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Degenerate Fermi gas perturbations at standard background cosmology

The hypothesis of a tiny fraction of the cosmic inventory evolving cosmologically as a degenerate Fermi gas test fluid at some dominant cosmological background is investigated. Our analytical results allow for performing preliminary computations to the evolution of perturbations for relativistic and non-relativistic test fluids. The density fluctuation, $δ$, the fluid velocity divergence, $θ$, and an explicit expression for the dynamics of the shear stress, $σ$, are obtained for a degenerate Fermi gas in the background regime of radiation. Extensions to the dominance of matter and to the $Λ$CDM cosmological background are also investigated and lessons concerning the formation of large structures of degenerate Fermi gas are depicted.