How did the big bang's low entropy (which comes from gravity) get converted to sunlight?

Question

In many places you will read that just after the big bang, the universe was filled with very hot gas which appeared to be in thermal equilibrium. You will then read that this is actually quite a low entropy state, due to gravity. Though all the matter particles and radiation are in thermal equilibrium, the spacetime where they live is unusually flat. A state of much higher entropy would be to have things clumped together in complicated ways, with a bunch of large black holes hanging around.

Fast forward several billion years, and we get to today, where the sun is shining, allowing us Earth lifeforms to exist. This works because space is cold, while the sun is hot, so we can live off the temperature difference. If we ask why the sun is hot, we find that it's hot because it's fusing hydrogen into helium.

So I know the beginning of the story and the end of the story, but not the middle. How do we get from "spacetime is unusually flat" to "there are hydrogen atoms around that you can fuse into helium"? In particular, how does gravity make a difference: if $G$ was 0, would all the nuclei in universe already be helium (or I guess iron)?

EDIT: To clarify the question consider the following two scenarios:

• The "no fusion" universe: In this universe, nuclear fusion is impossible. Stars still form due to gravity and they still get hot as they collapse, but they don't shine for nearly as long, since there are no fusion reactions happening in the core to replace the energy lost to radiation. Stars rapidly become white dwarfs without passing through a fusion stage. This example makes it seem like nuclear physics is somehow important to answering this question.

• The $G=0$ universe: This universe has no force of gravity, it's spatially uniform. We can still allow it to expand like our own universe, but I guess it wouldn't be due to dark energy or anything, that would just be the shape that spacetime happens to have. After 13 billion years, I'm guessing this universe would be uniformly full of cold hydrogen gas? Though the lack of gravity definitely rules out the existence of stars, it seems like an alien civilization that travelled to this universe could sustain themselves by collecting hydrogen gas and building fusion reactors. If an alien civilization could live there, then entropy must not be at a maximum yet. This example makes it seem like gravity is almost irrelevant to the issue, though I don't think that can actually be right.

Answer 1

Nadav answers this well, but since you want an explicit discussion of the entropy I will try to do that. Right after recombination, when the universe was a nearly homogeneous gas of hydrogen and helium, it sat at the top of three potential wells: gravity, nuclear, and dark energy or the cosmological constant. Thus it was at low entropy compared to what was possible if it fell down these potentials.

At first, there was simple density perturbation growth by gravity which increases entropy because there are many ways this random process can occur and velocities dispersions increase. Then collapse continued via gas dissipation as gravity compressed and heated the gas thus emitting many photons that roam the universe. The gas and dust collapsed (and continue to collapse) until stars formed.

Gravity compresses stars which heat and begin nuclear burning at their cores so the nuclei start falling down their nuclear potential wells which was not possible in the earlier configurations. This generates gamma rays, more particles, which convert to many more low-energy photons by the time they escape from the surface of the stars.

Now we see that dark energy is accelerating the expansion rate of the universe and entropy increases as this potential energy is transformed into more space and higher expansion velocities.

Answer 2

Gravity is what allows a the small initial fluctuations in the matter density after the "big bang" (or after exiting inflation), to grow into large differences. Dark matter, followed by baryonic (ordinary) matter, clump, thanks to gravity, into various filaments, galaxies, and in the small(er) scale, stars. Our Sun is one of these stars which gravity clumped together from a cloud of dilute matter, mostly hydrogen. As gravity continues to act, at some point the hydrogen density in the cloud exceeded some density where fusion begins to happen - and the Sun "turned on".

There's a popular misconception that the Sun needed to reach extremely high densities and temperatures to guarantee fusion. This is not true - the Sun is not a thermonuclear bomb, and does not fuse all its hydrogen in one big explosion. Instead, the Sun is well, well, below the temperature needed to sustain fusion, and the reason why a bit of fusion is happening is quantum tunneling - even though the protons (hydrogen nuclei) in the sun do not have enough energy to fuse, they sometimes (with very low probability) "loan" the missing energy, fuse, and "return" the loan from the huge amount of energy produced in the fusion reaction. The rest of the energy heats up the Sun and causes it to shine as we know it.

The energy produced by fusion is also what generates the pressure which prevents the Sun from collapsing further with gravity. When the fusion processes in the Sun will eventually die out, this pressure will disappear, and the sun will collapse into a so-called "white dwarf" (our Sun isn't massive enough to collapse into a neutron star or a black hole).