Massive Fermi gas in the expanding universe
Abstract
The behavior of a decoupled ideal Fermi gas in a homogeneously expanding threedimensional 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 nondegenerate gas can only be described by an effective temperature if there are strong enough selfinteractions such as to maintain an equilibrium distribution. Assuming perpetual equilibration, we study a decoupled gas which is relativistic at decoupling and then is redshifted until it becomes nonrelativistic. 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 FermiDirac integral, which is for our purpose superior to the wellknown 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 nonthermal cosmicmore »
 Authors:
 Bethe Center for Theoretical Physics and Physikalisches Institut der Universität Bonn, Nussallee 12, 53115 Bonn (Germany)
 Publication Date:
 OSTI Identifier:
 22679983
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 03; Other Information: Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COMPARATIVE EVALUATIONS; COSMIC NEUTRINOS; DECOUPLING; DENSITY; DISTRIBUTION; EQUILIBRIUM; EXPANSION; FERMI GAS; INTERACTIONS; PHASE SPACE; RED SHIFT; RELATIVISTIC RANGE; SPECTRA; THREEDIMENSIONAL CALCULATIONS; UNIVERSE; VELOCITY
Citation Formats
Trautner, Andreas, Email: atrautner@unibonn.de. Massive Fermi gas in the expanding universe. United States: N. p., 2017.
Web. doi:10.1088/14757516/2017/03/019.
Trautner, Andreas, Email: atrautner@unibonn.de. Massive Fermi gas in the expanding universe. United States. doi:10.1088/14757516/2017/03/019.
Trautner, Andreas, Email: atrautner@unibonn.de. Wed .
"Massive Fermi gas in the expanding universe". United States.
doi:10.1088/14757516/2017/03/019.
@article{osti_22679983,
title = {Massive Fermi gas in the expanding universe},
author = {Trautner, Andreas, Email: atrautner@unibonn.de},
abstractNote = {The behavior of a decoupled ideal Fermi gas in a homogeneously expanding threedimensional 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 nondegenerate gas can only be described by an effective temperature if there are strong enough selfinteractions such as to maintain an equilibrium distribution. Assuming perpetual equilibration, we study a decoupled gas which is relativistic at decoupling and then is redshifted until it becomes nonrelativistic. 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 FermiDirac integral, which is for our purpose superior to the wellknown 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 nonthermal cosmic neutrino background.},
doi = {10.1088/14757516/2017/03/019},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 03,
volume = 2017,
place = {United States},
year = {Wed Mar 01 00:00:00 EST 2017},
month = {Wed Mar 01 00:00:00 EST 2017}
}

Recent highredshift surveys for 21 cm absorption in damped Ly{alpha} absorption systems (DLAs) take the number of published searches at z{sub abs} > 2 to 25, the same number as at z{sub abs} < 2, although the detection rate at high redshift remains significantly lower (20% compared to 60%). Using the known properties of the DLAs to estimate the unknown profile widths of the 21 cm nondetections and including the limits via a survival analysis, we show that the mean spin temperature/covering factor degeneracy at high redshift is, on average, double that of the lowredshift sample. This value is significantlymore »

Pair Correlations of an Expanding Superfluid Fermi Gas
The pair correlation function of an expanding gas is investigated with an emphasis on the BECBCS crossover of a superfluid Fermi gas at zero temperature. At unitarity quantum Monte Carlo simulations reveal the occurrence of a sizable bunching effect due to interactions in the spin updown channel which, at short distances, is larger than that exhibited by thermal bosons in the HanburyBrownTwiss effect. We propose a local equilibrium ansatz for the pair correlation function which we predict will remain isotropic during the expansion even if the trapping potential is anisotropic, in contrast with the behavior of the density. The isotropymore » 
Inflation of the early cold Universe filled with a nonlinear scalar field and a nonideal relativistic Fermi gas
We consider a possible scenario for the evolution of the early cold Universe born from a fairly large quantum fluctuation in a vacuum with a size a{sub 0} ≫ l{sub P} (where l{sub P} is the Planck length) and filled with both a nonlinear scalar field φ, whose potential energy density U(φ) determines the vacuum energy density λ, and a nonideal Fermi gas with shortrange repulsion between particles, whose equation of state is characterized by the ratio of pressure P(n{sub F}) to energy density ε(n{sub F}) dependent on the number density of fermions n{sub F}. As the early Universe expands,more » 
Deviation of an expanding Universe which on the average is isotropic, from the Friedman Universe (in Russian)
Expansion of a Universe, which on the average is isotropic, is considered at the stage of applicability of the equation of state p = epsilon /3. A highfrequency expansion of the Einstein equations is carried out under the assumption that the characteristic wavelengths of the metric deviations from an isotropic one are much smaller than the radius of curvature. Averaging of the equations derived over large scales yields the deviation of the Universe expansion from the isotropic Friedman solution which is due to the inverse effect of highfrequency metric perturbations. The dependence of the metric penturbation amplitudes for the highfrequencymore » 
Life, the Universe, and Nothing: Life and Death in an Everexpanding Universe
Current evidence suggests that the cosmological constant is not zero, or that we live in an open universe. We examine the implications for the future under these assumptions, and find that they are striking. If the universe is cosmological constantdominated, our ability to probe the evolution of largescale structure will decrease with time; presently observable distant sources will disappear on a timescale comparable to the period of stellar burning. Moreover, while the universe might expand forever, the integrated conscious lifetime of any civilization will be finite, although it can be astronomically long. We argue that this latter result is farmore »