

Two different sources of redshift: Top, Doppler shift: the star moving to the left emits light that is blue shifted in the direction of the receiving antenna that the star approaches, and red shifted in the direction of the receiving antenna that the star is leaving. Center and bottom panels: cosmological expansion: The distance between the emitting star and both antennas increases while the light is propagating, increasing the wavelength of the light seen by both antennas. Each panel shows the propagation of light over two periods: in the center panel at time of emission the wavelength is short, and in the bottom panel at time of reception the wavelength has stretched with the expansion of space. Patterned after Koupelis & Kuhn.[25] The reader is cautioned that too literal an interpretation of this figure can be misleading.[26] In particular, the Doppler shift panel is seen from a single inertial frame, that of the two antennas. The cosmological expansion panels are a concatenation of local inertial frames spanning the space between the various locally stationary objects.[27]

with ρcrit the critical density demarcating a universe that eventually crunches from one that simply expands. This density is about three hydrogen atoms per thousand liters of space.[28] At large redshifts one finds:

where H0 = present-day Hubble constant, and z = redshift.[29][30][31]

The redshifts of galaxies include both a component related to recessional velocity from expansion of the universe, and a component related to peculiar motion (Doppler shift). The redshift due to expansion of the universe depends upon the recessional velocity in a fashion determined by the cosmological model chosen to describe the expansion of the universe, which is very different from how Doppler redshift depends upon local velocity. Harrison provides a summary of this and related distinctions.[32] Describing the cosmological expansion origin of redshift, Harrison says: “Light leaves a galaxy, which is stationary in its local region of space, and is eventually received by observers who are stationary in their own local region of space. Between the galaxy and the observer, light travels through vast regions of expanding space. As a result, all wavelengths of the light are stretched by the expansion of space. It is as simple as that.” See Harrison, p. 315.[21] “The increase of wavelength from emission to absorption of light does not depend on the rate of change of a(t) [here a(t) is the Robertson-Walker scale factor] at the times of emission or absorption, but on the increase of a(t) in the whole period from emission to absorption.”[33]

Nonetheless, popular literature often uses the expression "Doppler redshift" instead of "cosmological redshift" to describe the redshift of galaxies dominated by the expansion of spacetime, despite the fact that the redshift is not found using the relativistic Doppler equation.[34] In particular, Doppler redshift is bound by special relativity; thus v > c is impossible while, in contrast, v > c is possible for cosmological redshift because the space which separates the objects (for example, a quasar from the Earth) can expand faster than the speed of light.[35] More mathematically, the viewpoint that "distant galaxies are receding" and the viewpoint that "the space between galaxies is expanding" are related by changing coordinate systems. Expressing this precisely requires working with the mathematics of the Friedmann-Robertson-Walker metric.[36]

Gravitational redshift

Main article: Gravitational redshift

In the theory of general relativity, there is time dilation within a gravitational well. This is known as the gravitational redshift or Einstein Shift.[37] The theoretical derivation of this effect follows from the Schwarzschild solution of the Einstein equations which yields the following formula for redshift associated with a photon traveling in the gravitational field of an uncharged, nonrotating, spherically symmetric mass:

where

This gravitational redshift result can be derived from the assumptions of special relativity and the equivalence principle; the full theory of general relativity is not required.[38]

The effect is very small but measurable on Earth using the Mössbauer effect and was first observed in the Pound-Rebka experiment.[39] However, it is significant near a black hole, and as an object approaches the event horizon the red shift becomes infinite. It is also the dominant cause of large angular-scale temperature fluctuations in the cosmic microwave background radiation (see Sachs-Wolfe effect).[40]

Observations in astronomy

The redshift observed in astronomy can be measured because the emission and absorption spectra for atoms are distinctive and well known, calibrated from spectroscopic experiments in laboratories on Earth. When the redshift of various absorption and emission lines from a single astronomical object is measured, z is found to be remarkably constant. Although distant objects may be slightly blurred and lines broadened, it is by no more than can be explained by thermal or mechanical motion of the source. For these reasons and others, the consensus among astronomers is that the redshifts they observe are due to some combination of the three established forms of Doppler-like redshifts. Alternative hypotheses and explanations for redshift such as tired light are not generally considered plausible.[41]

Spectroscopy, as a measurement, is considerably more difficult than simple photometry, which measures the brightness of astronomical objects through certain filters.[42] When photometric data is all that is available (for example, the Hubble Deep Field and the Hubble Ultra Deep Field), astronomers rely on a technique for measuring photometric redshifts.[43] Due to the filter being sensitive to a range of wavelengths and the technique relying on making many assumptions about the nature of the spectrum at the light-source, errors for these sorts of measurements can range up to δz = 0.5, and are much less reliable than spectroscopic determinations.[44] However, photometry does allow at least for a qualitative characterization of a redshift. For example, if a sun-like spectrum had a redshift of z = 1, it would be brightest in the infrared rather than at the yellow-green color associated with the peak of its blackbody spectrum, and the light intensity will be reduced in the filter by a factor of two (1+z) (see K correction for more details on the photometric consequences of redshift).[45]

Local observations

A picture of the solar corona taken with the LASCO C1 coronagraph. The picture is a color coded image of the doppler shift of the FeXIV 5308 Å line, caused by the coronal plasma velocity towards or away from the satellite.

In nearby objects (within our Milky Way galaxy) observed redshifts are almost always related to the line-of-sight velocities associated with the objects being observed. Observations of such redshifts and blue shifts have enabled astronomers to measure velocities and parametrize the masses of the orbiting stars in spectroscopic binaries, a method first employed in 1868 by British astronomer William Huggins.[7] Similarly, small redshifts and blue shifts detected in the spectroscopic measurements of individual stars are one way astronomers have been able to diagnose and measure the presence and characteristics of planetary systems around other stars.[46] Measurements of redshifts to fine detail are used in helioseismology to determine the precise movements of the photosphere of the Sun.[47] Redshifts have also been used to make the first measurements of the rotation rates of planets,[48] velocities of interstellar clouds,[49] the rotation of galaxies,[2] and the dynamics of accretion onto neutron stars and black holes which exhibit both Doppler and gravitational redshifts.[50] Additionally, the temperatures of various emitting and absorbing objects can be obtained by measuring Doppler broadening — effectively redshifts and blue shifts over a single emission or absorption line.[51] By measuring the broadening and shifts of the 21-centimeter hydrogen line in different directions, astronomers have been able to measure the recessional velocities of interstellar gas, which in turn reveals the rotation curve of our Milky Way.[2] Similar measurements have been performed on other galaxies, such as Andromeda.[2] As a diagnostic tool, redshift measurements are one of the most important spectroscopic measurements made in astronomy.

Extragalactic observations

The most distant objects exhibit larger redshifts corresponding to the Hubble flow of the universe. The largest observed redshift, corresponding to the greatest distance and furthest back in time, is that of the cosmic microwave background radiation; the numerical value of its redshift is about z = 1089 (z = 0 corresponds to present time), and it shows the state of the Universe about 13.7 billion years ago, and 379,000 years after the initial moments of the Big Bang.[52]

The luminous point-like cores of quasars were the first "high-redshift" (z > 0.1) objects discovered before the improvement of telescopes allowed for the discovery of other high-redshift galaxies.

For galaxies more distant than the Local Group and the nearby Virgo Cluster, but within a thousand megaparsecs or so, the redshift is approximately proportional to the galaxy's distance. This correlation was first observed by Edwin Hubble and has come to be known as Hubble's law. Vesto Slipher was the first to discover galactic redshifts, in about the year 1912, while Hubble correlated Slipher's measurements with distances he measured by other means to formulate his Law. In the widely accepted cosmological model based on general relativity, redshift is mainly a result of the expansion of space: this means that the farther away a galaxy is from us, the more the space has expanded in the time since the light left that galaxy, so the more the light has been stretched, the more redshifted the light is, and so the faster it appears to be moving away from us. Hubble's law follows in part from the Copernican principle.[23] Because it is usually not known how luminous objects are, measuring the redshift is easier than more direct distance measurements, so redshift is sometimes in practice converted to a crude distance measurement using Hubble's law.

Gravitational interactions of galaxies with each other and clusters cause a significant scatter in the normal plot of the Hubble diagram. The peculiar velocities associated with galaxies superimpose a rough trace of the mass of virialized objects in the universe. This effect leads to such phenomena as nearby galaxies (such as the Andromeda Galaxy) exhibiting blue shifts as we fall towards a common barycenter, and redshift maps of clusters showing a Finger of God effect due to the scatter of peculiar velocities in a roughly spherical distribution.[23] This added component gives cosmologists a chance to measure the masses of objects independent of the mass to light ratio (the ratio of a galaxy's mass in solar masses to its brightness in solar luminosities), an important tool for measuring dark matter.[53]

The Hubble law's linear relationship between distance and redshift assumes that the rate of expansion of the universe is constant. However, when the universe was much younger, the expansion rate, and thus the Hubble "constant", was larger than it is today. For more distant galaxies, then, whose light has been travelling to us for much longer times, the approximation of constant expansion rate fails, and the Hubble law becomes a non-linear integral relationship and dependent on the history of the expansion rate since the emission of the light from the galaxy in question. Observations of the redshift-distance relationship can be used, then, to determine the expansion history of the universe and thus the matter and energy content.

While it was long believed that the expansion rate has been continuously decreasing since the Big Bang, recent observations of the redshift-distance relationship using Type Ia supernovae have suggested that in comparatively recent times the expansion rate of the universe has begun to accelerate.

Highest redshifts

Currently, the objects with the highest known redshifts are galaxies and the objects producing gamma ray bursts. The most reliable redshifts are from spectroscopic data, and the highest confirmed spectroscopic redshift of a galaxy is that of IOK-1,[54] at a redshift z = 6.96, corresponding to just 750 million years after the Big Bang. Slightly less reliable are Lyman-break redshifts, the highest of which is the lensed galaxy A1689-zD1 at a redshift z = 7.6[55] and the next highest being z = 7.0[56] while as-yet unconfirmed reports by Ellis R. et al. from a gravitational lens observed in a distant galaxy cluster may indicate a galaxy with a redshift of z = 10.1.

The most distant observed gamma ray burst was GRB 090423, which had a redshift of 8.2.[57]

The most distant known quasar, CFHQS J2329-0301, is at z = 6.43.[58] The highest known redshift radio galaxy (TN J0924-2201) is at a redshift z = 5.2[59] and the highest known redshift molecular material is the detection of emission from the CO molecule from the quasar SDSS J1148+5251 at z = 6.42[60]

Extremely red objects (EROs) are astronomical sources of radiation that radiate energy in the red and near infrared part of the electromagnetic spectrum. These may be starburst galaxies that have a high redshift accompanied by reddening from intervening dust, or they could be highly redshifted elliptical galaxies with an older (and therefore redder) stellar population.[61] Objects that are even redder than EROs are termed hyper extremely red objects (HEROs).[62]

The Cosmic Microwave Background has a redshift of more than 1,000, corresponding to an age of approximately 379,000 years after the Big Bang and a distance of more than 13 billion light years. Other high-redshift events predicted by physics but not presently observable are the cosmic neutrino background, from about two seconds after the Big Bang, and first light from the oldest Population III stars, not long after atoms first formed and the CMB ceased to be absorbed almost completely.

Redshift surveys

Main article: Redshift survey

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Rendering of the 2dFGRS data

With the advent of automated telescopes and improvements in spectroscopes, a number of collaborations have been made to map the universe in redshift space. By combining redshift with angular position data, a redshift survey maps the 3D distribution of matter within a field of the sky. These observations are used to measure properties of the large-scale structure of the universe. The Great Wall, a vast supercluster of galaxies over 500 million light-years wide, provides a dramatic example of a large-scale structure that redshift surveys can detect.[63]

The first redshift survey was the CfA Redshift Survey, started in 1977 with the initial data collection completed in 1982.[64] More recently, the 2dF Galaxy Redshift Survey determined the large-scale structure of one section of the Universe, measuring z-values for over 220,000 galaxies; data collection was completed in 2002, and the final data set was released 30 June 2003.[65] (In addition to mapping large-scale patterns of galaxies, 2dF established an upper limit on neutrino mass.) Another notable investigation, the Sloan Digital Sky Survey (SDSS), is ongoing as of 2005 and aims to obtain measurements on around 100 million objects.[66] SDSS has recorded redshifts for galaxies as high as 0.4, and has been involved in the detection of quasars beyond z = 6. The DEEP2 Redshift Survey uses the Keck telescopes with the new "DEIMOS" spectrograph; a follow-up to the pilot program DEEP1, DEEP2 is designed to measure faint galaxies with redshifts 0.7 and above, and it is therefore planned to provide a complement to SDSS and 2dF.[67]

Effects due to physical optics or radiative transfer

The interactions and phenomena summarized in the subjects of radiative transfer and physical optics can result in shifts in the wavelength and frequency of electromagnetic radiation. In such cases the shifts correspond to a physical energy transfer to matter or other photons rather than being due to a transformation between reference frames. These shifts can be due to such physical phenomena as coherence effects or the scattering of electromagnetic radiation whether from charged elementary particles, from particulates, or from fluctuations of the index of refraction in a dielectric medium as occurs in the radio phenomenon of radio whistlers.[2] While such phenomena are sometimes referred to as "redshifts" and "blue shifts", in astrophysics light-matter interactions that result in energy shifts in the radiation field are generally referred to as "reddening" rather than "redshifting" which, as a term, is normally reserved for the effects discussed above.[2]

In many circumstances scattering causes radiation to redden because entropy results in the predominance of many low-energy photons over few high-energy ones (while conserving total energy).[2] Except possibly under carefully controlled conditions, scattering does not produce the same relative change in wavelength across the whole spectrum; that is, any calculated z is generally a function of wavelength. Furthermore, scattering from random media generally occurs at many angles, and z is a function of the scattering angle. If multiple scattering occurs, or the scattering particles have relative motion, then there is generally distortion of spectral lines as well.[2]

In interstellar astronomy, visible spectra can appear redder due to scattering processes in a phenomenon referred to as interstellar reddening[2] — similarly Rayleigh scattering causes the atmospheric reddening of the Sun seen in the sunrise or sunset and causes the rest of the sky to have a blue color. This phenomenon is distinct from redshifting because the spectroscopic lines are not shifted to other wavelengths in reddened objects and there is an additional dimming and distortion associated with the phenomenon due to photons being scattered in and out of the line-of-sight.

For a list of scattering processes, see Scattering.

References

Notes

Articles

    • Odenwald, S. & Fienberg, RT. 1993; "Galaxy Redshifts Reconsidered" in Sky & Telescope Feb. 2003; pp31–35 (This article is useful further reading in distinguishing between the 3 types of redshift and their causes.)

    • Lineweaver, Charles H. and Tamara M. Davis, "Misconceptions about the Big Bang", Scientific American, March 2005. (This article is useful for explaining the cosmological redshift mechanism as well as clearing up misconceptions regarding the physics of the expansion of space.)

Book references

External links

Wikimedia Commons has media related to: Redshift

Retrieved from "http://en.wikipedia.org/wiki/Redshift"

Categories: Astronomical spectroscopy | Doppler effects | Physical cosmology | Physical quantities

THE HUBBLE CONSTANT from Wikipedia

Hubble's law describes the observation in physical cosmology that the velocity at which various galaxies are receding from the Earth is proportional to their distance from us.[1] The law was first formulated by Edwin Hubble in 1929[2] after nearly a decade of observations. The recession velocity of the objects was inferred from their redshifts, many measured much earlier by Vesto Slipher (1917) and related to velocity by him.[3] It is considered the first observational basis for the expanding space paradigm and today serves as one of the pieces of evidence most often cited in support of the Big Bang model.

The law is often expressed by the equation v = H0D, with H0 the constant of proportionality (the Hubble constant) between the distance D to a galaxy and its velocity v. The SI unit of H0 is s-1 but it is most frequently quoted in (km/s)/Mpc, thus giving the speed in km/s of a galaxy one Megaparsec away. The reciprocal of H0 is the Hubble time.

The most recent observational determination of the proportionality constant obtained in 2009 by using the Hubble Space Telescope (HST) yielded a value of H0 = 74.2 ± 3.6 (km/s)/Mpc.[4] The results agree closely with an earlier measurement of H0 = 72 ± 8 km/s/Mpc obtained in 2001 also by the HST.[5] In August 2006, a less-precise figure was obtained independently using data from NASA's Chandra X-ray Observatory: H0 = 77 (km/s)/Mpc or about 2.5×10−18 s−1 with an uncertainty of ± 15%.[6] NASA summarizes existing data to indicate a constant of 70.8 ± 1.6 (km/s)/Mpc if space is assumed to be flat, or 70.8 ± 4.0 (km/s)/Mpc otherwise.[7]

Discovery

A decade before Hubble made his observations, a number of physicists and mathematicians had established a consistent theory of the relationship between space and time by using Einstein's field equations of general relativity. Applying the most general principles to the nature of the universe yielded a dynamic solution that conflicted with the then prevailing notion of a static universe.

FLRW equations

In 1922, Alexander Friedmann derived his Friedmann equations from Einstein's field equations, showing that the universe might expand at a rate calculable by the equations.[8] The parameter used by Friedmann is known today as the scale factor which can be considered as a scale invariant form of the proportionality constant of Hubble's Law. Georges Lemaître independently found a similar solution in 1927. The Friedmann equations are derived by inserting the metric for a homogeneous and isotropic universe into Einstein's field equations for a fluid with a given density and pressure. This idea of an expanding spacetime would eventually lead to the Big Bang and Steady State theories of cosmology.

Shape of the universe

Before the advent of modern cosmology, there was considerable talk about the size and shape of the universe. In 1920, the famous Shapley-Curtis debate took place between Harlow Shapley and Heber D. Curtis over this issue. Shapley argued for a small universe the size of the Milky Way galaxy and Curtis argued that the universe was much larger. The issue was resolved in the coming decade with Hubble's improved observations.

Cepheid variable stars outside of the Milky Way

Edwin Hubble did most of his professional astronomical observing work at Mount Wilson Observatory, the world's most powerful telescope at the time. His observations of Cepheid variable stars in spiral nebulae enabled him to calculate the distances to these objects. Surprisingly, these objects were discovered to be at distances which placed them well outside the Milky Way. They continued to be called "nebulae" and it was only gradually that the term "galaxies" took over.

Combining redshifts with distance measurements

Fit of redshift velocities to Hubble's law; patterned after William C. Keel (2007). The Road to Galaxy Formation. Berlin: Springer published in association with Praxis Pub., Chichester, UK. ISBN 3540725342. http://books.google.com/books?id=BUgJGypUYF0C&pg=PA8. Various estimates for the Hubble constant exist. The HST Key H0 Group fitted type Ia supernovae for redshifts between 0.01 and 0.1 to find that H0 = 71 ± 2(statistical) ± 6 (systematic) km s−1Mpc−1,[9] while Sandage et al. find H0 = 62.3 ± 1.3 (statistical) ± 5 (systematic) km s−1Mpc−1.[10]

The parameters that appear in Hubble’s law: velocities and distances, are not directly measured. In reality we determine, say, a supernova brightness, which provides information about its distance, and the redshift z = ∆λ/λ of its spectrum of radiation. Hubble correlated brightness and parameter z.

Combining his measurements of galaxy distances with Vesto Slipher's measurements of the redshifts associated with the galaxies, Hubble discovered a rough proportionality between redshift of an object and its distance. Though there was considerable scatter (now known to be caused by peculiar velocities), Hubble was able to plot a trend line from the 46 galaxies he studied and obtain a value for the Hubble constant of 500 km/s/Mpc (much higher than the currently accepted value due to errors in his distance calibrations). (See cosmic distance ladder for details.)

At the time of discovery and development of Hubble’s law it was acceptable to explain redshift phenomenon as a Doppler shift in the context of special relativity, and use the Doppler formula to associate redshift z with velocity. Today the velocity-distance relationship of Hubble's law is viewed as a theoretical result with velocity to be connected with observed redshift not by the Doppler effect, but by a cosmological model relating recessional velocity to the expansion of the universe. Even for small z the velocity entering the Hubble law is no longer interpreted as a Doppler effect, although at small z the velocity-redshift relation for both interpretations is the same.

In 1958, the first good estimate of H0, 75 km/s/Mpc, was published by Allan Sandage[11], but it would be decades before a consensus was achieved.

Hubble Diagram

Hubble's Law can be easily depicted in a "Hubble Diagram" in which the velocity (assumed approximately proportional to the redshift) of an object is plotted with respect to its distance from the observer.[12] A straight line of positive slope on this diagram is the visual depiction of Hubble's Law.

The cosmological constant abandoned

Main article: Cosmological constant

After Hubble's discovery was published, Albert Einstein abandoned his work on the cosmological constant (which he had designed to allow for a static solution to his equations). He later termed this work his "greatest blunder" since the assumption of a static universe had prevented him from predicting the expanding universe. Einstein made a famous trip to Mount Wilson in 1931 to thank Hubble for providing the observational basis for modern cosmology. However, the cosmological constant has regained attention in recent decades as a hypothesis for dark energy.

Interpretation

A variety of possible recessional velocity vs. redshift functions including the simple linear relation v = cz; a variety of possible shapes from theories related to general relativity; and a curve that does not permit speeds faster than light in accordance with special relativity. All curves are linear at low redshifts. See Davis and Lineweaver.[13]

The discovery of the linear relationship between redshift and distance, coupled with a supposed linear relation between recessional velocity and redshift, yields a straightforward mathematical expression for Hubble's Law as follows:

where

    • v is the recessional velocity, typically expressed in km/s.

    • H0 is Hubble's constant and corresponds to the value of H (often termed the Hubble parameter which is a value that is time dependent) in the Friedmann equations taken at the time of observation denoted by the subscript 0. This value is the same throughout the universe for a given comoving time.

    • D is the proper distance from the galaxy to the observer, measured in mega parsecs (Mpc), in the 3-space defined by given cosmological time. (Recession velocity is just v = dD/dt).

Hubble's law is considered a fundamental relation between recessional velocity and distance. However, the relation between recessional velocity and redshift depends on the cosmological model adopted, and is not established except for small redshifts.

For distances D larger than the radius of the Hubble sphere rHS , objects recede at a rate faster than the speed of light:[14]

Inasmuch as the Hubble "constant" is not constant at all, but varies with time in a manner dictated by the choice of cosmological model, the radius of the Hubble sphere may increase or decrease over various time intervals. The subscript '0' indicates the value of the Hubble constant today.[15]

Redshift velocity and recessional velocity

Redshift can be measured by determining the wavelength of a known transition, such as hydrogen α-lines for distant quasars, and finding the fractional shift compared to a stationary reference. Thus redshift is a quantity unambiguous for experimental observation. The relation of redshift to recessional velocity is another matter. For an extensive discussion, see Harrison.[16]

Redshift velocity

The redshift z often is described as a redshift velocity, which is the recessional velocity that would produce the same redshift if it were caused by a linear Doppler effect (which, however, is not the case, as the shift is caused in part by a cosmological expansion of space, and because the velocities involved are too large to use a non-relativistic formula for Doppler shift). This redshift velocity can easily exceed the speed of light.[17] In other words, to determine the redshift velocity vrs, the relation:

is used.[18][19] That is, there is no fundamental difference between redshift velocity and redshift: they are rigidly proportional, and not related by any theoretical reasoning. The motivation behind the "redshift velocity" terminology is that the redshift velocity agrees with the velocity from a low-velocity simplification of the so-called Fizeau-Doppler formula[20]

Here, λo, λe are the observed and emitted wavelengths respectively. The "redshift velocity" vrs is not so simply related to real velocity at larger velocities, however, and this terminology leads to confusion if interpreted as a real velocity. Next, the connection between redshift or redshift velocity and recessional velocity is discussed. This discussion is based on Sartori.[21]

Recessional velocity

Suppose R(t) is called the scale factor of the universe, and increases as the universe expands in a manner that depends upon the cosmological model selected. Its meaning is that all measured distances D(t) between co-moving points increase proportionally to R. (The co-moving points are not moving relative to each other except as a result of the expansion of space.) In other words:

where t0 is some reference time. If light is emitted from a galaxy at time te and received by us at t0, it is red shifted due to the expansion of space, and this redshift z is simply:

Suppose a galaxy is at distance D, and this distance changes with time at a rate dtD . We call this rate of recession the "recession velocity" vr:

We now define the Hubble constant as

and discover the Hubble law:

From this perspective, Hubble's law is a fundamental relation between (i) the recessional velocity contributed by the expansion of space and (ii) the distance to an object; the connection between redshift and distance is a crutch used to connect Hubble's law with observations. This law can be related to redshift z approximately by making a Taylor series expansion:

If the distance is not too large, all other complications of the model become small corrections and the time interval is simply the distance divided by the speed of light:

or

According to this approach, the relation cz = vr is an approximation valid at low redshifts, to be replaced by a relation at large redshifts that is model-dependent. See velocity-redshift figure.

Observability of parameters

Strictly speaking, neither v nor D in the formula are directly observable, because they are properties now of a galaxy, whereas our observations refer to the galaxy in the past, at the time that the light we currently see left it.

For relatively nearby galaxies (redshift z much less than unity), v and D will not have changed much, and v can be estimated using the formula v = zc where c is the speed of light. This gives the empirical relation found by Hubble.

For distant galaxies, v (or D) cannot be calculated from z without specifying a detailed model for how H changes with time. The redshift is not even directly related to the recession velocity at the time the light set out, but it does have a simple interpretation: (1+z) is the factor by which the universe has expanded while the photon was travelling towards the observer.

Expansion velocity vs relative velocity

In using Hubble's law to determine distances, only the velocity due to the expansion of the universe can be used. Since gravitationally interacting galaxies move relative to each other independent of the expansion of the universe, these relative velocities, called peculiar velocities, need to be accounted for in the application of Hubble's law.

The Finger of God effect is one result of this phenomenon discovered in 1938 by Benjamin Kenneally. In systems that are gravitationally bound, such as galaxies or our planetary system, the expansion of space is a much weaker effect than the attractive force of gravity.

Idealized Hubble's Law

The mathematical derivation of an idealized Hubble's Law for a uniformly expanding universe is a fairly elementary theorem of geometry in 3-dimensional Cartesian/Newtonian coordinate space, which, considered as a metric space, is entirely homogeneous and isotropic (properties do not vary with location or direction). Simply stated the theorem is this:

Any two points which are moving away from the origin, each along straight lines and with speed proportional to distance from the origin, will be moving away from each other with a speed proportional to their distance apart.

In fact this applies to non-Cartesian spaces as long as they are locally homogeneous and isotropic; specifically to the negatively- and positively-curved spaces frequently considered as cosmological models (see shape of the universe).

An observation stemming from this theorem is that seeing objects recede from us on Earth is not an indication that Earth is near to a center from which the expansion is occurring, but rather that every observer in an expanding universe will see objects receding from them.

The ‘ultimate fate’ and age of the universe

The age and ultimate fate of the universe can be determined by measuring the Hubble constant today and extrapolating with the observed value of the deceleration parameter, uniquely characterized by values of density parameters (ΩM and ΩΛ). A "closed universe" with ΩM > 1 and ΩΛ = 0 comes to an end in a Big Crunch and is considerably younger than its Hubble age. An "open universe" with ΩM ≤ 1 and ΩΛ = 0 expands forever and has an age that is closer to its Hubble age. For the accelerating universe with nonzero ΩΛ that we inhabit, the age of the universe is coincidentally very close to the Hubble age.

The value of the Hubble parameter changes over time either increasing or decreasing depending on the sign of the so-called deceleration parameter q which is defined by

In a universe with a deceleration parameter equal to zero, it follows that H = 1/t, where t is the time since the Big Bang. A non-zero, time-dependent value of q simply requires integration of the Friedmann equations backwards from the present time to the time when the comoving horizon size was zero.

It was long thought that q was positive, indicating that the expansion is slowing down due to gravitational attraction. This would imply an age of the universe less than 1/H (which is about 14 billion years). For instance, a value for q of 1/2 (once favoured by most theorists) would give the age of the universe as 2/(3H). The discovery in 1998 that q is apparently negative means that the universe could actually be older than 1/H. However, estimates of the age of the universe are very close to 1/H.

Olbers' paradox

Main article: Olbers' paradox

The expansion of space summarized by the Big Bang interpretation of Hubble's Law is relevant to the old conundrum known as Olbers' paradox: if the universe were infinite, static, and filled with a uniform distribution of stars (notice that this also requires an infinite number of stars), then every line of sight in the sky would end on a star, and the sky would be as bright as the surface of a star. However, the night sky is largely dark. Since the 1600s, astronomers and other thinkers have proposed many possible ways to resolve this paradox, but the currently accepted resolution depends in part upon the Big Bang theory and in part upon the Hubble expansion. In a universe that exists for a finite amount of time, only the light of finitely many stars has had a chance to reach us yet, and the paradox is resolved. Additionally, in an expanding universe distant objects recede from us, which causes the light emanating from them to be redshifted and diminished in brightness. Although both effects contribute, the redshift is the less important of the two.[22]

Determining the Hubble constant

The value of the Hubble constant is estimated by measuring the redshift of distant galaxies and then determining the distances to the same galaxies (by some other method than Hubble's law). Uncertainties in the physical assumptions used to determine these distances have caused varying estimates of the Hubble constant. For most of the second half of the 20th century the value of H0 was estimated to be between 50 and 90 (km/s)/Mpc.

Disputes over Hubble's constant

“

Astrophysicists are always wrong, but never in doubt. ... RP Kirshner[23]

”

The value of the Hubble constant was the topic of a long and rather bitter controversy between Gérard de Vaucouleurs who claimed the value was around 100 and Allan Sandage who claimed the value was near 50.[24]

In 1996, a debate moderated by John Bahcall between Gustav Tammann and Sidney van den Bergh was held in similar fashion to the earlier Shapley-Curtis debate over these two competing values.

This difference was partially resolved with the introduction of the ΛCDM model of the universe in the late 1990s.

The ΛCDM model

With the ΛCDM model observations of high-redshift clusters at X-ray and microwave wavelengths using the Sunyaev-Zel'dovich effect, measurements of anisotropies in the cosmic microwave background radiation, and optical surveys all gave a value of around 70 for the constant.[citation needed]

Using Hubble space telescope data

The Hubble Key Project (led by Dr. Wendy L. Freedman, Carnegie Observatories) used the Hubble space telescope to establish the most precise optical determination in May 2001[25] of 72 ± 8 (km/s)/Mpc, consistent with a measurement of H0 based upon Sunyaev-Zel'dovich effect observations of many galaxy clusters having a similar accuracy.

Using WMAP data

The most precise cosmic microwave background radiation determinations were 71 ± 4 (km/s)/Mpc, by WMAP in 2003, and 70.4 +1.5−1.6 (km/s)/Mpc, for measurements up to 2006.[26] The five year release from WMAP in 2008 finds 71.9 +2.6−2.7 (km/s)/Mpc.[1]

These values arise from fitting a combination of WMAP and other cosmological data to the simplest version of the ΛCDM model. If the data is fitted with more general versions, H0 tends to be smaller and more uncertain: typically around 67 ± 4 (km/s)/Mpc although some models allow values near 63 (km/s)/Mpc.[27]

Using Chandra X-ray Observatory data

In August 2006, using NASA's Chandra X-ray Observatory, a team from NASA's Marshall Space Flight Center (MSFC) found the Hubble constant to be 77 (km/s)/Mpc, with an uncertainty of about 15%.[28] The consistency of the measurements from all these methods lends support to both the measured value of H0 and the ΛCDM model.

Acceleration of the expansion

A value for q measured from standard candle observations of Type Ia supernovae, which was determined in 1998 to be negative, surprised many astronomers with the implication that the expansion of the universe is currently "accelerating" (although the Hubble factor is still decreasing with time; see the articles on dark energy and the ΛCDM model).

Derivation of the Hubble parameter

Start with the Friedmann equation:

where H is the Hubble parameter, a is the scale factor, G is the gravitational constant, k is the normalised spatial curvature of the universe and equal to −1, 0, or +1, and Λ is the cosmological constant.

Matter-dominated universe (with a cosmological constant)

If the universe is matter-dominated, then the mass density of the universe ρ can just be taken to include matter so

where is the density of matter today. We know for nonrelativistic particles that their mass density decreases proportional to the inverse volume of the universe so the equation above must be true. We can also define (see density parameter for Ωm)

so ρ = ρcΩm / a3. Also, by definition,

and

where the subscript nought refers to the values today, and a0 = 1. Substituting all of this in into the Friedman equation at the start of this section and replacing a with a = 1 / (1 + z) gives

Matter- and dark energy-dominated universe

If the universe is both matter-dominated and dark energy-dominated, then the above equation for the Hubble parameter will also be a function of the equation of state of dark energy. So now:

ρ = ρm(a) + ρde(a),

where ρde is the mass density of the dark energy. By definition an equation of state in cosmology is P = wρc2, and if we substitute this into the fluid equation, which describes how the mass density of the universe evolves with time,

If w is constant,

Therefore for dark energy with a constant equation of state w, . If we substitute this into the Friedman equation in a similar way as before, but this time set k = 0 which is assuming we live in a spatially flat universe, (see Shape of the Universe)

If dark energy does not have a constant equation-of-state w, then

and to solve this we must parametrize w(a), for example if w(a) = w0 + wa(1 − a), giving

Units derived from the Hubble constant

Hubble time

The Hubble constant H0 has units of inverse time, i.e. H0 ~ 2.29×10−18 s−1. “Hubble time” is defined as 1 / H0. The value of Hubble time in the standard cosmological model is 4.35×1017 s or 13.8 billion years. (Liddle 2003, p. 57) The phrase "expansion timescale" means "Hubble time".[2]. If the value of H0 were to stay constant, a naive interpretion of the Hubble time is that it is the time taken for the universe to increase in size by a factor of e (because the solution of dx/dt = xH0 is x = s0exp(H0t), where s0 is the size of some feature at some arbitrary initial condition t = 0). However, over long periods of time the dynamics are complicated by general relativity, dark energy, inflation, etc., as explained above.

Hubble length

The Hubble length is a unit of distance in cosmology, defined as c / H0—the speed of light multiplied by the Hubble time. It is equivalent to 4228 million parsecs or 13.8 billion light years. (The numerical value of the Hubble length in light years is, by definition, equal to that of the Hubble time in years.)

Hubble volume

The Hubble volume is sometimes defined as a volume of the universe with a comoving size of c / H0. The exact definition varies: it is sometimes defined as the volume of a sphere with radius c / H0, or alternatively, a cube of side c / H0. Some cosmologists even use the term Hubble volume to refer to the volume of the observable universe, although this has a radius approximately three times larger.

See also

Notes

References

  • Kutner, Marc (2003), Astronomy: A Physical Perspective, New York: Cambridge University Press, ISBN 0521529271

  • Hubble, E. P. (1937), The Observational Approach to Cosmology, Oxford: Clarendon Press

  • Eng, A. E. (1985), A New Approach to Starlight Runs, Oswego

  • Liddle, Andrew R. (2003), An Introduction to Modern Cosmology (2nd ed.), Chichester: Wiley, ISBN 0470848359

External links

Retrieved from "http://en.wikipedia.org/wiki/Hubble%27s_law"

Categories: Large-scale structure of the cosmos | Physical cosmology

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Wilkinson Microwave Anisotropy Probe

How Old is the Universe?

Until recently, astronomers estimated that the Big Bang occurred between 12 and 14 billion years ago. To put this in perspective, the Solar System is thought to be 4.5 billion years old and humans have existed as a genus for only a few million years. Astronomers estimate the age of the universe in two ways: 1) by looking for the oldest stars; and 2) by measuring the rate of expansion of the universe and extrapolating back to the Big Bang; just as crime detectives can trace the origin of a bullet from the holes in a wall.

Older Than the Oldest Stars?

Astronomers can place a lower limit to the age of the universe by studying globular clusters. Globular clusters are a dense collection of roughly a million stars. Stellar densities near the center of the globular cluster are enormous. If we lived near the center of one, there would be several hundred thousand stars closer to us than Proxima Centauri, the star nearest to the Sun.

Text Link to the HST press release describing this image

The life cycle of a star depends upon its mass. High mass stars are much brighter than low mass stars, thus they rapidly burn through their supply of hydrogen fuel. A star like the Sun has enough fuel in its core to burn at its current brightness for approximately 9 billion years. A star that is twice as massive as the Sun will burn through its fuel supply in only 800 million years. A 10 solar mass star, a star that is 10 times more massive than the Sun, burns nearly a thousand times brighter and has only a 20 million year fuel supply. Conversely, a star that is half as massive as the Sun burns slowly enough for its fuel to last more than 20 billion years.

All of the stars in a globular cluster formed at roughly the same time, thus they can serve as cosmic clocks. If a globular cluster is more than 20 million years old, then all of its hydrogen burning stars will be less massive than 10 solar masses. This implies that no individual hydrogen burning star will be more than 1000 times brighter than the Sun. If a globular cluster is more than 2 billion years old, then there will be no hydrogen-burning star more massive than 2 solar masses.

The oldest globular clusters contain only stars less massive than 0.7 solar masses. These low mass stars are much dimmer than the Sun. This observation suggests that the oldest globular clusters are between 11 and 18 billion years old. The uncertainty in this estimate is due to the difficulty in determining the exact distance to a globular cluster (hence, an uncertainty in the brightness (and mass) of the stars in the cluster). Another source of uncertainty in this estimate lies in our ignorance of some of the finer details of stellar evolution. Presumably, the universe itself is at least as old as the oldest globular clusters that reside in it.

Extrapolating Back to the Big Bang

An alternative approach to estimating is the age of the universe is to measure the “Hubble constant”. The Hubble constant is a measure of the current expansion rate of the universe. Cosmologists use this measurement to extrapolate back to the Big Bang. This extrapolation depends on the history of the expansion rate which in turn depends on the current density of the universe and on the composition of the universe.

If the universe is flat and composed mostly of matter, then the age of the universe is

2/(3 Ho)

where Ho is the value of the Hubble constant.

If the universe has a very low density of matter, then its extrapolated age is larger:

1/Ho

If the universe contains a form of matter similar to the cosmological constant, then the inferred age can be even larger.

Many astronomers are working hard to measure the Hubble constant using a variety of different techniques. Until recently, the best estimates ranged from 65 km/sec/Megaparsec to 80 km/sec/Megaparsec, with the best value being about 72 km/sec/Megaparsec. In more familiar units, astronomers believe that 1/Ho is between 12 and 14 billion years.

An Age Crisis?

If we compare the two age determinations, there is a potential crisis. If the universe is flat, and dominated by ordinary or dark matter, the age of the universe as inferred from the Hubble constant would be about 9 billion years. The age of the universe would be shorter than the age of oldest stars. This contradiction implies that either 1) our measurement of the Hubble constant is incorrect, 2) the Big Bang theory is incorrect or 3) that we need a form of matter like a cosmological constant that implies an older age for a given observed expansion rate.

Some astronomers believe that this crisis will pass as soon as measurements improve. If the astronomers who have measured the smaller values of the Hubble constant are correct, and if the smaller estimates of globular cluster ages are also correct, then all is well for the Big Bang theory, even without a cosmological constant.

WMAP Can Measure the Age of the Universe

Measurements by the WMAP satellite can help resolve this crisis. If current ideas about the origin of large-scale structure are correct, then the detailed structure of the cosmic microwave background fluctuations will depend on the current density of the universe, the composition of the universe and its expansion rate. WMAP has been able to determine these parameters with an accuracy of better than than 3% of the critical density. In turn, knowing the composition with this precision, we can estimate the age of the universe to about 1%: 13.7 ± 0.13 billion years!

How does WMAP data enable us to determine the age of the universe is 13.7 billion years, with an uncertainty of 1%? The key to this is that by knowing the composition of matter and energy density in the universe, we can use Einstein's General Relativity to compute how fast the universe has been expanding in the past. With that information, we can turn the clock back and determine when the universe had "zero" size, according to Einstein. The time between then and now is the age of the universe. There is one caveat to keep in mind that affects the certainty of the age determination: we assume that the universe is flat, which is well supported by WMAP and other data. If we relax this assumption within the allowed range, the uncertainty increases to a bit over 2%. However, theorists have long known that a nearly-flat universe is very difficult to produce, whereas inflation naturally predicts a flat universe.

The expansion age measured by WMAP is larger than the oldest globular clusters, so the Big Bang theory has passed an important test using data independent of the type collected by WMAP. If the expansion age measured by WMAP had been smaller than the oldest globular clusters, then there would have been something fundamentally wrong about either the Big Bang theory or the theory of stellar evolution. Either way, astronomers would have needed to rethink many of their cherished ideas. But our current estimate of age fits well with what we know from other kinds of measurements.

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