Generalized Boltzmann hierarchy for massive neutrinos in cosmology

Boltzmann solvers are an important tool for the computation of cosmological observables in linear regime. In presence massive neutrinos, they involve solving equation followed by integration momentum space to arrive at desired fluid properties, a procedure which is known be computationally slow. this work we introduce so-called generalized hierarchy (GBH) neutrinos cosmology, alternative usual hierarchy, where dependence integrated out leaving us with two-parameter infinite set ordinary differential equations. Along expansion multipoles, there now also higher velocity weight integrals distribution function. Using toy code, show that GBH produces density contrast neutrino transfer function $\lesssim 0.5\%$ accuracy both large and intermediate scales compared free-streaming scale, thus providing proof-of-principle GBH. We comment on implementation state art solver.