Can gravitational waves halt the expansion of the universe?

TL;DR

This paper investigates how gravitational waves in a universe with a positive cosmological constant can influence cosmic expansion, revealing critical behaviors and proposing boundary conditions that may slow expansion temporarily.

Contribution

It introduces a numerical framework for studying non-linear gravitational wave propagation in de Sitter space and explores conditions under which they can significantly affect universe expansion.

Findings

Critical behaviors depend on wave profile and cosmological constant.

Boundary data near bifurcations can produce false steady states.

Proposed boundary conditions can temporarily slow cosmic expansion.

Abstract

We numerically investigate the propagation of plane gravitational waves in the form of an initial boundary value problem with de Sitter initial data. The full non-linear Einstein equations with positive cosmological constant $\lambda$ are written in the Friedrich-Nagy gauge which yields a wellposed system. The propagation of a single wave and the collision of two with colinear polarization are studied and contrasted with their Minkowskian analogues. Unlike with $\lambda=0$, critical behaviours are found with $\lambda>0$ and are based on the relationship between the wave profile and $\lambda$. We find that choosing boundary data close to one of these bifurcations results in a "false" steady state which violates the constraints. Simulations containing (approximate) impulsive wave profiles are run and general features are discussed. Analytic results of Woodard and Tsamis, which describe how gravitational waves could affect an expansion rate at an initial instance of time, are explored and generalized to the entire space-time. Finally we put forward boundary conditions that, at least locally, slow down the expansion considerably for a time.