Cosmological perturbations: Noncold relics without the Boltzmann hierarchy

Abstract

We present a formulation of cosmological-perturbation theory where the Boltzmann hierarchies that evolve the neutrino phase-space distributions are replaced by integrals that can be evaluated easily with fast Fourier transforms. The simultaneous evaluation of these integrals combined with the differential equations for the rest of the system (dark matter, photons, baryons) are then solved with an iterative scheme that converges quickly. The formulation is particularly powerful for massive neutrinos, where the effective phase space is three dimensional rather than two dimensional, and even more so for three different neutrino mass eigenstates. Therefore, it has the potential to significantly speed up the computation times of cosmological-perturbation calculations. This approach should also be applicable to models with other noncold collisionless relics.