Initial Conditions for Accurate N-Body Simulations of Massive Neutrino
  Cosmologies
  The set-up of the initial conditions in cosmological N-body simulations is
usually implemented by rescaling the desired low-redshift linear power spectrum
to the required starting redshift consistently with the Newtonian evolution of
the simulation. The implementation of this practical solution requires more
care in the context of massive neutrino cosmologies, mainly because of the
non-trivial scale-dependence of the linear growth that characterises these
models. In this work we consider a simple two-fluid, Newtonian approximation
for cold dark matter and massive neutrinos perturbations that can reproduce the
cold matter linear evolution predicted by Boltzmann codes such as CAMB or CLASS
with a 0.1% accuracy or below for all redshift relevant to nonlinear structure
formation. We use this description, in the first place, to quantify the
systematic errors induced by several approximations often assumed in numerical
simulations, including the typical set-up of the initial conditions for massive
neutrino cosmologies adopted in previous works. We then take advantage of the
flexibility of this approach to rescale the late-time linear power spectra to
the simulation initial redshift, in order to be as consistent as possible with
the dynamics of the N-body code and the approximations it assumes. We implement
our method in a public code providing the initial displacements and velocities
for cold dark matter and neutrino particles that will allow accurate, i.e.
one-percent level, numerical simulations for this cosmological scenario.
