Gravitational Waves in the Presence of Viscosity

Abstract

We analyze gravitational waves propagating in an isotropic cosmic fluid endowed with a bulk viscosity $\zeta$ and a shear viscosity $\eta$, assuming these coefficients to vary with fluid density $\rho$ as ${\rho }^{\lambda }$, with $\lambda =1/2$ favored by experimental evidence. We give the general governing equation for the gravitational waves, and focus thereafter on two examples. The first concerns waves in the very late universe, close to the Big Rip, where the fate of the comic fluid is dependent highly on the values of the parameters. Our second example considers the very early universe, the lepton era; the motivation for this choice being that the microscopical bulk viscosity as calculated from statistical mechanics is then at maximum. We find that the gravitational waves on such an underlying medium are damped, having a decay constant equal to the inverse of the conformal Hubble parameter. Our results turn out to be in good agreement with other viscosity-based approaches.

Version to appear in IJMPD. LaTeX 14 pages

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• Microphysical manifestations of viscosity and consequences for anisotropies in the very early universe
• Linearized propagation equations for metric fluctuations in a general (non-vacuum) background geometry
• Viscous attenuation of gravitational waves propagating through an inhomogeneous background
• Gravitational Wave emission in Binary Neutron Star early post-merger within a dark environment
• The effect of redshift degeneracy and the damping effect of viscous medium on the information extracted from gravitational wave signals