Degrees of freedom of gravitational radiation with positive cosmological constant

TL;DR

This paper investigates the radiative degrees of freedom of gravitational fields in spacetimes with a positive cosmological constant, using geometric methods and connection spaces, revealing key differences from asymptotically flat cases.

Contribution

It introduces a new geometric framework for isolating gravitational radiation in de Sitter-like spacetimes, adapting methods from asymptotically flat scenarios and identifying fundamental degrees of freedom.

Findings

Half of the radiative degrees of freedom are identified.

These degrees of freedom determine gravitational radiation in algebraically special cases.

Differences arise due to the space-like conformal boundary.

Abstract

Results on the isolation of the radiative degrees of freedom of the gravitational field with a positive cosmological constant in full General Relativity are put forward. Methods employed in a recent geometric characterisation of gravitational radiation are used and, inspired by Ashtekar's work on asymptotically flat space-times, a space of connections is defined. Ground differences emerge due to the space-like character of the conformal boundary, and one has to put into play a fundamental result by Friedrich concerning the initial value problem for space-times with a positive cosmological constant. Based on this, half of the radiative degrees of freedom are identified; remarkably, they utterly determine the gravitational radiation content for space-times with algebraically special rescaled Weyl tensor at infinity. Directions for defining the phase space in the general case are proposed.