Thermal History of the Early Universe and Primordial Gravitational Waves from Induced Scalar Perturbations

TL;DR

This paper investigates how scalar perturbations in the early universe induce gravitational waves, revealing their spectrum's dependence on the universe's thermal history and potential observability with future detectors.

Contribution

It provides a detailed calculation of the induced gravitational wave background considering the evolution of standard model degrees of freedom, highlighting effects around phase transitions.

Findings

Induced GWs are affected differently by standard model degrees of freedom than first-order tensor GWs.

Scalar perturbations can source tensor modes significantly during phase transitions.

Potential observability of effects with future gravitational wave detectors if scalar spectral index > 1 or non-Gaussianities are present.

Abstract

We study the induced primordial gravitational waves (GW) coming from the effect of scalar perturbation on the tensor perturbation at the second order of cosmological perturbation theory. We use the evolution of the standard model degrees of freedom with respect to temperature in the early Universe to compute the induced gravitational waves bakcground. Our result shows that the spectrum of the induced GW is affected differently by the standard model degrees of freedom than the GW coming from first order tensor perturbation. This phenomenon is due to the presence of scalar perturbations as a source for tensor perturbations and it is effective around the quark gluon deconfinement and electroweak transition. In case of considering a scalar spectral index larger than one at small scales or a non-Gaussian curvature power spectrum this effect can be observed by gravitational wave observatories.