Infrared Behavior of Induced Gravitational Waves from Isocurvature Perturbations

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 $3-4/\ln ({\tilde{k}}_{\ast }^2/6k^2)$, where ${\tilde{k}}_{\ast }$ 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.

6 pages, 4 figures