Cosmological evolution of the gravitational entropy of the large-scale structure

Abstract

We consider the entropy associated with the large-scale structure of the Universe in the linear regime, where the Universe can be described by a perturbed Friedmann-Lemaître spacetime. In particular, we compare two different definitions proposed in the literature for the entropy using a spatial averaging prescription. For one definition, the entropy of the large-scale structure for a given comoving volume always grows with time, both for a CDM and a $Λ$CDM model. In particular, while it diverges for a CDM model, it saturates to a constant value in the presence of a cosmological constant. The use of a light-cone averaging prescription in the context of the evaluation of the entropy is also discussed.

10 pages, 4 figures. Presentation improved, typos corrected, previous subsection III.B merged with subsection II.C, comments, clarifications and a reference added. Version accepted for publication in GRG