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.

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.

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. You could argue that on this scale, the universe does not look like it is the same everywhere (homogeneous).

The Sloan Digital Sky Survey was an even more extensive mapping of galaxies. 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.

Recently, the Sloan Digital Sky Survey (SDSS) was extended from the earlier 2-D slices into a fully 3-D survey to include four million galaxies and quasars between 2014 and 2020. The new, extended map also includes four types of galaxies: nearby galaxies, red galaxies, more distant star-forming galaxies and quasars. The SDSS provides information about the accelerated expansion of the universe by mapping the redshift pattern of the galaxies in 3-D space.

This video from the Extended Baryon Oscillation Spectroscopic Survey (eBOSS) describes the mapping mission and illustrates the 3-D map produced by the Sloan Digital Sky Survey, highlighting the spectral analysis of the galactic redshifts.

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 another 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.

This graphic illustrates that if two objects are farther apart on an expanding sphere, they move relatively faster.

Point A is 2 cm away at the start, and Point B is 1 cm away. After one second, the sphere has doubled in diameter. Point A has doubled its distance away and so has Point B.

Point A has moved at a speed of 1 cm/s and Point B has moved at a speed of 2 cm/s. 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.

The same is true of galaxies. As the universe expands, the farther a galaxy is away from us, the faster it appears to be moving. Notice that in our graphic, the dots themselves did not expand. Objects like planets, stars and galaxies do not expand as the universe expands, they just get farther apart.

Expansion of the universe affects light differently than it does matter objects. 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.