Gravitational waves from primordial scalar and tensor perturbations

TL;DR

This paper analyzes the generation of second order gravitational waves from primordial scalar and tensor perturbations during the radiation era, providing explicit spectra and assessing detectability with LISA.

Contribution

It derives explicit expressions for second order gravitational wave spectra induced by primordial perturbations and evaluates their observability with future detectors.

Findings

Second order GWs have explicit power spectra expressions.

Tensor perturbations can significantly enhance GW signals.

LISA could detect these primordial GW signals for certain parameters.

Abstract

We investigate the second order gravitational waves induced by the primordial scalar and tensor perturbations during radiation-dominated era. The explicit expressions of the power spectra of the second order GWs are presented. We calculate the energy density spectra of the second order GWs for a monochromatic primordial power spectra. For large $k$ $\left( k>k_* \right)$, the effects of the primordial tensor perturbation with tensor-to-scalar ratio $r=A_{h}/A_{\zeta}=0.2$ lead to an around $50\% $ increase of the signal-to-noise ratio (SNR) for LISA observations.