Dark matter transfer function: Free streaming, particle statistics, and memory of gravitational clustering

Journal Article · Mon Sep 15 00:00:00 EDT 2008 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.78.063546· OSTI ID:21250854

Boyanovsky, D ^[1]; Vega, H deJ ^[2]; Sanchez, N G ^[3]

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1. Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 (United States)
2. LPTHE, Laboratoire Associe au CNRS UMR 7589, Universite Pierre et Marie Curie (Paris VI) et Denis Diderot (Paris VII), Tour 24, 5 eme. etage, 4, Place Jussieu, 75252 Paris, Cedex 05 (France)
3. Observatoire de Paris, LERMA, Laboratoire Associe au CNRS UMR 8112, 61, Avenue de l'Observatoire, 75014 Paris (France)

The transfer function T(k) of dark matter (DM) perturbations during matter domination is obtained by solving the linearized collisionless Boltzmann-Vlasov equation. We provide an exact expression for T(k) for arbitrary distribution functions of decoupled particles and initial conditions, which can be systematically expanded in a Fredholm series. An exhaustive numerical study of thermal relics for different initial conditions reveals that the first two terms in the expansion of T(k) provide a remarkably accurate and simple approximation valid on all scales of cosmological relevance for structure formation in the linear regime. The natural scale of suppression is the free-streaming wave vector at matter-radiation equality, k{sub fs}(t{sub eq})=[4{pi}{rho}{sub 0M}/[<V-vector{sup 2}>(1+z{sub eq})]]{sup 1/2}. An important ingredient is a nonlocal kernel determined by the distribution functions of the decoupled particles which describes the memory of the initial conditions and gravitational clustering and yields a correction to the fluid description. This correction is negligible at large scales k<<k{sub fs}(t{sub eq}) but it becomes important at small scales k{>=}k{sub fs}(t{sub eq}). Distribution functions that favor the small momentum region yield longer-range memory kernels and lead to an enhancement of power at small scales k>k{sub fs}(t{sub eq}). Fermi-Dirac and Bose-Einstein statistics lead to long-range memory kernels, with longer-range for bosons, both resulting in enhancement of T(k) at small scales. For DM thermal relics that decoupled while ultrarelativistic we find k{sub fs}(t{sub eq}){approx_equal}0.003(g{sub d}/2){sup 1/3} (m/keV) [kpc]{sup -1}, where g{sub d} is the number of degrees of freedom at decoupling. For WIMPS we obtain k{sub fs}(t{sub eq})=5.88(g{sub d}/2){sup 1/3} (m/100 GeV){sup 1/2} (T{sub d}/10 MeV){sup 1/2} [pc]{sup -1}. For k<<k{sub fs}(t{sub eq}), T(k){approx}1-C[k/k{sub fs}(t{sub eq})]{sup 2} where C=O(1) and independent of statistics for thermal relics. We provide simple and accurate fits for T(k) in a wide range of small scales k>k{sub fs}(t{sub eq}) for thermal relics and different initial conditions. The numerical and analytic results for arbitrary distribution functions and initial conditions allow an assessment of DM candidates through their impact on structure formation.

• OSTI ID: 21250854
• Journal Information: Physical Review. D, Particles Fields, Vol. 78, Issue 6; Other Information: DOI: 10.1103/PhysRevD.78.063546; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
APPROXIMATIONS
BOLTZMANN-VLASOV EQUATION
BOSE-EINSTEIN STATISTICS
BOSONS
CORRECTIONS
DECOUPLING
DEGREES OF FREEDOM
DISTRIBUTION FUNCTIONS
DISTURBANCES
FLUIDS
NONLUMINOUS MATTER
NUMERICAL ANALYSIS
PARTICLES
PERTURBATION THEORY
RELATIVISTIC RANGE
TRANSFER FUNCTIONS