Impact of anisotropic stress of free-streaming particles on gravitational waves induced by cosmological density perturbations

Shohei Saga, Kiyotomo Ichiki, and Naoshi Sugiyama
Phys. Rev. D 91, 024030 – Published 22 January 2015

Abstract

Gravitational waves (GWs) are inevitably induced at second order in cosmological perturbations through nonlinear couplings with first-order scalar perturbations, the existence of which 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 suppresses that of GWs by about 30% on small scales k1.0hMpc1 compared to the case without anisotropic stress. The second-order anisotropic stress does not affect GWs with wave numbers k1.0hMpc1. The result is in marked contrast with the case at linear order, where the effect of anisotropic stress is damping in the amplitude of GWs.

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  • Received 3 December 2014

DOI:https://doi.org/10.1103/PhysRevD.91.024030

© 2015 American Physical Society

Authors & Affiliations

Shohei Saga1,*, Kiyotomo Ichiki1,2, and Naoshi Sugiyama1,2,3

  • 1Department of Physics and Astrophysics, Nagoya University, Aichi 464-8602, Japan
  • 2Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602, Japan
  • 3Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), The University of Tokyo, Chiba 277-8582, Japan

  • *saga.shohei@nagoya-u.jp

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Issue

Vol. 91, Iss. 2 — 15 January 2015

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