Reproducing neutrino effects on the matter power spectrum through a degenerate Fermi gas approach

TL;DR

This paper analytically investigates how a degenerate Fermi gas influences the matter power spectrum in cosmology, providing insights into its effects during different cosmic eras and comparing with neutrino contributions.

Contribution

It introduces an analytical framework for modeling a degenerate Fermi gas's impact on the matter power spectrum across various cosmological epochs, extending previous neutrino-based analyses.

Findings

Analytical expressions for density fluctuations and velocity divergence of DFG.

Quantified deviations from standard $\\Lambda$CDM predictions due to DFG.

Comparison with neutrino effects in matter power spectrum calculations.

Abstract

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.