Relic gravitons from stiff curvature perturbations

TL;DR

This paper investigates the generation of relic gravitons during a stiff fluid phase after inflation, analyzing how curvature inhomogeneities and sound speed influence their spectral energy density, and finds secondary effects to be negligible.

Contribution

It introduces a detailed analysis of secondary gauge-dependent contributions to relic graviton spectra from curvature inhomogeneities during stiff fluid domination.

Findings

Secondary contributions are suppressed inside the sound horizon.

The spectral energy density is primarily determined by the first-order effects.

Secondary effects are negligible for phenomenological considerations.

Abstract

The tensor modes reentering the Hubble radius when the plasma is dominated by a stiff fluid lead to a spectral energy density whose blue slope depends on the total post-inflationary sound speed. This result gets however corrected by a secondary (gauge-dependent) term coming from the curvature inhomogeneities that reenter all along the same stage of expansion. In comparison with the first-order result, the secondary contribution is shown to be always suppressed inside the sound horizon and its effect on the total spectral energy density of the relic gravitons is therefore negligible for all phenomenological purposes. It is also suggested that the effective anisotropic stress of the curvature inhomogeneities can be obtained from the functional derivative of the second-order action of curvature inhomogeneities with respect to the background metric.