Horizon Complementarity and Casimir Violations of the Null Energy Condition

TL;DR

This paper explores horizon complementarity in cosmology, proposing that quantum effects like Casimir energy from compact negatively curved spaces can violate the null energy condition, with implications for eternal inflation.

Contribution

It introduces a novel application of horizon complementarity to cosmological horizons using negatively curved geometries and predicts the gravitational Casimir coupling from this framework.

Findings

Casimir energy arises from compact negatively curved spaces.

The gravitational Casimir coupling is constrained and explicitly predicted.

Implications for null energy condition violations in cosmology.

Abstract

The principle of horizon complementarity is an attempt to extend ideas about black hole complementarity to all horizons, including cosmological ones. The idea is that the degrees of freedom necessary to describe the interior of the cosmic horizon of one observer in a given universe are in fact sufficient to account for the physics of that entire universe: the remainder is just a set of redundant copies of the interior of a single cosmic horizon. These copies must be factored out, just as one has to factor out gauge redundancies to identify the true degrees of freedom in gauge theory. Motivated by the observation that quantum cosmology favours compactified negatively curved spatial sections, we propose to use such geometries to implement horizon complementarity for eternal Inflation. We point out that the "effective finiteness" of such universes has important consequences for physics inside the observer's horizon: there is a non-local effect, represented by a Casimir energy. We use our proposed interpretation of complementarity to constrain the gravitational Casimir coupling in two very different ways; the result is an explicit prediction for the value of the coupling.