Entropy of universe as entanglement entropy

TL;DR

This paper proposes that the entropy of the universe, associated with a causal diamond, can be understood as entanglement entropy, and demonstrates its non-decreasing behavior in various cosmological models consistent with the generalized second law.

Contribution

It introduces a novel entanglement entropy framework for the universe's entropy based on causal diamonds and tests its validity across different cosmological spacetimes.

Findings

Entropy equals the area of the boundary divided by 4G.

Entropy is a non-decreasing function over time in flat and open FRW universes.

The framework aligns with the generalized second law of thermodynamics.

Abstract

We note that the observable part of universe at a certain time t_P is necessarily limited, when there is a beginning of universe. We argue that an appropriate spacetime region associated with an observer from tI to t_P is the causal diamond which is the overlap of the past/future of the observer at t_P/t_I respectively. We also note that the overlap surface \partial D of the future and the past lightcones bisects the spatial section including \partial D into two regions D and \bar D where D is the region inside the causal diamond and \bar D the remaining part of the spatial section. We propose here that the entropy of universe associated with a causal diamond is given by an entanglement entropy where one is tracing over the Hilbert space associated with the region \bar D which is not accessible by the observer. We test our proposal for various examples of cosmological spacetimes, including flat or open FRW universes, by showing that the entropy as the area of \partial D divided by 4G is a non-decreasing function of time t_P as dictated by the generalized second law of thermodynamics. The closed, recollapsing universe corresponds to a finite system and there is no reason to expect the validity of the generalized second law for such a finite system.