Massive neutrinos in cosmology: Analytic solutions and fluid approximation

Details Massive neutrinos in cosmology: Analytic solutions and fluid approximation Massive neutrinos in cosmology: Analytic solutions and fluid approximation

Jun 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010phrvd..81l3516s&link_type=abstract

Physical Review D, vol. 81, Issue 12, id. 123516

Physics

5

Superclusters, Large-Scale Structure Of The Universe, Background Radiations, Particle-Theory And Field-Theory Models Of The Early Universe

Scientific paper

We study the evolution of linear density fluctuations of free-streaming massive neutrinos at redshift of z<1000, with an explicit justification on the use of a fluid approximation. We solve the collisionless Boltzmann equation in an Einstein de-Sitter (EdS) universe, truncating the Boltzmann hierarchy at lmax⁡=1 and 2, and compare the resulting density contrast of neutrinos δνfluid with that of the exact solutions of the Boltzmann equation that we derive in this paper. Roughly speaking, the fluid approximation is accurate if neutrinos were already nonrelativistic when the neutrino density fluctuation of a given wave number entered the horizon. We find that the fluid approximation is accurate at subpercent levels for massive neutrinos with mν>0.05eV at the scale of k≲1.0hMpc-1 and redshift of z<100. This result validates the use of the fluid approximation, at least for the most massive species of neutrinos suggested by the neutrino oscillation experiments. We also find that the density contrast calculated from fluid equations (i.e., continuity and Euler equations) becomes a better approximation at a lower redshift, and the accuracy can be further improved by including an anisotropic stress term in the Euler equation. The anisotropic stress term effectively increases the pressure term by a factor of 9/5.

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