# Gravitational waves induced by scalar perturbations as probes of the small-scale primordial spectrum

## TL;DR

This paper explores how gravitational waves induced by scalar perturbations can serve as probes for the small-scale primordial spectrum, providing new constraints using advanced calculations and experimental sensitivities.

## Contribution

It introduces precise methods to calculate induced gravitational waves and assesses their detectability, offering novel constraints on small-scale primordial perturbations.

## Key findings

- Existing limits on small-scale primordial spectrum derived from gravitational wave observations.
- Projected sensitivities of future GW detectors can significantly improve constraints.
- Accurate modeling of induced GWs enhances the understanding of small-scale primordial fluctuations.

## Abstract

Compared to primordial perturbations on large scales, roughly larger than $1$ megaparsec, those on smaller scales are not severely constrained. We revisit the issue of probing small-scale primordial perturbations using gravitational waves (GWs), based on the fact that, when large-amplitude primordial perturbations on small scales exist, GWs with relatively large amplitudes are induced at second order in scalar perturbations, and these induced GWs can be probed by both existing and planned gravitational-wave projects. We use accurate methods to calculate these induced GWs and take into account sensitivities of different experiments to induced GWs carefully, to report existing and expected limits on the small-scale primordial spectrum.