Evolution of the phase-space density and the Jeans scale for dark matter derived from the Vlasov-Einstein equation

We discuss solutions of Vlasov-Einstein equation for collisionless dark matter particles in the context of a flat Friedman universe. We show that, after decoupling from the pridominal plasma, the dark matter phase-space density indicator Q = [rho]/([sigma] super(2) sub(1D)) super(3/2) remains consta...

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Bibliographic Details
Published in:Journal of cosmology and astroparticle physics 2013-11, Vol.2013 (11), p.I-16, Article 002
Main Authors: Piattella, O F, Rodrigues, D C, Fabris, J C, Pacheco, J A de Freitas
Format: Article
Language:English
Subjects:
ASTROPHYSICS, COSMOLOGY AND ASTRONOMY
Constants
Cosmology
Dark matter
Density
Dispersions
EINSTEIN FIELD EQUATIONS
GEV RANGE 100-1000
Indicators
Mathematical analysis
NONLUMINOUS MATTER
PHASE SPACE
RELATIVISTIC RANGE
UNIVERSE
Wavenumber
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Summary:We discuss solutions of Vlasov-Einstein equation for collisionless dark matter particles in the context of a flat Friedman universe. We show that, after decoupling from the pridominal plasma, the dark matter phase-space density indicator Q = [rho]/([sigma] super(2) sub(1D)) super(3/2) remains constant during the expansion of the universe, prior to structure formation. This well known result is valid for non-relativistic particles and is not "observer dependent" as in solutions derived from the Vlasov-Poisson system. In the linear regime, the inclusion of velocity dispersion effects permits to define a physical Jeans length for collisionless matter as function of the primordial phase-space density indicator: [Lambda] sub(J) = (5[pi]/G) super(1/2)Q super(-1/3)[rho] super(-1/6) sub(dm). The comoving Jeans wavenumber at matter-radiation equality is smaller by a factor of 2-3 than the comoving wavenumber due to free-streaming, contributing to the cut-off of the density fluctuation power spectrum at the lowest scales. We discuss the physical differences between these two scales. For dark matter particles of mass equal to 200 GeV, the derived Jeans mass is 4.3 x 10 super(-6) M in
ISSN:1475-7516
1475-7516
DOI:10.1088/1475-7516/2013/11/002