A calculation of the full neutrino phase space in cold + hot dark matter models

This paper presents a general-relativistic N-body technique for evolving the phase space distribution of massive neutrinos in linear perturbation theory. The method provides a much more accurate sampling of the neutrino phase space for the HDM initial conditions of N-body simulations in a cold+hot dark matter universe than previous work. Instead of directly sampling the phase space at the end of the linear era, we first compute the evolution of the metric perturbations by numerically integrating the coupled, linearized Einstein, Boltzmann, and fluid equations for all particle species. We then sample the phase space shortly after neutrino decoupling at redshift z=10⁹ when the distribution is Fermi-Dirac. To follow the trajectory of each neutrino, we subsequently integrate the geodesic equations for each neutrino in the perturbed background spacetime from z=10⁹ to z=13. 55, using the linearized metric found in the previous calculation to eliminate discreteness noise. The positions and momenta resulting from this integration represent a fair sample of the full neutrino phase space and can be used as HDM initial conditions for N-body simulations of nonlinear structure evolution in this model. A total of 21 million neutrino particles are used in a 100 Mpc box, with Omegacdm=0. 65, Omegaₕdm=0. 30, Omegabaryon=0. 05, and Hubble constant H₀=50. We find that correlations develop in the neutrino densities and momenta which are absent when only the zeroth-order Fermi-Dirac distribution is considered.