Probing small-scale primordial power spectra with induced gravitational waves

TL;DR

This paper investigates how second-order tensor-scalar induced gravitational waves can be used to probe small-scale primordial perturbations, providing analytical tools and discussing observational prospects with pulsar timing arrays.

Contribution

It introduces the concept of tensor-scalar induced gravitational waves (TSIGWs), derives their analytical spectra, and explores their potential to constrain small-scale primordial fluctuations.

Findings

TSIGWs include scalar-scalar, tensor-scalar, and tensor-tensor contributions.

Analytical kernel functions and energy density spectra for TSIGWs are provided.

TSIGWs from monochromatic spectra could dominate current PTA observations.

Abstract

Large-scale primordial perturbations have been well constrained by current cosmological observations, but the properties of small-scale perturbations remain elusive. This study focuses on second-order induced gravitational waves generated by large-amplitude primordial scalar and tensor perturbations on small scales. In this case, the induced gravitational waves include contributions from three types of source terms: scalar-scalar, tensor-scalar, and tensor-tensor. To distinguish them from second-order scalar induced gravitational waves (SIGWs), we refer to those generated by these three source terms as tensor-scalar induced gravitational waves (TSIGWs). We provide the analytical expressions for the kernel functions and the corresponding energy density spectra of second-order TSIGWs. By combining observations of stochastic gravitational wave background (SGWB) across different scales, TSIGWs can be used to constrain small-scale primordial curvature perturbations and primordial gravitational waves. Furthermore, we discuss the feasibility of TSIGWs dominating the current pulsar timing array (PTA) observations under various primordial power spectra scenarios. Our results indicate that TSIGWs generated by monochromatic primordial power spectra might be more likely to dominate the current PTA observations.