Exploring the Spectral Shape of Gravitational Waves Induced by Primordial Scalar Perturbations and Connection with the Primordial Black Hole Scenarios

TL;DR

This paper analyzes the spectral shapes of gravitational waves induced by scalar perturbations in the early universe, linking them to primordial black hole scenarios and inflation models, and discusses their potential for constraining inflationary theories.

Contribution

It provides a detailed calculation of gravitational wave spectra during radiation and kination eras, connecting spectral features with inflation models and primordial black hole formation.

Findings

Spectral shapes differ between radiation and kination eras.

Tensor modes can constrain primordial curvature perturbation spectra.

Spectral features help discriminate among inflationary models.

Abstract

There is a growing expectation that the gravitational wave detectors will start probing the stochastic gravitational wave backgrounds in the following years. We explore the spectral shapes of gravitational waves induced to second order by scalar perturbations and presumably have been produced in the early universe. We calculate the gravitational wave spectra generated during radiation and kination eras together with the associated primordial black hole counterpart. We employ power spectra for the primordial curvature perturbation generated by $\alpha$-attractors and nonminimal derivative coupling inflation models as well as Gaussian and delta-type shapes. We demonstrate the ability of the tensor modes to constrain the spectrum of the primordial curvature perturbations and discriminate among inflationary models. Gravitational wave production during kination and radiation era can also be distinguished by their spectral shapes and amplitudes.