Will entropy continue to increase in an accelerating-expanding universe?

Question

Before/at/during the Big Bang, quantum fluctuations progressed until there was a constant energy density somewhere which caused inflation. The slight variations in energy due to those quantum fluctuations is now evident in the CMB. Thus, even the slightest energy differences developed patches in the Universe where galaxies now are.

We often leave no question or doubt on the statistical law that entropy increases in any closed system especially if that system is the universe itself. All of the predictions I hear are that the universe will eventually reach maximum entropy (or at least remain near it). At that point, no life or complexity can exist.

Even though expansion is currently accelerating, it isn't near the rate at which it was during inflation.

My question is: in the distant future when entropy is high and expansion is around the rate of inflation, wouldn't quantum fluctuations or even statistical ones lower entropy as they're rapidly enlarged to separate patches of varying energy densities?

Answer 1

If we go with the definition of entropy as the number of microstates and a continuously expanding universe, the phase space is expanding leading to a growing number of microstates.

$S=k_bln(Ω)$

Energy densities do not come into the count. Take a totally expanded universe having become photons , even with very low energydensity , as the phase space expands the microstates should multiply.