Induced gravitational waves: the effect of first order tensor perturbations

TL;DR

This paper explores how including first order tensor perturbations affects scalar-induced gravitational waves, providing analytical expressions and analyzing their significance for future gravitational wave observations.

Contribution

It introduces the effect of first order tensor perturbations as additional sources in the generation of scalar-induced gravitational waves, expanding previous scalar-only models.

Findings

Tensor contributions become significant on small scales.

Analytical expressions for new source terms are derived.

Implications for future gravitational wave detection are discussed.

Abstract

Scalar induced gravitational waves contribute to the cosmological gravitational wave background. They can be related to the primordial density power spectrum produced towards the end of inflation and therefore are a convenient new tool to constrain models of inflation. These waves are sourced by terms quadratic in perturbations and hence appear at second order in cosmological perturbation theory. While the focus of research so far was on purely scalar source terms we also study the effect of including first order tensor perturbations as an additional source. This gives rise to two additional source terms: a term quadratic in the tensor perturbations and a cross term involving mixed scalar and tensor perturbations. We present full analytical expressions for the spectral density of these new source terms and discuss their general behaviour. To illustrate the generation mechanism we study two toy models containing a peak on small scales. For these models we show that the scalar-tensor contribution becomes non-negligible compared to the scalar-scalar contribution on smaller scales. We also consider implications for future gravitational wave surveys.