A fast particle-mesh simulation of non-linear cosmological structure
  formation with massive neutrinos
  Quasi-N-body simulations, such as FastPM, provide a fast way to simulate
cosmological structure formation, but have yet to adequately include the
effects of massive neutrinos. We present a method to include neutrino particles
in FastPM, enabling computation of the CDM and total matter power spectra to
percent-level accuracy in the non-linear regime. The CDM-neutrino cross-power
can also be computed at a sufficient accuracy to constrain cosmological
observables. To avoid the shot noise that typically plagues neutrino particle
simulations, we employ a quasi-random algorithm to sample the relevant
Fermi-Dirac distribution when setting the initial neutrino thermal velocities.
We additionally develop an effective distribution function to describe a set of
non-degenerate neutrinos as a single particle to speed up non-degenerate
simulations. The simulation is accurate for the full range of physical
interest, $M_\nu \lesssim 0.6$eV, and applicable to redshifts $z\lesssim2$.
Such accuracy can be achieved by initializing particles with the two-fluid
approximation transfer functions (using the REPS package). Convergence can be
reached in $\sim 25$ steps, with a starting redshift of $z=99$. Probing
progressively smaller scales only requires an increase in the number of CDM
particles being simulated, while the number of neutrino particles can remain
fixed at a value less than or similar to the number of CDM particles. In turn,
the percentage increase in runtime-per-step due to neutrino particles is
between $\sim 5-20\%$ for runs with $1024^3$ CDM particles, and decreases as
the number of CDM particles is increased. The code has been made publicly
available, providing an invaluable resource to produce fast predictions for
cosmological surveys and studying reconstruction.
