Massive Fermi Gas in the Expanding Universe

Abstract

The behavior of a decoupled ideal Fermi gas in a homogeneously expanding three-dimensional volume is investigated, starting from an equilibrium spectrum. In case the gas is massless and/or completely degenerate, the spectrum of the gas can be described by an effective temperature and/or an effective chemical potential, both of which scale down with the volume expansion. In contrast, the spectrum of a decoupled massive and non-degenerate gas can only be described by an effective temperature if there are strong enough self-interactions such as to maintain an equilibrium distribution. Assuming perpetual equilibration, we study a decoupled gas which is relativistic at decoupling and then is red-shifted until it becomes non-relativistic. We find expressions for the effective temperature and effective chemical potential which allow us to calculate the final spectrum for arbitrary initial conditions. This calculation is enabled by a new expansion of the Fermi-Dirac integral, which is for our purpose superior to the well-known Sommerfeld expansion. We also compute the behavior of the phase space density under expansion and compare it to the case of real temperature and real chemical potential. Using our results for the degenerate case, we also obtain the mean relic velocity of the recently proposed non-thermal cosmic neutrino background.

arXiv comment19 pages, 16 figures; v2:references added, matches published version

References in corpus (30)

• Planck 2015 results. XIII. Cosmological parameters
• Observational evidence for self-interacting cold dark matter
• Cosmological Perturbation Theory in the Synchronous vs. Conformal Newtonian Gauge
• Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges
• The Temperature of the Cosmic Microwave Background
• Massive neutrinos and cosmology
• Relic neutrino decoupling including flavour oscillations
• Neutrinos in cosmology
• The non-gravitational interactions of dark matter in colliding galaxy clusters
• Gravitational clustering of relic neutrinos and implications for their detection
• A ménage à trois of eV-scale sterile neutrinos, cosmology, and structure formation
• Production Regimes for Self-Interacting Dark Matter
• How secret interactions can reconcile sterile neutrinos with cosmology
• Updated constraints on non-standard neutrino interactions from Planck
• Neutrino cosmology and Planck
• Constraining invisible neutrino decays with the cosmic microwave background
• Pseudoscalar - sterile neutrino interactions: reconciling the cosmos with neutrino oscillations
• Cosmology with self-interacting sterile neutrinos and dark matter - A pseudoscalar model
• Small neutrino masses from gravitational $\theta$-term
• Neutrino Clustering in Cold Dark Matter Halos : Implications for Ultra High Energy Cosmic Rays
• Tight bonds between sterile neutrinos and dark matter
• Are cosmological neutrinos free-streaming?
• Neutrino Superfluidity
• Non-thermal cosmic neutrino background
• Annual Modulation of Cosmic Relic Neutrinos
• Neutrino Condensate as Origin of Dark Energy
• Self-Interacting Dark Matter
• Experimental signatures of cosmological neutrino condensation
• Probing nonstandard neutrino cosmology with terrestrial neutrino experiments
• Cosmological Neutrino Condensates

Cited by in corpus (7)

• The Cosmological Evolution of Self-interacting Dark Matter
• Cosmology of strongly interacting fermions in the early universe
• Dark matter self-interactions in the matter power spectrum
• Neutron Stars as a Probe of Cosmic Neutrino Background
• Fermi-Dirac Integrals in Degenerate Regimes: A Novel Asymptotic Expansion
• Numerical treatment of annual modulation of relic neutrinos
• Living on the Fermi Edge: On Baryon Transport and Fermi Condensation