Gravitational Wave luminosity distance in viscous cosmological models

Abstract

We study the so-called Gravitational Wave luminosity distance-redshift relation $d_L^{GW}(z)$ during cosmological eras driven by non-perfect fluids. In particular, we show that the presence of a shear viscosity in the energy momentum tensor turns out to be the most relevant effect. Within this scenario, a constant shear viscosity imprints the gravitational wave propagation through a friction term $\delta (z)$ with a uniquely given redshift dependence. This peculiar evolution predicts a specific shape for the ratio $d_L^{GW}/d_L^{EM}$ which tends to a constant value when the sources are at $z\gtrsim 1$, whereas scales linearly with the shear viscosity at lower redshifts, regardless of the value of ${\Omega }_{m0}$. According to our final discussion, the predicted redshift dependence $\delta (z)$ provided by a shear viscosity could be tested by upcoming surveys of multi-messenger sources against analogous scenarios provided by some widely studied theories of modified gravity.

19 pages, 4 figures. References and clarifications added. Conclusions unchanged. Accepted for publication in JCAP

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