Localized Gravity, de Sitter, and the Horizon Criterion

TL;DR

This paper examines the role of cosmological horizons in de Sitter solutions within string theory, proposing a refined horizon criterion based on causal contact for observers on end-of-the-world branes.

Contribution

It introduces a new causal contact criterion for cosmological horizons, addressing limitations of previous horizon-based conditions in string-theoretic models with dynamical boundaries.

Findings

Refined the horizon criterion to include causal contact among boundary observers.

Analyzed scalar field effects on end-of-the-world branes.

Identified conditions under which de Sitter solutions may be consistent in string theory.

Abstract

Realizing de Sitter-like solutions in string theory remains challenging, prompting speculation about which specific feature might be responsible for their inconsistency in quantum gravity. In this work, we focus on the `Horizon Criterion', which identifies spacetimes as problematic if they exhibit cosmological horizons. In particular, we study the implications for spacetimes with dynamical boundaries. We argue that requiring inertial observers localized on an end-of-the-world (ETW) brane to be in causal contact with every other observer is too restrictive as there exist string-theoretic solutions without this property. Hence, if one does not want to abandon the idea of cosmological horizons being the fundamental issue with de Sitter, a refined condition is needed. The requirement that inertial, boundary-localized observers should be in causal contact with all other observers on the same ETW brane is such an appropriate refinement. We explore the consequences of this criterion for ETW branes whose energy density is governed by a scalar field, considering two cases: First, with a scalar field confined to the ETW brane, and second, with a bulk modulus subject to a brane-localized potential.