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

2010-03-04

arxiv.org/abs/1003.0942v3

Phys.Rev.D81:123516,2010; Erratum-ibid.D82:089901,2010

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

18 pages, 7 figures. (v2) with up-dated reference, minor typos corrected. (v3) An error in the normalization on the scale fact

Scientific paper

10.1103/PhysRevD.81.123516 10.11

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, \delta_{\nu}^{fluid}, 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 non-relativistic when the neutrino density fluctuation of a given wavenumber entered the horizon. We find that the fluid approximation is accurate at few to 25% for massive neutrinos with 0.05

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