Cosmological perturbations: non-cold relics without the Boltzmann hierarchy

TL;DR

This paper introduces a new method for cosmological perturbation calculations that replaces traditional Boltzmann hierarchies with integral evaluations, greatly improving computational efficiency especially for massive neutrinos.

Contribution

The authors develop an integral-based formulation of cosmological perturbation theory that simplifies and accelerates calculations involving non-cold relics like neutrinos.

Findings

Significantly faster computation times for neutrino perturbations.

Effective for multiple neutrino mass eigenstates.

Applicable to other non-cold collisionless relics.

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 moreso 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 non-cold collisionless relics.