The work shows that free-streaming dark radiation isocurvature produces a qualitatively different gravitational wave spectrum than cold dark matter isocurvature and derives constraints on isocurvature power spectra around 10^6 Mpc^{-1} from NANOGrav data.
Impact of anisotropic stress of free-streaming particles on gravitational waves induced by cosmological density perturbations
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abstract
Gravitational waves (GWs) are inevitably induced at second-order in cosmological perturbations through non-linear couplings with first order scalar perturbations, whose existence is well established by recent cosmological observations. So far, the evolution and the spectrum of the secondary induced GWs have been derived by taking into account the sources of GWs only from the product of first order scalar perturbations. Here we newly investigate the effects of purely second-order anisotropic stresses of photons and neutrinos on the evolution of GWs, which have been omitted in the literature. We present a full treatment of the Einstein-Boltzmann system to calculate the spectrum of GWs with anisotropic stress based on the formalism of the cosmological perturbation theory. We find that photon anisotropic stress amplifies the amplitude of GWs by about $150 %$ whereas neutrino anisotropic stress suppress that of GWs by about $30 %$ on small scales $k\gtrsim 1.0 h{\rm Mpc}^{-1}$ compared to the case without anisotropic stress. The second order anisotropic stress does not affect GWs with wavenumbers $k\lesssim 1.0 h{\rm Mpc}^{-1}$. The result is in marked contrast with the case at linear order, where the effect of anisotropic stress is damping in amplitude of GWs.
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A review that unifies analytical expressions for scalar-induced gravitational waves and emphasizes calculations for non-radiation-dominated cosmologies.
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Isocurvature Induced Gravitational Waves at Pulsar Timing Arrays
The work shows that free-streaming dark radiation isocurvature produces a qualitatively different gravitational wave spectrum than cold dark matter isocurvature and derives constraints on isocurvature power spectra around 10^6 Mpc^{-1} from NANOGrav data.
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Scalar induced gravitational waves review
A review that unifies analytical expressions for scalar-induced gravitational waves and emphasizes calculations for non-radiation-dominated cosmologies.