Quantum Modifications to Gravity Waves in de Sitter Spacetime

Abstract

We study the effect of the vacuum fluctuations of a massless conformally invariant field on tensor perturbations of spatially flat de Sitter spacetime. We find that de Sitter spacetime is stable within the regime of the semiclassical theory. Next we investigate the modification of linearized plane gravity waves by the effects of the quantum stress tensor. We find a correction term whose amplitude depends on the initial time η0. If this initial time is the beginning of inflation, then as long as the energy scale of inflation and the proper frequency of the mode at η0 are well below the Planck scale, the fractional correction is small. Nonetheless, modes which are transplanckian at the onset of inflation may have a significant correction. The increase in amplitude can be potentially observed through a modification of the power spectrum of tensor perturbations in inflationary cosmology. This enhancement of the power spectrum depends upon the initial time, and is greater for shorter wavelengths.