Suppression of the induced gravitational wave background due to third-order perturbations

Abstract: In this work, we revisit and evaluate new source terms which contribute to the induced gravitational wave background. We study their respective contributions to the stochastic gravitational wave background by computing their spectral densities in a radiation-dominated universe. These terms appear at third order in cosmological perturbation theory, however, their correlations with primordial gravitational waves are non-trivial and appear at the same order as so-called scalar induced and scalar-tensor induced gravitational waves. We find that these gravitational wave sources suppress the spectral density at the scales we consider. Furthermore, similarly to scalar-tensor source terms at second order, we find that some terms are enhanced when the input primordial power spectrum of scalar fluctuations is not sufficiently peaked. Hence, where possible, we show that under certain limits the integrands of these terms diverge in the UV sector.