Role of spacetime shear for cosmological gravitational waves, in presence of imperfect fluids

Abstract

In this paper, we show that a general geometric and thermodynamic but shear-free perturbation of homogeneous and isotropic universes are necessarily silent, without any gravitational waves, in spite of the presence of nonzero electric and magnetic Weyl. We prove this in two steps. First, we establish that a shear-free perturbation of these universes is acceleration-free and the fluid flow geodesics of the background universe map onto themselves in the perturbed universe. This effect then decouples the evolution equations of the electric and magnetic parts of the Weyl tensor in the perturbed spacetimes and the magnetic part no longer contains any tensor modes. Although the electric part that drives the tidal forces does have tensor modes sourced by the anisotropic stress, these modes have homogeneous oscillations at every point on a time slice without any wave propagation. We also show the presence of vorticity vector waves that are sourced by the curl of heat flux. This analysis shows the critical role of the shear tensor in generating cosmological gravitational waves in an expanding universe.