Cosmological evolution of warm dark matter fluctuations I: Efficient computational framework with Volterra integral equations

Abstract

We study the complete cosmological evolution of dark matter (DM) density fluctuations for DM particles that decoupled being ultrarelativistic during the radiation dominated era which is the case of keV scale warm DM (WDM). The new framework presented here can be applied to other types of DM and in particular we extend it to cold DM (CDM). The collisionless and linearized Boltzmann-Vlasov equations (B-V) for WDM and neutrinos in the presence of photons and coupled to the linearized Einstein equations are studied in detail in the presence of anisotropic stress with the Newtonian potential generically different from the spatial curvature perturbations. We recast this full system of B-V equations for DM and neutrinos into a system of coupled Volterra integral equations. These Volterra-type equations are valid both in the radiation dominated (RD) and matter dominated (MD) eras during which the WDM particles are ultrarelativistic and then nonrelativistic. This generalizes the so-called Gilbert integral equation only valid for nonrelativistic particles in the MD era. We succeed to reduce the system of four Volterra integral equations for the density and anisotropic stress fluctuations of DM and neutrinos into a system of only two coupled Volterra equations. The kernels and inhomogeneities in these equations are explicitly given functions. Combining the Boltzmann-Vlasov equations and the linearized Einstein equations constrain the initial conditions on the distribution functions and gravitational potentials. In the absence of neutrinos the anisotropic stress vanishes and the Volterra-type equations reduce to a single integral equation. These Volterra integral equations provide a useful and precise framework to compute the primordial WDM fluctuations over a wide range of scales including small scales up to k ~ 1/5 kpc.

26 pages, 1 figure. To appear in Phys Rev D

References in corpus (18)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Sterile neutrinos, dark matter, and the pulsar velocities in models with a Higgs singlet
• Dark-matter sterile neutrinos in models with a gauge singlet in the Higgs sector
• Opening a new window for warm dark matter
• The velocity function in the local environment from LCDM and LWDM constrained simulations
• Relic keV sterile neutrinos and reionization
• Constraints on dark matter particles from theory, galaxy observations and N-body simulations
• Imprints of Relic Gravitational Waves in Cosmic Microwave Background Radiation
• Searching for dark matter in X-rays: how not to check the dark matter origin of a spectral feature
• Soft L_e-L_mu-L_tau flavour symmetry breaking and sterile neutrino keV Dark Matter
• Supernova bound on keV-mass sterile neutrinos reexamined
• Small-scale structure formation properties of chilled sterile neutrinos as dark matter
• Small scale aspects of warm dark matter : power spectra and acoustic oscillations
• Constraining warm dark matter with cosmic shear power spectra
• The dark matter transfer function: free streaming, particle statistics and memory of gravitational clustering
• Cosmological evolution of warm dark matter fluctuations II: Solution from small to large scales and keV sterile neutrinos
• A No-Truncation Approach to Cosmic Microwave Background Anisotropies
• Probing the Warm Dark Matter with High-z Quasar Luminosity Function

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• Warm dark matter primordial spectra and the onset of structure formation at redshift z
• Constraining the Warm Dark Matter Particle Mass through Ultra-Deep UV Luminosity Functions at z=2
• Cosmological evolution of warm dark matter fluctuations II: Solution from small to large scales and keV sterile neutrinos
• Snowmass-2013 Cosmic Frontier 3 (CF3) Working Group Summary: Non-WIMP dark matter
• Boltzmann hierarchies for self-interacting warm dark matter scenarios
• Impact of a Warm Dark Matter late-time velocity dispersion on large-scale structures
• Hollow cores in Warm Dark Matter halos from the Vlasov-Poisson equation
• Differentiating Warm Dark Matter Models through 21cm Line Intensity Mapping: A Convolutional Neural Network Approach
• Warm Dark Matter from Higher-Dimensional Gauge Theories
• Warm dark matter sterile neutrinos in electron capture and beta decay spectra
• Analytical warm dark matter power spectrum on small scales
• Cosmological Perturbations Engendered by Discrete Relativistic Species