Induced gravitational waves as a probe of thermal history of the universe

TL;DR

This paper demonstrates that the spectrum of scalar perturbation induced gravitational waves can reveal details about the universe's thermal history, including the equation of state during different cosmological stages.

Contribution

It introduces a method to use the gravitational wave spectrum to probe the universe's thermal history and equation of state, extending previous work on primordial density perturbations.

Findings

Infrared slope of gravitational wave spectrum relates to the universe's equation of state.

The spectrum exhibits a broken power-law shape around the reheating scale.

A peak appears in the spectrum for specific equations of state and scalar spectrum features.

Abstract

The scalar perturbation induced gravitational waves are a probe of the primordial density perturbation spectrum on small scales. In this paper, we show that they can also probe the thermal history of the universe. We assume the universe underwent a stage with a constant equation of state parameter $w$, followed by the radiation-dominated stage of the conventional big bang universe. We find that the infrared slope of the power spectrum of the induced stochastic gravitational wave background for decelerating cosmologies is related to the equation of state of the universe. Furthermore, the induced gravitational wave spectrum has in general a broken power-law shape around the scale of reheating. Interestingly, below the threshold $w=0$ of the equation of state parameter, the broken power-law presents a peak for a Dirac delta peak in the scalar spectrum. For a finite width peak, the threshold changes to $w=-1/15$ depending on the value of the width. In some cases, such a broken power-law gravitational wave spectrum may degenerate to the spectrum from other sources like phase transitions or global cosmic strings.