Primordial gravitational waves amplification from causal fluids

TL;DR

This paper investigates how causal relativistic fluids in the early universe can amplify primordial gravitational waves, revealing a new scale-dependent interaction that enhances the wave spectrum during the radiation era.

Contribution

It introduces a novel analysis of super-Hubble gravitational wave evolution considering causal fluid dynamics with a relaxation time, highlighting a scale-dependent amplification effect.

Findings

Fluid-graviton interaction increases GW amplitude by ~30% for certain modes.

The relaxation time introduces a new relevant scale affecting GW spectrum.

Amplification occurs during the electroweak transition in the early universe.

Abstract

We consider the evolution of the gravitational wave spectrum for super-Hubble modes in interaction with a relativistic fluid, which is regarded as an effective description of fluctuations in a light scalar minimally coupled field, during the earliest epoch of the radiation dominated era after the end of inflation. We obtain the initial conditions for gravitons and fluid from quantum fluctuations at the end of inflation, and assume instantaneous reheating. We model the fluid by using relativistic causal hydrodynamics. There are two dimensionful parameters, the relaxation time $\tau$ and temperature. In particular we study the interaction between gravitational waves and the non trivial tensor (spin 2) part of the fluid energy-momentum tensor. Our main result is that the new dimensionful parameter $\tau$ introduces a new relevant scale which distinguishes two kinds of super-Hubble modes. For modes with $H^{-1}<\lambda<\tau$ the fluid-graviton interaction increases the amplitude of the primordial gravitational wave spectrum at the electroweak transition by a factor of about $1.3$ with respect to the usual scale invariant spectrum.