alt Hacker NewsYou have it backwards. The lowest entropy state of the universe would be if there were no attractive forces, only repellent forces, as then all particles would be forced into something of an expanding lattice, but with all particles equidistant from all nearest neighbors (of the same type).
It is gravity which disrupts this and causes clumping, and that _increases_ entropy.
I know it's confusing because normally one would think of a cloud of gas as more disordered than the star it might collapse into, but that is not so. For one the star would be much hotter, and the motions of every particle in the star much more chaotic.
If everything must be constrained to the lattice points, yes. However, empty space has high Boltzmann entropy: you can cut a patch of empty space from here and swap it for the same volume of empty space from there, and the two coarse grain macrostates will be indistinguishable.
Expanding de Sitter quasi-vacuum has tremendous growth in entropy. Gibbons and Hawking gives this (for 3+1d de Sitter) as a quarter of the horizon area: S_H = \frac{Area_{H}}{4} \sim H^{-2} with the "quasi-" giving us increasing growth in the horizon area as DoFs exit the horizon compared to classical pure de Sitter vacuum.
I'm not sure how confining some species of matter to expanding lattice is different from quasi-vacuum in the limit where the lattice spacing is large. I guess you have to abolish continuum spacetime in favour of a taxicab geometry with an analogue of dark energy? Otherwise, how does it differ from an isotropic homogeneous FLRW dust?