On Causality Conditions in de Sitter Spacetime

TL;DR

This paper investigates causality conditions in de Sitter spacetime by analyzing time delays caused by black holes and shockwaves, and explores how these conditions relate to those in AdS and flat spacetimes, with a focus on boundary measurements and specific field propagation examples.

Contribution

It extends causality analysis techniques from AdS and flat spacetime to de Sitter spacetime, including boundary-based causality conditions and field propagation in shockwave backgrounds.

Findings

Causality conditions can be adapted from AdS and flat spacetime to de Sitter.

Boundary measurements of spatial shifts define fastest null geodesics in de Sitter.

Propagation of a massless spin-1 field illustrates causality constraints in shockwave backgrounds.

Abstract

We carefully consider the Shapiro time delay due to black holes and shockwaves in de Sitter spacetime and study the implications for causality. We discuss how causality conditions of AdS and flat spacetime can be applied in de Sitter spacetime, using spatial shifts measured on the boundary to define ``fastest null geodesics" and taking into account the ``stretching" of the de Sitter Penrose diagram. We consider the propagation of a massless spin-1 field with an $RFF$ coupling in a de Sitter shockwave background as an illustrative example. We also briefly discuss connections to the ANEC.