  Modifications on the predictions about the matter power spectrum based on the
hypothesis of a tiny contribution from a degenerate Fermi gas (DFG) test-fluid
to some dominant cosmological scenario are investigated. Reporting about the
systematic way of accounting for all the cosmological perturbations, through
the Boltzmann equation we obtain the analytical results for density
fluctuation, $\delta$, and fluid velocity divergence, $\theta$, of the DFG.
Small contributions to the matter power spectrum are analytically obtained for
the radiation-dominated background, through an ultra-relativistic
approximation, and for the matter-dominated and $\Lambda$-dominated eras,
through a non-relativistic approximation. The results can be numerically
reproduced and compared with those of considering non-relativistic and
ultra-relativistic neutrinos into the computation of the matter power spectrum.
Lessons concerning the formation of large scale structures of a DFG are
depicted, and consequent deviations from standard $\Lambda$CDM predictions for
the matter power spectrum (with and without neutrinos) are quantified.
