Describing massive neutrinos in cosmology as a collection of independent flows

A new analytical approach allowing to account for massive neutrinos in the non-linear description of the growth of the large-scale structure of the universe is proposed. Unlike the standard approach in which neutrinos are described as a unique hot fluid, it is shown that the overall neutrino fluid can be equivalently decomposed into a collection of independent flows. Starting either from elementary conservation equations or from the evolution equation of the phase-space distribution function and assuming that there is no shell-crossing, we derive the two non-linear motion equations that each of these flows satisfies. Those fluid equations describe the evolution of macroscopic fields. We explain in detail the connection between the collection of flows we defined and the standard massive neutrino fluid. Then, in the particular case of adiabatic initial conditions, we explicitly check that, at linear order, the resolution of this new system of equations reproduces the results obtained in the standard approach based on the collisionless Boltzmann hierarchy. Besides, the approach advocated in this paper allows to show how each neutrino flow settles into the cold dark matter flow depending on initial velocities. Although valid up to shell-crossing only, it is a further step towards a fully non-linear treatment of the dynamical evolution of neutrinos in the framework of large-scale structure growth.