Induced gravitational waves in a general cosmological background

TL;DR

This paper derives new analytical formulas for induced gravitational waves in a general cosmological background, enhancing understanding of their role in primordial fluctuations and black hole formation.

Contribution

It provides the first general integral formulas for induced gravitational waves beyond matter and radiation domination eras.

Findings

New analytic integral formulas for subhorizon induced gravitational waves

Application to peaked primordial spectra and black hole scenarios

Enhanced understanding of gravitational wave generation in diverse cosmological backgrounds

Abstract

Gravitational waves are inevitably produced by second order terms in cosmological perturbation theory. Most notably, the so-called induced gravitational waves are a window to the small scales part of the primordial spectrum of fluctuations and a key counterpart to the primordial black hole scenario. However, semi-analytical solutions are only known for matter and radiation domination eras. In this paper, we present new analytic integral formulas for the induced gravitational waves on subhorizon scales in a general cosmological background with a constant equation of state. We also discuss applications to a peaked primordial scalar power spectrum and the primordial black hole scenario.