$\nu\scriptstyle{\rm CO}N{\rm CEPT}$: Cosmological neutrino simulations from the non-linear Boltzmann hierarchy

In this paper the non-linear effect of massive neutrinos on cosmological structures is studied in a conceptually new way. We have solved the non-linear continuity and Euler equations for the neutrinos on a grid in real space in $N$-body simulations, and closed the Boltzmann hierarchy at the non-linear Euler equation using the stress and pressure perturbations from linear theory. By comparing with state-of-the art cosmological neutrino simulations, we are able to simulate the non-linear neutrino power spectrum very accurately. This translates into a negligible error in the matter power spectrum, and so our $\scriptstyle{\rm CO}N{\rm CEPT}$ code is ideally suited for extracting the neutrino mass from future high precision non-linear observational probes such as Euclid.