Image source: hubblesite.org

The cosmological principle is based on two observations and an assumption, that the universe is the same everywhere, and the same in every direction, and that the laws of physics are the same everywhere. The first statement regards the universe on very large scales. If you look at the distribution of matter in a galaxy and outside of a galaxy, the matter distribution is obviously not the same. If you look at the the Hubble Deep Field, it is easier to see what the cosmological principle means. A large expanse of the universe contains many galaxies.

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This image is the result of the first slice galaxy survey, mapping about 1000 galaxies over a wide field, using their redshifts to determine their distances away. The figure in the center was dubbed the "Stickman" by Margaret Geller upon its discovery. The body and arms of the Stickman are huge walls of galaxies. Notably, there are large bubble-like voids, stretching several million light years across.

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The Sloan Digital Sky Survey was an even more extensive galaxy survey. The homogeneous nature of the universe becomes apparent with large enough sampling. The walls and voids tend to show up everywhere. If you sample big enough slices of the universe, it starts to look the same everywhere.

What is the difference between homogeneous and isotropic? If something is the same in every direction, isn't it also the same everywhere? This piece of corduroy is an example of something that is homogeneous but not isotropic. If you sample the corduroy anywhere, you see it is the same, but it is very different if you look upward, along the grain, or across the wales. Corduroy is not the same in every direction - it is not isotropic.

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A pencil-beam survey is a very high resolution, narrow focus image of the universe. The larger the redshift of the object, the farther back in time the image. The highest redshift galaxies are very early in formation. Farther back in time, we would be able to see the first stars. Even farther back is an era we call the Dark Ages, because it is the time before the first stars formed, so there were no stars shining. Before that, was the age of recombination, when the universe cooled off enough for the first atoms to be formed (electrons bound to protons). At this time, the universe went from being opaque to transparent because only light of particular wavelengths interacted with atoms.

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Our third point of the cosmological principle is that the laws of physics are the same everywhere. For instance, if we learn about the behaviors of subatomic particles by examining data from a particle accelerator like the Large Hadron Collider, we can infer what must have happened with particles at high energies like those that existed in the early stages of the universe, shortly after the big bang.

We can make a rough estimate of when the universe was born by considering Hubble's law. Remember, Hubble's law came about by recognizing that the farther away galaxies are, the higher their redshifts and the higher their recessional speeds. If we turn the clock backwards, the galaxies would all rush toward the same point. We can calculate how long it would take them to get to that point, by noticing that velocity = distance/time.

Time is distance/velocity. From Hubble's law, distance/velocity = 1/H0. We can get H0 experimentally, so we can calculate 1/H0. Using this method, we calculate the age of the universe to be about 14 billion years.

Now we need to consider the second question, where was the universe born? If we look out at the galaxies in the universe, they closest galaxies might be moving toward or away from us, but the faraway galaxies all seem to be moving away, and the farther they are, the faster they are moving away.

That's what it looks like from our Milky Way galaxy. What if we were in a galaxy very far away? Two main possibilities exist. The first is that the Milky Way is special, that it happens to lie at just the right place so that all of the galaxies are moving away from us. The second possibility is that we are not special. It would look like this from any other galaxy, that all of the other galaxies were moving away, the farther, the faster.

There is roughly a one in two hundred billion chance that we are special and happen to lie at the center of the universe. It is much more likely that the second possibility is true, that it would look like this to any galaxy.

Another way of resolving this question is to think back to the cosmological principle. If the universe is the same everywhere and in every direction, then nowhere is special. There is no center and no edge to the universe. Those would be "special" places.

The farther away any two dots start on this expanding sphere, the more they have moved apart between the first time and the second time.

When the universe expands, individual objects like planets, stars and galaxies do not expand, they just get farther apart. When light travels through expanding space, it does expand. The wavelength gets longer, so it is redshifted.