# Gravitational Waves in the Presence of Viscosity

## TL;DR

This paper investigates how bulk and shear viscosities in an isotropic cosmic fluid affect gravitational wave propagation, revealing damping effects and parameter-dependent behaviors near the Big Rip and during the early universe.

## Contribution

It provides a general equation for gravitational waves in viscous cosmic fluids and analyzes specific early and late universe scenarios, highlighting damping effects.

## Key findings

- Gravitational waves are damped in viscous media.
- Decay constant equals inverse conformal Hubble parameter.
- Results align with other viscosity-based models.

## 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.