Massive neutrinos in cosmology: Analytic solutions and fluid approximation

Journal Article · Tue Jun 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.123516· OSTI ID:21408050

Shoji, Masatoshi; Komatsu, Eiichiro ^[1]

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1. Texas Cosmology Center and Department of Astronomy, University of Texas at Austin, 1 University Station, C1400, Austin, Texas, 78712 (United States)

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 l{sub max}=1 and 2, and compare the resulting density contrast of neutrinos {delta}{sub {nu}}{sup 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 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 m{sub {nu}>}0.05 eV at the scale of k < or approx. 1.0h Mpc{sup -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.

• OSTI ID: 21408050
• Journal Information: Physical Review. D, Particles Fields, Vol. 81, Issue 12; Other Information: DOI: 10.1103/PhysRevD.81.123516; (c) 2010 The American Physical Society; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
ANALYTICAL SOLUTION
ANISOTROPY
APPROXIMATIONS
BOLTZMANN EQUATION
BOLTZMANN-VLASOV EQUATION
COMPARATIVE EVALUATIONS
COSMOLOGY
DE SITTER SPACE
DENSITY
EXACT SOLUTIONS
FLUCTUATIONS
FLUIDS
NEUTRINO OSCILLATION
NEUTRINOS
RED SHIFT
UNIVERSE
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
ELEMENTARY PARTICLES
EQUATIONS
EVALUATION
FERMIONS
INTEGRO-DIFFERENTIAL EQUATIONS
KINETIC EQUATIONS
LEPTONS
MASSLESS PARTICLES
MATHEMATICAL SOLUTIONS
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
SPACE
VARIATIONS