Infrared Behavior of Induced Gravitational Waves from Isocurvature Perturbations

TL;DR

This paper investigates the spectral properties of gravitational waves induced by isocurvature perturbations, revealing a unique infrared spectral slope that can distinguish them from adiabatic-induced waves, aiding early universe studies.

Contribution

It provides a novel analytical characterization of the infrared spectral slope of isocurvature-induced gravitational waves, highlighting a distinctive log-dependent form.

Findings

Infrared spectral slope depends on a logarithmic function of wave number.

Distinct spectral behavior from adiabatic-induced gravitational waves.

Offers a potential observational discriminant for primordial perturbation modes.

Abstract

Induced gravitational waves provide a powerful probe of primordial perturbations in the early universe through their distinctive spectral properties. We analyze the spectral energy density $\Omega_{\text{GW}}$ of gravitational waves induced by isocurvature scalar perturbations. In the infrared regime, we find that the spectral slope $n_{\text{GW}} \equiv \text{d} \ln\Omega_\mathrm{GW}/\text{d}\ln k$ takes the log-dependent form $3-4/ \ln (\tilde{k}_*^2 / 6k^2)$, where $\tilde{k}_*$ represents the effective peak scale of the primordial scalar power spectrum. This characteristic behavior differs markedly from that of adiabatic-induced gravitational waves, establishing a robust observational discriminant between isocurvature and adiabatic primordial perturbation modes.