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