Positive vacuum energy and the N-bound

TL;DR

This paper demonstrates that in universes with a positive cosmological constant, the total observable entropy is finite and bounded by the inverse of the cosmological constant, supporting the idea of a finite fundamental theory.

Contribution

It introduces a novel Bekenstein-like bound on matter entropy in asymptotically de Sitter spaces and extends the covariant entropy bound to a broader class of cosmologies.

Findings

Total observable entropy is bounded by the inverse of the cosmological constant.

Entropy cannot be observed unless it is both in the past and future of the observer.

Supports the idea that universes with positive cosmological constant have a finite number of degrees of freedom.

Abstract

We argue that the total observable entropy is bounded by the inverse of the cosmological constant. This holds for all space-times with a positive cosmological constant, including cosmologies dominated by ordinary matter, and recollapsing universes. The argument involves intermediate steps which may be of interest in their own right. We note that entropy cannot be observed unless it lies both in the past and in the future of the observer's history. This truncates space-time to a diamond-shaped subset well-suited to the application of the covariant entropy bound. We further require, and derive, a novel Bekenstein-like bound on matter entropy in asymptotically de Sitter spaces. Our main result lends support to the proposal that universes with positive cosmological constant are described by a fundamental theory with only a finite number of degrees of freedom.