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Massive neutrinos make up a fraction of the dark matter, but due to theirlarge thermal velocities, cluster significantly less than cold dark matter(CDM) on small scales. An accurate theoretical modelling of their effect duringthe non-linear regime of structure formation is required in order to properlyanalyse current and upcoming high-precision large-scale structure data, andconstrain the neutrino mass. Taking advantage of the fact that massiveneutrinos remain linearly clustered up to late times, this paper treats thelinear growth of neutrino overdensities in a non-linear CDM background. Theevolution of the CDM component is obtained via N-body computations. The smoothneutrino component is evaluated from that background by solving the Boltzmannequation linearised with respect to the neutrino overdensity. CDM and neutrinosare simultaneously evolved in time, consistently accounting for their mutualgravitational influence. This method avoids the issue of shot-noise inherent toparticle-based neutrino simulations, and, in contrast with standardFourier-space methods, properly accounts for the non-linear potential wells inwhich the neutrinos evolve. Inside the most massive late-time clusters, wherethe escape velocity is larger than the neutrino thermal velocity, neutrinos canclump non-linearly, causing the method to formally break down. It is shown thatthis does not affect the total matter power spectrum, which can be veryaccurately computed on all relevant scales up to the present time.

An efficient implementation of massive neutrinos in non-linear structure formation simulations