Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations

TL;DR

This paper derives the complete spectrum of gravitational waves generated by primordial scalar perturbations, highlighting their scale-dependent features and potential dominance over primordial tensor signals in certain cosmological models.

Contribution

The authors provide a model-independent calculation of the scalar-induced gravitational wave spectrum across all observable wavelengths, including analytical and numerical validation.

Findings

Spectrum is scale-invariant on small scales

Enhanced gravitational waves on large/intermediate scales

Scalar-induced waves can dominate primordial signals in some models

Abstract

We derive the complete spectrum of gravitational waves induced by primordial scalar perturbations ranging over all observable wavelengths. This scalar-induced contribution can be computed directly from the observed scalar perturbations and general relativity and is, in this sense, independent of the cosmological model for generating the perturbations. The spectrum is scale-invariant on small scales, but has an interesting scale-dependence on large and intermediate scales, where scalar-induced gravitational waves do not redshift and are hence enhanced relative to the background density of the Universe. This contribution to the tensor spectrum is significantly different in form from the direct model-dependent primordial tensor spectrum and, although small in magnitude, it dominates the primordial signal for some cosmological models. We confirm our analytical results by direct numerical integration of the equations of motion.