Higher fundamental forms of the conformal boundary of asymptotically de Sitter spacetimes

TL;DR

This paper investigates the geometric structure of the conformal boundary in asymptotically de Sitter spacetimes, establishing constraints that connect stress-energy tensor asymptotics with conformal geometric data through higher conformal fundamental forms.

Contribution

It introduces a partial characterization of the conformal infinity using higher conformal fundamental forms, generalizing previous geometric concepts to higher order.

Findings

Derived constraints linking stress-energy tensor asymptotics with conformal geometry.

Introduced higher conformal fundamental forms to describe boundary geometry.

Extended the trace-free part of the second form to higher order for boundary hypersurfaces.

Abstract

We provide a partial characterization of the conformal infinity of asymptotically de Sitter spacetimes by deriving constraints that relate the asymptotics of the stress-energy tensor with conformal geometric data. The latter is captured using recently defined objects, called higher conformal fundamental forms. For the boundary hypersurface, these generalize to higher order the trace-free part of the second form.