An acoustic-type metric with a spatially varying velocity field yields an imperfect fluid with zero isotropic density, nonzero anisotropic pressure, and a Yukawa-like potential that leads to rapidly damped geodesics.
Matter Growth in Imperfect Fluid Cosmology
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abstract
Extensions of Einstein's General Relativity (GR) can formally be given a GR structure in which additional geometric degrees of freedom are mapped on an effective energy-momentum tensor. The corresponding effective cosmic medium can then be modeled as an imperfect fluid within GR. The imperfect fluid structure allows us to include, on a phenomenological basis, anisotropic stresses and energy fluxes which are considered as potential signatures for deviations from the cosmological standard $\Lambda$-cold-dark-matter ($\Lambda$CDM) model. As an example, we consider the dynamics of a scalar-tensor extension of the standard model, the $e_{\Phi}\Lambda$CDM model. We constrain the magnitudes of anisotropic pressure and energy flux with the help of redshift-space distortion (RSD) data for the matter growth function $f \sigma_8$.
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Accelerating imperfect fluid
An acoustic-type metric with a spatially varying velocity field yields an imperfect fluid with zero isotropic density, nonzero anisotropic pressure, and a Yukawa-like potential that leads to rapidly damped geodesics.