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, 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. It opens the way to a fully non-linear
treatment of the dynamical evolution of neutrinos in the framework of
large-scale structure growth.
