Gravitational Waves in Open de Sitter Space

TL;DR

This paper calculates the spectrum of primordial gravitational waves in open de Sitter space, demonstrating a unique, well-behaved correlator free from infrared divergences by addressing gauge mode contributions.

Contribution

It provides a novel computation of gravitational wave spectra in open de Sitter space using Euclidean path integrals, resolving previous issues with infrared divergences.

Findings

The correlator is unique and well-behaved in the infrared.

Infrared divergence is caused by a discrete gauge mode.

The method uses analytic continuation from Euclidean to Lorentzian spacetime.

Abstract

We compute the spectrum of primordial gravitational wave perturbations in open de Sitter spacetime. The background spacetime is taken to be the continuation of an O(5) symmetric instanton saddle point of the Euclidean no boundary path integral. The two-point tensor fluctuations are computed directly from the Euclidean path integral. The Euclidean correlator is then analytically continued into the Lorentzian region where it describes the quantum mechanical vacuum fluctuations of the graviton field. Unlike the results of earlier work, the correlator is shown to be unique and well behaved in the infrared. We show that the infrared divergence found in previous calculations is due to the contribution of a discrete gauge mode inadvertently included in the spectrum.