The scalar modes of the relic gravitons

TL;DR

This paper investigates how long-wavelength relic gravitons induce scalar fluctuations during and after inflation, showing that their effects grow over time but are largely balanced by their spectral properties.

Contribution

It provides an explicit calculation of scalar perturbations caused by relic gravitons in a standard thermal history, highlighting the interplay between growth and spectral slope effects.

Findings

Curvature perturbations grow over post-inflationary evolution.

Growth is approximately balanced by the spectral slope of graviton energy density.

Long wavelength gravitons induce scalar fluctuations during and after inflation.

Abstract

In conformally flat background geometries the long wavelength gravitons can be described in the fluid approximation and they induce scalar fluctuations both during inflation and in the subsequent radiation-dominated epoch. While this effect is minute and suppressed for a de Sitter stage of expansion, the fluctuations of the energy-momentum pseudo-tensor of the graviton fluid lead to curvature perturbations that increase with time all along the post-inflationary evolution. An explicit calculation of these effects is presented for a standard thermal history and it is shown that the growth of the curvature perturbations caused by the long wavelength modes is approximately compensated by the slope of the power spectra of the energy density, pressure and anisotropic stress of the relic gravitons.