how did the accretion of galaxies occurred through expansion and cooling of the universe?

Answer 1

Good try, but those sources largely address the word accretion, and accretion onto supermassive blackholes.

What you are looking for concerns the formation of structure in the universe; how a fairly uniform medium of particles "curdled" over time forming clumps that became superclusters of galaxies, sheets of these clusters, and individual galaxies within them.

Essentially the whole thing is driven by gravity. If you have an infinite (or near infinite) uniform density gas, then it tends to stay that way. Anyplace you go there is no net force of gravity because you experience gravity from the same amount of matter in all directions; the forces cancel out. The gas is unstable to collapse; if you make a little spot in it a little denser, it will pull together, and draw in more stuff around it. This is called the "Jeans" instability after the Frenchman(?) named Jeans who is first credited with describing this situation mathematically.

The thermal kinetic energy of the particles (temperature) in a gas resist this collapse. Example: Earth cannot hang onto small fast moving molecules of hydrogen in its atmosphere, but if the air was much colder, the hydrogen would be moving more slowly and would stay around.

So, as the universe cools, the size of the mass necessary to cause a Jeans type collapse gets smaller, and the lumpiness in the primordial gas begins to become enough to start structures forming.

Answer 2

Does this help?