Saturating the holographic entropy bound

TL;DR

This paper demonstrates that the covariant entropy bound can be saturated in certain cosmological scenarios, disproving the proposed stronger bound S< A^{3/4} and refining our understanding of entropy limits in the universe.

Contribution

It constructs light-sheets with entropy exceeding A^{3/4}, showing the covariant bound can be saturated but not violated, and clarifies maximum observable entropy in different cosmological constants.

Findings

Light-sheets can have entropy arbitrarily larger than A^{3/4}.

The covariant entropy bound is robust and can be saturated.

Maximum observable entropy scales with the cosmological constant as Lambda^{-1} or Lambda^{-2}.

Abstract

The covariant entropy bound states that the entropy, S, of matter on a light-sheet cannot exceed a quarter of its initial area, A, in Planck units. The gravitational entropy of black holes saturates this inequality. The entropy of matter systems, however, falls short of saturating the bound in known examples. This puzzling gap has led to speculation that a much stronger bound, S< A^{3/4}, may hold true. In this note, we exhibit light-sheets whose entropy exceeds A^{3/4} by arbitrarily large factors. In open FRW universes, such light-sheets contain the entropy visible in the sky; in the limit of early curvature domination, the covariant bound can be saturated but not violated. As a corollary, we find that the maximum observable matter and radiation entropy in universes with positive (negative) cosmological constant is of order Lambda^{-1} (Lambda^{-2}), and not |Lambda|^{-3/4} as had hitherto been believed. Our results strengthen the evidence for the covariant entropy bound, while showing that the stronger bound S< A^{3/4} is not universally valid. We conjecture that the stronger bound does hold for static, weakly gravitating systems.