Slow neutrinos: non-linearity and momentum-space emulation

ABSTRACT Recent cosmological bounds on the sum of neutrino masses, $M_\nu =\sum m_\nu$, are in tension with laboratory oscillation experiments, making cosmological tests of neutrino free-streaming imperative. In order to study the scale-dependent clustering of massive neutrinos, we develop a fast linear response method, fast-$\nu f$, applicable to neutrinos and other non-relativistic hot dark matter. Using it as an accurate linear approximation to help us reduce the dynamic range of emulator training data, based upon a non-linear perturbation theory for massive neutrinos, we improve the emulator’s accuracy at small $M_\nu$ and length scales by a factor of 2. We significantly sharpen its momentum resolution for the slowest neutrinos, which, despite their small mass fraction, dominate small-scale clustering. Furthermore, we extend the emulator from the degenerate to the normal and inverted mass orderings. Applying this new emulator, Cosmic-E$\nu$-II, to large haloes in N-body simulations, we show that non-linear perturbation theory can reproduce the neutrino density profile in the halo outskirts, $2R_{\rm v}\lesssim r \lesssim 10R_{\rm v}$, to better than $10{{\ \rm per\ cent}}$.