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How old is the universe and how big is it? Is the universe expanding? How do we know? Can we describe how fast the universe is expanding? And since the universe is so big, how do we measure distances to nearby stars and galaxies?
In this Unit, we will look at some of the basic properties of our universe to answer all of these questions. We will look at some videos, look at some equations, and write some code to make predictions about the fate of our universe.
Olbers' Paradox: Is the Universe Infinite?
Olbers' Paradox: Is the Universe Infinite?
In the 1700's it was believed that the universe was infinitely large and infinitely old. German astronomer Heinrich Olbers thought about this and thought of this question: If the universe is infinite, why is the night sky dark? If the universe is infinite, there should be an infinite amount of stars so any direction you look from the Earth you'll spot a star. Also, since the starlight has had an infinite amount of time to reach the Earth, the night sky should not be dark but brighter than the sun. Check out this short video which talks about Olbers' paradox and how a finite, expanding universe answers the question Olbers asked nearly 300 years ago.
After viewing, we will be making some comments in Google Jamboard. If you're not familiar with this technology, click here for an introduction.
JAMBOARD ACTIVITY: There are three slides to this Jamboard. Each board is dedicated to one of the following questions. Think about these questions when you watch the video. Then, using a sticky note post:
In your own words, a summary Olbers' Paradox.
Something interesting you learned in this video.
Something you want to know more about.
Homogeneity and Isotropy: The Universe is uniform with no preferred direction
Homogeneity and Isotropy: The Universe is uniform with no preferred direction
The Cosmological Principle states that the universe, on average, looks
Homogeneous, which means that the universe is uniform in density
Isotropic, which means that the universe has no preferred direction
Now if I told you that the universe was uniform in density with no preferred direction, you would probably look at me like I was crazy. You may say "OBVIOUSLY the universe isn't uniform. There's only one me and one earth and there's millions of miles of empty space between the Earth and the nearest planet. Plus, the Earth orbits around the Sun so there's definitely a preferred direction. No way!"
And you'd be right, actually. It's only when you look at very large distances that the universe looks how I describe it.
Take a look at the interactive module below that shows just how big and how small things in the universe are. When we say the universe is homogeneous and isotropic, we are looking at scales larger than hundreds of Megaparsecs, or around a yottameter. These distances are so mind-mindbogglingly large that they don't seem real or relevant to our lives.
Researchers have tried to simulate the evolution of the universe by putting a bunch of particles in a box and letting gravity do its thing, but simulating something so large would take thousands of lifetimes to compute. They then simulated boxes small enough to compute but large enough to observe important features of the universe. Take a look at these images from the Millennium Simulations which simulated how massive particles evolved over time in a simulated universe. Regions of high-density are bright yellow, regions of low-density are black, and everything in between is purple. When we zoom in, we see the universe is clumpy and definitely breaks the Cosmological Principle. However when we zoom out and observe the cosmic web, we can't really pick out one region from another. It's looking at the evolution of the universe at these distance scales which cosmologists use to justify the Cosmological Principle. Click the drop-downs below to see for yourself!
Small scales
Medium scales
Large scales
Test your understanding!
Test your understanding!
Complete the quiz below to see just how vast the universe really is!
The Scale Factor: How the size of the universe has changed over time
The Scale Factor: How the size of the universe has changed over time
Based off the Standard Cosmological Model, we know that the universe is expanding. That means that the universe was smaller in the past relative to its size today. We characterize the size of the universe relative to today using the scale factor, a. Since the universe is homogeneous and isotropic, there is no reason why one part of the universe should be larger or smaller than the rest of the universe at any given time. That means the scale factor, too, obeys the Cosmological Principle; the scale factor doesn't depend on where you're looking in space and is only a function of time.
The Hubble Parameter: How fast the universe is expanding
The Hubble Parameter: How fast the universe is expanding
The Hubble Parameter tells us the rate of expansion of the universe relative to its size. Its formula is given on the right. We're also interested in constraining the universe's rate of expansion today: H0. In general, when you see a "0" in a subscript, take that to mean that the value that has it is evaluated at today's time.
The units of the Hubble Parameter are given in (km/s)/Mpc. These units are a little funky, so let's deconstruct what they're telling us. The numerator, given in km/s, tells us how fast distant objects are coming towards us or going away from us. The denominator, given in Mpc, tells us how far away the object is. If the objects we're looking at are close enough to us, we can describe their motion with Hubble's Law, which tells us that the velocity of an object is equal to its distance from us times the Hubble Parameter. What we observe is that galaxies far from us are moving away faster than galaxies close to us.
How to Measure Distances in Space
How to Measure Distances in Space
Light takes time to travel
Light takes time to travel
When we're trying to figure out the physical distance in the universe between us and some far away object, though, we need to take into account the fact that the universe is expanding and that light takes time to reach us. As astronomers, we observe the light emitted from a far-away object. That light will continue to travel towards us as the universe expands, decreasing its energy along the way. Light travels at a constant speed in space, so the light we observe was emitted a long time ago. Since then, the expansion of the universe has also increased the physical distance between us and where the object is now. In order to accurately say where these objects are today, we need to take this into account!
Remember that light has a wavelength. As the universe expands, the wavelength also expands and stretches. A increasing the wavelength of light places it at lower energy than before towards the red, infrared, and microwave portions of the light spectrum. This phenomenon is known as the redshift of light. We can calculate the redshift, z, by knowing the wavelength of light when it was first emitted and the wavelength that we observe now. Click here to see some animations made by NASA showing what a redshift physically looks like.
We can also relate the redshift to the scale factor! Since the scale factor describes the relative size of the universe at different times, we can use this fact to describe the relative size of the wavelength of light. The wavelength we observe today has been scaled by the expansion of the universe to a value larger than what it was when it was first emitted.
Plugging this expression into the one for redshift, we can then relate the scale factor to the redshift. This will be an important relationship for us going forward. We can directly observe the redshift of light, but we cannot directly observe the scale factor. This relationship will allow us to connect observations to theoretical calculations. Try to find this relationship between z and a on your own using some algebra and reveal the answer below.
a = 1/(1+z)
As the scale factor decreases in the past, the redshift increases. Using the formula, the redshift corresponding to today is z=0.
Getting into Distance Measurements
Getting into Distance Measurements
Now that we have a way to describe the rate of the universe's expansion, how do we measure it? Well, we first need to figure out how to measure distances to objects before we can figure out how fast they're moving. Strangely, there are more than a few definitions of the distance when it comes to astronomy based on the properties of the object we observe. Click on the definitions below to learn more about them!
dL: Luminosity Distance (Observational)
This perceived distance is found when you are measuring the distance to a far away object in the sky with some known luminosity.
dA: Angular Distance (Observational)
This perceived distance is found when you are measuring the distance to a far away object in the sky with some known shape or size.
χ: Comoving Distance (Physical)
This corresponds to the distance from you to an object if we negated the cosmological expansion, as if your ruler was expanding at the same rate as the universe.
dp: Proper Distance (Physical)
This corresponds to the actual physical distance an object is from you, including effects from the expansion of the universe and the object's own individual motion.
We'll define these mathematically now, but start by describing how we typically measure distances on Earth. If we were trying to measure the distance to a point that is a distance b away from us on a table, we can write it down using an integral like on the right to find the distance. It's a little silly, though, since the distance is just b. The integral is telling us to sum up each little contribution of distance between the points, maybe a centimeter at a time.
We then want to find the comoving distance between two objects, which takes into account the time light takes to get to its destination when the universe is expanding. We can see the mathematical form of it here on the right. But how we observe an object affects the perceived distance to that object! We will go over the details of what the angular diameter distance and the luminosity distance are in the following Google Colab notebook.
CALCULATE DISTANCES NOTEBOOK
CALCULATE DISTANCES NOTEBOOK
When you're ready, open your Google Drive folder for this course (that you downloaded here) and open the "Cosmic Distances.ipynb" file in Google Colab. Here, we will discuss the differences in the angular diameter distance and the luminosity distance. At the end of the notebook, you will be calculating and plotting these distances numerically and ending with some discussion of interesting features in these distance measurements.
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