The Covariant Entropy Bound, Brane Cosmology, and the Null Energy Condition

TL;DR

This paper examines the relationship between the Null Energy Condition, the Covariant Entropy Bound, and brane cosmology, showing that violations of the NEC in cosmological models conflict with holographic principles.

Contribution

It introduces a modified brane cosmology model with NEC-violating matter that maintains finite entropy but still conflicts with the Covariant Entropy Bound, suggesting holography constrains NEC violations.

Findings

Entropy on lightsheets remains finite despite NEC violation.

The spacetime fails the Bousso-Randall consistency condition.

Holography likely forbids cosmological NEC violations.

Abstract

In discussions of Bousso's Covariant Entropy Bound, the Null Energy Condition is always assumed, as a sufficient {\em but not necessary} condition which helps to ensure that the entropy on any lightsheet shall necessarily be finite. The spectacular failure of the Strong Energy Condition in cosmology has, however, led many astrophysicists and cosmologists to consider models of dark energy which violate {\em all} of the energy conditions, and indeed the current data do not completely rule out such models. The NEC also has a questionable status in brane cosmology: it is probably necessary to violate the NEC in the bulk in order to obtain a "self-tuning" theory of the cosmological constant. In order to investigate these proposals, we modify the Karch-Randall model by introducing NEC-violating matter into $AdS_5$ in such a way that the brane cosmological constant relaxes to zero. The entropy on lightsheets remains finite. However, we still find that the spacetime is fundamentally incompatible with the Covariant Entropy Bound machinery, in the sense that it fails the Bousso-Randall consistency condition. We argue that holography probably forbids all {\em cosmological} violations of the NEC, and that holography is in fact the fundamental physical principle underlying the cosmological version of the NEC.