Abstract
ABSTRACT Cosmology places the strongest current limits on the sum of neutrino masses. Future observations will further improve the sensitivity and this will require accurate cosmological simulations to quantify possible systematic uncertainties and to make predictions for non-linear scales, where much information resides. However, shot noise arising from neutrino thermal motions limits the accuracy of simulations. In this paper, we introduce a new method for simulating large-scale structure formation with neutrinos that accurately resolves the neutrinos down to small scales and significantly reduces the shot noise. The method works by tracking perturbations to the neutrino phase-space distribution with particles and reduces shot noise in the power spectrum by a factor of $\mathcal {O}\left(10^2\right)$ at z = 0 for minimal neutrino masses and significantly more at higher redshifts, without neglecting the back-reaction caused by neutrino clustering. We prove that the method is part of a family of optimal methods that minimize shot noise subject to a maximum deviation from the non-linear solution. Compared to other methods, we find per mille level agreement in the matter power spectrum and per cent level agreement in the large-scale neutrino bias, but large differences in the neutrino component on small scales. A basic version of the method can easily be implemented in existing N-body codes and allows neutrino simulations with significantly reduced particle load. Further gains are possible by constructing background models based on perturbation theory. A major advantage of this technique is that it works well for all masses, enabling a consistent exploration of the full neutrino parameter space.
Highlights
The discovery of neutrino masses (Fukuda et al 1998; Ahmad et al 2002; Eguchi et al 2003) calls for extensions of the standard model of particle physics and provides the only known form of dark matter
We see that the linear theory method does not suffer from shot noise, but fails to reproduce the small-scale behaviour resolved by the particle and δf methods
Shot noise in N-body simulations is a major obstacle to modelling the non-linear evolution of light relic neutrinos
Summary
The discovery of neutrino masses (Fukuda et al 1998; Ahmad et al 2002; Eguchi et al 2003) calls for extensions of the standard model of particle physics and provides the only known form of dark matter. Measuring the masses is crucial for understanding their origin and for constraining cosmological parameters. Cosmology plays a vital role in this programme due to its ability to provide an independent and complementary constraint on the sum of neutrino masses, mν (Bond, Efstathiou & Silk 1980; Hu, Eisenstein & Tegmark 1998) with a potential sensitivity below 0.02 eV (Font-Ribera et al 2014; Chudaykin & Ivanov 2019; Sprenger et al 2019). Ongoing and planned neutrino experiments will establish the mass ordering with a discovery expected by the end of the decade.
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