In the next decade, cosmological surveys will have the statistical power to detect the absolute neutrino mass scale. N-body simulations of large-scale structure formation play a central role in interpreting data from such surveys. Yet these simulations are Newtonian in nature. We provide a quantitative study of the limitations to treating neutrinos, implemented as N-body particles, in N-body codes, focusing on the error introduced by neglecting special relativistic effects. Special relativistic effects are potentially important due to the large thermal velocities of neutrino particles in the simulation box. We derive a self-consistent theory of linear perturbations in Newtonian and non-relativistic neutrinos and use this to demonstrate that N-body simulations overestimate the neutrino free-streaming scale, and cause errors in the matter power spectrum that depend on the initial redshift of the simulations. For $z_{i} \lesssim 100$, and neutrino masses within the currently allowed range, this error is $\lesssim 0.5\%$, though represents an up to $\sim 10\%$ correction to the shape of the neutrino-induced suppression to the cold dark matter power spectrum. We argue that the simulations accurately model non-linear clustering of neutrinos so that the error is confined to linear scales.
Including massive neutrinos in $N$-body simulations is a challenging task due to the large thermal velocities of the neutrinos. In particle based codes this leads to problems of shot-noise due to insufficient sampling of the neutrino momentum distribution function. In this paper we investigate the benefits and drawbacks of a scheme first suggested in a paper by Banerjee et al. in which the initial neutrino distribution is symmetrised in momentum space. We confirm that this method reduce shot-noise significantly, but we also find that it generates some spurious power in the neutrino power spect…
We present a new method for generating initial conditions for numerical cosmological simulations in which massive neutrinos are treated as an extra set of N-body (collisionless) particles. It allows us to accurately follow the density field for both Cold Dark Matter (CDM) and neutrinos at both high and low redshifts. At high redshifts, the new method is able to reduce the shot noise in the neutrino power spectrum by a factor of more than $10^7$ compared to previous methods, where the power spectrum was dominated by shot noise at all scales. We find that our new approach also helps to reduce th…
Using $N$-body simulations with massive neutrino density perturbations, we detect the scale-dependent linear halo bias with high significance. This is the first time that this effect is detected in simulations containing neutrino density perturbations on all scales, confirming the same finding from separate universe simulations. The scale dependence is the result of the additional scale in the system, i.e. the massive neutrino free-streaming length, and it persists even if the bias is defined with respect to the cold dark matter plus baryon (instead of total matter) power spectrum. The separat…
Discovering the mass of neutrinos is a principle goal in high energy physics and cosmology. In addition to cosmological measurements based on two-point statistics, the neutrino mass can also be estimated by observations of neutrino wakes resulting from the relative motion between dark matter and neutrinos. Such a detection relies on an accurate reconstruction of the dark matter-neutrino relative velocity which is affected by non-linear structure growth and galaxy bias. We investigate our ability to reconstruct this relative velocity using large N-body simulations where we evolve neutrinos as d…
The set-up of the initial conditions in cosmological N-body simulations is usually implemented by rescaling the desired low-redshift linear power spectrum to the required starting redshift consistently with the Newtonian evolution of the simulation. The implementation of this practical solution requires more care in the context of massive neutrino cosmologies, mainly because of the non-trivial scale-dependence of the linear growth that characterises these models. In this work we consider a simple two-fluid, Newtonian approximation for cold dark matter and massive neutrinos perturbations that c…
We present the results of cosmological simulations of large-scale structure formation with massive neutrinos. The phase-space distribution of the cosmic relic neutrinos is followed, for the first time, by directly integrating the six-dimensional Vlasov-Poisson equations. Our novel approach allows us to represent free streaming and clustering of neutrinos, and their gravitational interaction with cold dark matter accurately. We thus obtain solutions for the collisionless dynamics independent of conventional N-body methods. We perform a suite of hybrid N-body/Vlasov simulations with varying the …
Cosmological $N$-body simulations are typically purely run with particles using Newtonian equations of motion. However, such simulations can be made fully consistent with general relativity using a well-defined prescription. Here, we extend the formalism previously developed for $Λ$CDM cosmologies with massless neutrinos to include the effects of massive, but light neutrinos. We have implemented the method in two different $N$-body codes, CONCEPT and PKDGRAV, and demonstrate that they produce consistent results. We furthermore show that we can recover all appropriate limits, including the full…
Some of the dark matter in the Universe is made up of massive neutrinos. Their impact on the formation of large scale structure can be used to determine their absolute mass scale from cosmology, but to this end accurate numerical simulations have to be developed. Due to their relativistic nature, neutrinos pose additional challenges when one tries to include them in N-body simulations that are traditionally based on Newtonian physics. Here we present the first numerical study of massive neutrinos that uses a fully relativistic approach. Our N-body code, gevolution, is based on a weak-field for…
We present a description of cosmic neutrinos as a dispersive fluid. In this approach, the neutrino phase space is reduced to density and velocity fields alongside a scale-dependent sound speed. This sound speed depends on redshift, the initial neutrino phase space density and the cold dark matter gravitational potential. The latter is a new coupling between neutrinos and large scale structure not described by previous fluid approaches. We compute the sound speed in linear theory and find that it asymptotes to constants at small and large scales regardless of the gravitational potential. By com…
We study in detail how neutrino perturbations can be followed in linear theory by using only terms up to $l=2$ in the Boltzmann hierarchy. We provide a new approximation to the third moment and demonstrate that the neutrino power spectrum can be calculated to a precision of better than $\sim$ 5% for masses up to $\sim$ 1 eV. The matter and CMB power spectra can be calculated far more precisely and typically at least a factor of a few better than with existing approximations. We then proceed to study how the neutrino power spectrum can be reliably calculated even in the presence of non-linear g…
We report a Vlasov simulation of cosmic relic neutrinos combined with N-body simulation of cold dark matter in the context of large-scale structure formation in the Universe performed on Fugaku supercomputer. Gravitational dynamics of the neutrinos is followed, for the first time, by directly integrating the Vlasov equation in a six-dimensional phase space. Our largest simulation combines the Vlasov simulation on 400 trillion grids and 330 billion-body calculations in a self-consistent manner, and reproduces accurately the nonlinear dynamics of neutrinos in the Universe. The novel high-order V…
We present a novel method for including the impact of massive neutrinos in cold dark matter N-body simulations. Our approach is compatible with widely employed Newtonian N-body codes and relies on only three simple modifications. First, we use commonly employed backscaling initial conditions, based on the cold dark matter plus baryon power spectrum instead of the total matter power spectrum. Second, the accurate Hubble rate is employed in both the backscaling and the evolution of particles in the N-body code. Finally, we shift the final particle positions in a post-processing step to account f…
The non-trivial phase-space distribution of relic neutrinos is responsible for the erasure of primordial density perturbations on small scales, which is one of the main cosmological signatures of neutrino mass. In this paper, we present a new code, FastDF, for generating 1%-accurate particle realisations of the neutrino phase-space distribution using relativistic perturbation theory. We use the geodesic equation to derive equations of motion for massive particles moving in a weakly perturbed spacetime and integrate particles accordingly. We demonstrate how to combine geodesic-based initial con…
We study the clustering properties of dark matter halos in real- and redshift-space in cosmologies with massless and massive neutrinos through a large set of state-of-the-art N-body simulations. We provide quick and easy-to-use prescriptions for the halo bias on linear and mildly non-linear scales, both in real and redshift space, which are valid also for massive neutrinos cosmologies. Finally we present a halo bias emulator,$\textbf{BE-HaPPY}$, calibrated on the N-body simulations, which is fast enough to be used in the standard Markov Chain Monte Carlo approach to cosmological inference. For…
We present in this work a novel and yet extremely simple method for incorporating the effects of massive neutrinos in cosmological $N$-body simulations. This so-called "SuperEasy linear response" approach is based upon analytical solutions to the collisionless Boltzmann equation in the clustering and free-streaming limits, which are then connected by a rational function interpolation function with cosmology-dependent coefficients given by simple algebraic expressions of the cosmological model parameters. The outcome is a {\it one-line modification} to the gravitational potential that requires …
We investigate the cosmological effects of neutrino lumps in Growing Neutrino Quintessence. The strongly non-linear effects are resolved by means of numerical N-body simulations which include relativistic particles, non-linear scalar field equations and backreaction effects. For the investigated models with a constant coupling between the scalar field and the neutrinos the backreaction effects are so strong that a realistic cosmology is hard to realize. This points towards the necessity of a field dependent coupling in Growing Neutrino Quintessence. In this case realistic models of dynamical D…
We provide a quantitative analysis of the halo model in the context of massive neutrino cosmologies. We discuss all the ingredients necessary to model the non-linear matter and cold dark matter power spectra and compare with the results of N-body simulations that incorporate massive neutrinos. Our neutrino halo model is able to capture the non-linear behavior of matter clustering with a $\sim 20\%$ accuracy up to very non-linear scales of $k=10~h/$Mpc (which would be affected by baryon physics). The largest discrepancies arise in the range $k=0.5-1~h/$Mpc where the 1-halo and 2-halo terms are …
Since the report of the PeV-TeV neutrinos by the IceCube Collaboration, various particle physics models have been proposed to explain the neutrino spectrum by dark matter particles decaying into neutrinos and other Standard Model particles.In such scenarios, simultaneous $γ$-ray emission is commonly expected. Therefore, multi-messenger connections are generally important for the indirect searches of dark matters. The recent development of $γ$-ray astronomy puts stringent constraints on the properties of dark matter, especially by observations with the Fermi $γ$-ray satellite in the last severa…
Future direct observations of the Cosmic Neutrino Background (C$ν$B) have the potential to explore a neutrino lifetime, especially in the region of the age of the universe, $t_0=4.35\times 10^{17}\ {\rm s}$. We forecast constraints on neutrino decay via capture of the C$ν$B on tritium, with emphasis on the PTOLEMY-type experiment. In addition, in some cases of invisible neutrino decay into lighter neutrinos in the Standard Model and invisible particles, we can constrain not only the neutrino lifetime but also the masses of the invisible particles. For this purpose, we also formulate the energy…
We review the impact of massive neutrinos on cosmological observables at the linear order. By means of N-body simulations we investigate the signatures left by neutrinos on the fully non-linear regime. We present the effects induced by massive neutrinos on the matter power spectrum, the halo mass function and on the halo-matter bias in massive neutrino cosmologies. We also investigate the clustering of cosmic neutrinos within galaxy clusters.
Constraining neutrino mass remains an elusive challenge in modern physics. Precision measurements are expected from several upcoming cosmological probes of large-scale structure. Achieving this goal relies on an equal level of precision from theoretical predictions of neutrino clustering. Numerical simulations of the non-linear evolution of cold dark matter and neutrinos play a pivotal role in this process. We incorporate neutrinos into the cosmological N-body code CUBEP3M and discuss the challenges associated with pushing to the extreme scales demanded by the neutrino problem. We highlight co…
The non-zero mass of neutrinos suppresses the growth of cosmic structure on small scales. Since the level of suppression depends on the sum of the masses of the three active neutrino species, the evolution of large-scale structure is a promising tool to constrain the total mass of neutrinos and possibly shed light on the mass hierarchy. In this work, we investigate these effects via a large suite of N-body simulations that include massive neutrinos using an analytic linear-response approximation: the Cosmological Massive Neutrino Simulations (MassiveNuS). The simulations include the effects of…
We present a new N-body code, gevolution, for the evolution of large scale structure in the Universe. Our code is based on a weak field expansion of General Relativity and calculates all six metric degrees of freedom in Poisson gauge. N-body particles are evolved by solving the geodesic equation which we write in terms of a canonical momentum such that it remains valid also for relativistic particles. We validate the code by considering the Schwarzschild solution and, in the Newtonian limit, by comparing with the Newtonian N-body codes Gadget-2 and RAMSES. We then proceed with a simulation of …
