Expansion

This section describes the expansion of the universe, from the initial period of hyperexpansion called inflation to the steady expansion that took place over the last 14 billion years.

Overview

Just after the beginning of the universe, the period of inflation began. It lasted for 10^-34 seconds (a trillion, trillion, trillionth of a second). During inflation, the universe doubled in size 100 times and expanded at a rate that was much faster than the speed of light. Although light cannot travel faster than the speed of light, this does not mean that the universe cannot grow faster than the speed of light. During inflation, the universe grew from the size of a proton to the size of a grapefruit. This was followed by a period of steady expansion for the last 14 billion years. Three forces expanded the universe at different times (photon gas, kinetic energy, and dark energy) while gravity resisted expansion.

Based on the pattern of the Cosmic Microwave Background Radiation, there were quantum fluctuations in the universe when the universe was the size of a proton. Next, at 10^-37seconds after the beginning of the universe, expansion energy became extremely high and expanded the universe for 10^-34seconds. Next, the expansion energy dropped by 120 orders of magnitude to a value that would eventually result in steady expansion of the universe during the last 5 billion years. The expansion left behind extremely hot photons. Photon pressure was the primary driver of the expanding universe during the first 60,000 years of the universe. As photon pressure gradually decreased over time, there was seamless transition to expansion of the universe by kinetic energy of dark and normal matter. During this entire period of transition, the expanding forces of kinetic energy and photon pressure were perfectly balanced by the inward pull of gravity. As kinetic energy decreased more than the inward pull of gravity after 9 billion years, there was a seamless transition to the expanding force of dark energy. During this transition during the last five billion years, the combined expanding forces of kinetic energy and dark energy were balanced by the inward pull of gravity, resulting in continued steady expansion of the universe during the last 5 billion years. The following list summarizes the sequence of events in the expanding universe.

1. First 10^-37 seconds Establishment of pattern of quantum fluctuations in the universe

a. Patterns enabled collapse of matter into first stars

2. Next 10^-34 seconds Inflation, period of hyper expansion

a. Balanced expanding and contracting forces in the universe

b. Disconnected regions of space and thus enabled linear expansion

c. Froze patterns of quantum fluctuations in place

3. First 60,000 years

a. Photon pressure expanded universe and transferred energy to outward kinetic energy of matter, gravitational force descreases over time.

4. Next 9 billion years

a. Kinetic energy of matter and dark matter expanded the universe, gravitational force decreases over time.

5. Last 5 billion years

a. Transition to expansion by dark energy, gravitational force decreases over time.

The following four videos (made by a Cosmoszona associate member) provide a synopsis of the phases and causes of expansion.

Although controversial, CMBR data indicates that the universe began with one quantum fluctuation, and then there were two fluctuations and so on. When the universe reached the size of a proton, there were trillions of quantum fluctuations. Then an unknown force expanded the universe from the size of a proton to the size of a grapefruit in a trillion trillion trillionth of a second, freezing this sequence of quantum fluctuations in place, which we can see in the Cosmic Microwave Background Radiation. Can you see the two largest fluctuations in the CMBR?

The dark energy that expanded the universe during inflation dropped by 120 orders of magnitude after inflation to a precise and necessary value for later expansion. In comparison, let us say that you lost your wallet a trillion, trillion trillion, trillion, trillion, trillion, trillion, trillion times farther than the diameter of the universe, and then it dropped into your lap, and not 10 m or 100 m past you. This is the same scale and precision as the drop in dark energy. Of course, wallets don't just fly across the universe.

There are three expanding forces in the universe: photon gas pressure, outward kinetic energy of dark and normal matter, and dark energy. The energy density of the combination of expansion forces always equaled the inward force of gravity; thus, the expansion of the universe was constant, and the relative energy density was always 1.0. A gradual shift between expanding energies took place because of the changes with size of the universe in the lambda CDM equation.

In the first 60,000 years of the universe, the outward pressure of photon gas was the primary expansion force. As the universe expanded, the energy and density of photons decreased, but the kinetic energy of dark and normal matter smoothly replaced photon gas as the primary expanding force, maintaining the relative energy density at 1.0. As kinetic energy density decreased after 9 billion years, dark energy gradually replaced it and maintained the steady expansion of the universe during the last 5 billion years.

Inflation

Just after the beginning of the universe, the period of inflation began. It lasted for approximately 10^-36 seconds (a trillion, trillion, trillionth of a second). During inflation, the universe doubled in size 100 times. Almost all cosmologists think that the universe began with inflation. “Cosmological observations strongly suggest that structure in the universe originated from minute fluctuations present in the very early Universe, prior to the hot big bang,” [1] Data indicates that these fluctuations were due to quantum fluctuations frozen in place by cosmic inflation. [2] Similarly, Sanchis-Lozano stated, “In this sense, the homogeneity, thus long-range angular correlations of the cosmic microwave background (CMB) across the sky seen by the WMAP and Planck missions, strongly supports an inflationary era of the early Universe.” [3]

Although still controversial, data is beginning to support a relatively simple model of the early universe. There was one quantum fluctuation at Planck scale (10^-35 m), the smallest possible length scale in known physics, and then there were two fluctuations as the universe grew larger and so on. When the universe reached the size of a proton, there were trillions of quantum fluctuations. Then an unknown force expanded the universe from the size of a proton to the size of a grapefruit in a trillion trillion trillionth of a second, freezing this beautiful sequence of quantum fluctuation in place, which we can see in the Cosmic Microwave Background Radiation (Figure 1-45). The 180-degree pattern (entire sky) in the CMBR is from the first quantum fluctuation. The 90-degree patterns (Figure 1-53) are from the second quantum fluctuations, and so on. The trillions or possibly million trillions of fluctuations just prior to inflation, within our horizon, led to slight variations in density in the universe after inflation, and the higher density locations became the seeds of the first stars and then galaxies. We also do not know what is beyond our horizon. Many cosmologists think that the universe is infinite.

Also controversial, the CMBR data is supporting the plateau or slow roll model of inflation. In this scenario, inflation had a sudden beginning, the energy source maintained a relatively stable expansion energy during inflation, and then had a relatively sudden drop off, in which the expanding energy of inflation contributed to the formation of photons and a hot dense universe that was primed to continue expanding, but at a slower rate than during inflation. One of the reasons that this model of inflation is controversial is that it requires extreme fine tuning and thus is unlikely from the perspective of finding a natural explanation; however, there are other inflation models that also have proponents.

During inflation, the universe expanded at a rate that was much faster than the speed of light. Although light cannot travel faster than the speed of light, this does not mean that the universe cannot grow faster than the speed of light.

Inflation contributed two important developments that were essential to the long-term expansion of the universe. First, it balanced the expanding and contracting forces of the universe such that the universe did not collapse or expand too fast for galaxies, planets, and life to appear. It allowed for steady expansion in another way. It disconnected the parts of the universe, which allowed all parts of the universe to expand uniformly in a straight line and not be restricted by the expansion of adjacent sections of the universe.

Inflation solved one of the great problems of cosmology, which is that we can see 14 billion light years in all directions, but this implies that these parts are 28 billion years apart in time, older than the universe. In addition, all parts have the same properties, which means they were at one time connected. Inflation enabled this to happen because it disconnected parts of the universe. This was called the Horizon Problem: how could objects in the universe that we can see in both directions be farther apart (28 billion light-years) than the age of the universe would allow and yet have the same properties?

Even though it sounds wildly speculative, the inflation concept is strongly supported by data. Quantum fluctuations in the early universe prior to inflation would have been frozen in place by inflation. The pattern of the original fluctuations is now observed in the pattern of the CMBR (Figure 1-45 and Figure 1-53).

Figure 1‑45. Planck satellite image of the Cosmic Microwave Background in all directions. Credit ESA.

Although inflation is supported by the CMBR data, it has several fine-tuning problems. The universe would have needed to be extremely uniform in order to avoid becoming distorted. It must have had a much lower entropy (uniformity) than the present entropy.[4] Cal Tech astronomer Sean Carroll, a leading cosmologist, described the inflation fine-tuning problem.

“Although inflation does seem to create a universe like ours, it needs to start in a very particular kind of state. If the laws of physics are “unitary” (reversible, preserving information over time), then the number of states that would begin to inflate is actually much smaller than the number of states that just look like the hot Big Bang in the first place. So inflation seems to replace a fine-tuning of initial conditions with an even greater fine-tuning.” [5]

Another fine-tuning issue is that the expanding energy of inflation began at zero, then became extremely high, then dropped by 120 orders of magnitude to its current value in the universe, the value of which was necessary for the long-term expansion of the universe. These changes in expanding energy, possibly dark energy, all took place within a trillion trillion trillionth of a second.

Steady expansion

Since inflation, the universe steadily expanded for 14 billion years. There were three expanding forces and one contracting force, gravity. The expanding forces included photon gas pressure (early universe), kinetic energy of dark and normal matter (middle universe), and dark energy (late universe). The early universe was filled with highly energetic photons, and the pressure of this photon gas counteracted the force of gravity and expanded the universe. Photon gas is not like a normal gas: photons annihilate each other and form other particles when they impact each other, they have no mass, they cannot be tracked since they follow the laws of quantum mechanics, and the number of photons increases with volume. Although the rate of decrease of photon gas pressure in the universe is described by a simple equation (Equation 2), the derivation of the terms in this equation is complex because photon gas pressure is a function of photon energy (temperature), density, and complex collision dynamics. Both temperature and density decreased as the universe expanded. Thus, the simple equation for photon gas pressure can be considered as a finely tuned result of a set of complex equations in which several terms cancel out, from which a simple equation emerges.

The combination of photon gas pressure, outward kinetic energy of matter, and dark energy always and precisely equaled the inward force of gravity. This caused the universe to expand at a constant rate. Scientists refer to this balance between inward and outward forces as relative energy density = 1.0. Relative energy density is on the left axis of Figure 1-46. Figure 1-46 was constructed with the lambda CDM equation (Equation 3). Lambda refers to dark energy and CDM refers to Cold Dark Matter (LCDM). In the equation below, “a” is the diameter of the universe. The three types of expanding energy are represented by the omega symbols. Because they are divided by different powers of “a” (size), the expanding energies decrease at different rates. The energy of photon gas was higher than the others at the beginning of the universe but decreased fastest as the universe expanded because it was divided by the fourth power of a. The dark energy did not decrease with the expanding universe because it is not divided by a, which is why it grew with the expansion of the universe. If you are interested in this topic and have available time and are skilled in mathematics, then you might want to watch Matthias Bartelman's development of the terms in the lambda CDM equation at https://youtu.be/Zn-Lp8JOXDc.

where

Ω_m – relative energy density of matter (dark and normal matter)

Ω_rad – relative energy density of radiation (photon gas)

Ω_Λ – relative energy density of dark energy

H – expansion rate at any time

a – relative size of the universe (current size is 1.0, size at the beginning was zero)

Figure 1-46. This graph shows that the sum of relative energy densities (blue = radiation (photons), red = matter (kinetic energy), green = dark energy) always equaled 1.0. This means the sum of expanding energies always equaled the inward pull of gravity and thus maintained the expansion of the universe at a constant rate. The lower axis is a logarithmic scale, which stretches out the time in the early universe. Disclaimer: the kinetic energy to dark energy transition in this graph was developed with the assumption that the current relative energy density is 1.00; however, it is 1.02.

The following four graphs show the decrease in gravity over time in the universe and the corresponding changes in photon gas energy, kinetic energy, and dark energy based on the lambda CDM model (Equation 3). The gravitational force is a simplified estimate based on Newton’s law (F = G m² / R²), where F represents the total force of contraction in the universe, G is the universe gravitational constant, m is the mass of the universe (dark + normal), and R is the radius of the universe. Fortunately, God or the multiverse made an accurate calculation. The focus is on the order of magnitude changes in gravitational force rather than an accurate calculation. The black lines in Figure 1-46 to 1-49 represent the contracting force of gravity in the universe over time. The blue lines in Figure 1-46 to 1-49 represent the energy of photon gas expansion over time. The relative contribution from photon gas gradually decreased as the relative contribution from kinetic energy from outward moving dark and normal matter (red lines) gradually increased. Finally, in the late universe, the contribution from dark energy (green lines) gradually increased as the contribution from kinetic energy gradually decreased. 

Figure 1-47. Forces of contraction (gravity) and expansion vs. size of the universe with force on linear scale and size of the universe on logarithmic scale. E+51 refers to 10⁵¹

In the early universe, photon energy and a small amount of kinetic energy counteracted the force of gravity and expanded the universe; thus, the photon pressure (blue line) and the gravity lines almost overlap on the left side of Figure 1-47. The size of the universe axis is logarithmic, which stretches out the early part of the universe on the left. The total force of gravity fell from 10^64 Newtons to 10^50 Newtons. During this time, the decrease in photon pressure matched the decrease in gravity, thus maintaining a steadily expanding universe.

Figure 1-48. Forces of contraction (gravity) and expansion vs. size of the early universe with force on logarithmic scale and size of the universe on linear scale. Dark energy is off the scale.

Figure 1-48 focuses on the early universe. As the universe expanded, gravity and photon energy decreased, but kinetic energy decreased more slowly than the others. At one point, as photon pressure (blue line) decreased below gravity, kinetic energy replaced it as the force opposing gravity and expanding the universe. When photon pressure dropped to 10^50 Newtons, the force of kinetic energy began to replace photon pressure as the major expanding force of the universe. By the time gravity decreased to 10^48 Newton (decreased by a factor of 100), kinetic energy was the major expanding force in the universe, and photon pressure was a minor part of the expanding force of the universe. During this entire transition, the sum of photon pressure and kinetic energy precisely equaled the contracting force of gravity.

Figure 1-49. Forces of contraction (gravity) and expansion vs. size of the universe with force on logarithmic scale and size of the universe on logarithmic scale.

Figure 1-49 shows the entire history of the universe. In this graph the force axis is logarithmic, which stretches out the lower part of the graph. It shows the rise of dark energy (green line) during the history of the universe. During the first 9 billion years of the universe, the expanding force of dark energy. At precisely the time that kinetic energy began to drop below the contracting force of gravity, the force of dark energy had grown by 42 orders of magnitude to 10⁴² Newtons and began to replace kinetic energy as the major expanding force in the universe. The combination of dark energy and kinetic energy has maintained steady expansion for the last 5 billion years.

Figure 1-50. Forces of contraction (gravity) and expansion vs. size of the universe with force on logarithmic scale and size of the universe on linear scale.

Figure 1-50 has a linear length scale (lower axis); thus, the horizontal locations of the intersections of energy lines are representative of the time scale. Dark energy (green line) became a significant expanding force during the last 5 billion years as the magnitude of kinetic energy dropped below gravitational energy. By this time, photon energy was thousands of times lower than the three other forces.

Not only did the magnitudes of the expanding forces intersect at positions where each was precisely half the magnitude of gravity, but the rates of change of expanding forces on either side of the intersection points precisely balanced the rate of change of gravity. The change over time is referred to as the derivate or the slope. Considering that the rates of change (slopes) are constantly changing in Figures 1-47 to 1-50, this means that the second derivatives, which is the curvature, also perfectly balance the curvature of the gravitational force. In some parts of the graphs, it is also necessary that the rates of change of curvature of expanding forces, the third derivative, are balanced to maintain relative energy density = 1.0. What is the probability that four forces would cancel each other out for 14 billion years, while changing over tens of orders of magnitude, and that the first, second, and third derivatives (slope, curvature, and rate of change of curvature) of the primary expanding force would always align with those parameters in the gravitational force, and all of the expanding force parameters would also align in the regions where forces are transitioning. The magnitudes and rates of change are based on concentrations of fundamental particles in the universe and on the mathematics of the Lambda CDM model.

Because the sum of terms inside the parentheses in Equation 3 has always been 1.0, Equation 3 is simplified as Equation 4, where H is the expansion rate of the universe at any time, and H₀ is the current Hubble expansion rate.

Figure 1-51 was generated with Equation 4. The left side is the current size of the universe. The universe had no size 14 billion years ago, which is on the right side of the graph. The line is straight because the universe has always expanded at a constant rate for 14 billion years.

Figure 1‑51. Relative size (distance between galaxies) of the universe as a function of time, based on H_o = 72 km/sec/Mpc

Does the universe have a sort of cruise control that keeps the expansion of the universe at a constant rate just as cruise control in a car keeps a car traveling at the desired speed? The opposite is true. Any deviation from the constant expansion rate would have resulted in more deviation. If the universe had deviated slightly above the constant expansion rate, the universe would have begun accelerating uncontrollably, and galaxies and stars would not have formed. On the other hand, if the universe deviated slightly below the constant expansion rate, then it would have slowed down and eventually collapsed upon itself. Perhaps, you can get a feel for the consequences of uncontrolled expansion by watching the video on the left.

Figure 1-52. A 60 ft bowling alley. A light year bowling alley would be 6 trillion miles long. Credit: Biso. Used here per CC BY 3.0

Considering the instability of expansion, the fact that the universe expanded at a constant rate for 14 billion years is remarkable. The balanced expansion of the universe has been compared to throwing a bowling ball down a bowling lane that is one light-year long without the ball deviating into either gutter. Some scientists estimate that the initial value of the relative energy density of expansion needed to be precisely 1.000000000000000 in order to steadily expand for 14 billion years. Other scientists think the fine tuning of expansion had a precision of 1.0 with 62 zeros after the decimal point.

Cosmic inflation debate

If you are interested in thinking more about whether cosmic inflation happened, then you might be interested in what is considered the strongest evidence for inflation and the following debate between two leading cosmologists: Roger Penrose does not think that inflation took place, and Alan Guth is the person who discovered inflation.

The CMBR pattern is considered the strongest evidence for inflation. Based on the growth in the universe from Planck scale and the associated quantum fluctuations, Guth predicted the pattern of density variations due to quantum fluctuations. One way to evaluate this is to contruct a Fourier series graph, which analysis intensity vs. frequency or angle in the sky. Guth developed an equation for the fluctuation intensity vs. the distance separating the fluctuations. Assuming that the universe is composed of 26% dark matter, 4.8% ordinary matter, and 69.2% dark energy,” [6] (as it is), the green theoretical line in Figure 1‑53 perfectly overlaps the observed red dots in Figure 1‑5. This means that the predicted fluctuations perfectly match the observed fluctuations by the Planck satellite. The amazing thing is that Alan Guth, the founder of inflation, calculated this theoretical line way back in the 1980s, when he developed the inflation theory. Then, 30 years later, the Planck satellite confirmed it. This graph is the strongest argument for the fact that inflation took place. In the graph, there is a peak at 90 degrees, which I am guessing is from the time in the universe when there were two fluctuations. Based on the pattern of fluctuations, the strongest frequency response is at approximately 1 degree. Then, there is another peak at 0.4 degrees. After that, the fluctuation frequency dampens out. There were trillions to a billion trillion fluctuations just before inflation; however, these do not show up on the graph. Even though they are not represented on the graph, they are the locations where galaxies formed.

Figure 1-53. Power spectrum of CMBR. Credit: NASA/WMAP science team.

Roger Penrose (https://youtu.be/yDqny7UzyR4) is a mathematical physicist who won or shared two Nobel Prizes for his work on the physics of black holes. He is an atheist. Penrose argues that cosmic inflation is not possible. He calculated the required uniformity of the universe (low entropy) prior to inflation as 10^10^123. According to Penrose, this level of fine tuning is so precise that it does not allow for random chance in the multiverse and the anthropic principle. The anthropic principle is that we live in one universe suitable for life out of infinite universes because we are here to think about it, which allows for the probability argument of the multiverse hypothesis. Penrose believes in a cyclic universe. In the following video, Guth argues that such extreme fine tuning as Penrose describes is not necessary for inflation.

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Quantum fluctuations in a void such as in the early universe prior to inflation. The pattern of fluctuation was propagated into the pattern of the CMBR. Credit: Ahmed Neutron. Used here per CC BY-SA 4.0.

References

[1] Green, Daniel, and Rafael A. Porto. "Signals of a quantum universe." Physical Review Letters 124, no. 25 (2020): 251302.

[2] Green, Signals

[3] Sanchis-Lozano, Miguel-Angel, Edward K. Sarkisyan-Grinbaum, Juan-Luis Domenech-Garret, and Nicolas Sanchis-Gual. "Cosmological analogies in the search for new physics in high-energy collisions." Physical Review D 102, no. 3 (2020): 035013.

[4] Penrose, Roger. "Difficulties with Inflationary Cosmology a." Annals of the New York Academy of Sciences 571, no. 1 (1989): 249-264.

[5] Sean Carroll, The Eternally Existing, Self-Reproducing, Frequently Puzzling Inflationary Universe, Sean Carroll blog site, Accessed at <http://www.preposterousuniverse.com/blog/2011/10/21/the-eternally-existing-self-reproducing-frequently-puzzling-inflationary-universe/> on October 12, 2013. (Posted on October 21, 2011)

[6] Van den Heuvel. 2016. Chapter 14: Ripples in the Cosmic Microwave Background Radiation. In The Amazing Unity of the Universe. pg. 199.

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