Log-dependent slope of scalar induced gravitational waves in the infrared regions

TL;DR

This paper analytically derives a log-dependent slope for scalar induced gravitational waves in the infrared region, providing a new template to distinguish SIGWs from other sources based on their spectral behavior.

Contribution

The authors present an analytical calculation revealing a unique log-dependent spectral slope of SIGWs in the infrared, which is a novel feature for identifying these waves.

Findings

Derived the spectral slope formulas for SIGWs in the infrared region.

Identified the log-dependent slope as a distinctive signature of SIGWs.

Proposed the slope as a new template for observational differentiation.

Abstract

We analytically calculate the scalar induced gravitational waves (SIGWs) and find a log-dependent slope of SIGW in the infrared regions $(f<f_c)$, namely $n_{\mathrm{GW}}(f)=3-2/\ln(f_c/f)$, and $n_{\mathrm{GW}}(f)=2-2/\ln(f_c/f)$ near the peak if the power spectrum of scalar curvature perturbation is quite narrow, where $f_c$ is roughly the frequency at the peak of SIGW. Such a log-dependent slope can be taken as a new template for distinguishing SIGW from other sources.