Holography, Cosmology and the Second Law of Thermodynamics

TL;DR

<3-5 sentence high-level summary>We address how holography should be applied in time-dependent cosmologies. We argue the generalized second law, δS_mat + δS_bh ≥ 0, is the overarching principle, reducing to the holographic bound in static limits. For isotropic flat and open universes with a fixed equation of state, the generalized second law yields a Fischler–Susskind–type bound on regions up to the particle horizon, while closed universes and interiors of black holes lack a simple area-entropy relation. After inflation, a modified bound applies to post-inflationary regions smaller than the Hubble volume, clarifying entropy constraints in early-universe cosmology.

Abstract

We propose that in time dependent backgrounds the holographic principle should be replaced by the generalized second law of thermodynamics. For isotropic open and flat universes with a fixed equation of state, the generalized second law agrees with the cosmological holographic principle proposed by Fischler and Susskind. However, in more complicated spacetimes the two proposals disagree. A modified form of the holographic bound that applies to a post-inflationary universe follows from the generalized second law. However, in a spatially closed universe, or inside a black hole event horizon, there is no simple relationship that connects the area of a region to the maximum entropy it can contain.