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 ΛCDM 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 GR solution in linear perturbation theory at the per mille level of precision.

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 νconcept code is ideally suited for extracting the neutrino mass from future high precision non-linear observational probes such as EUCLID.

We present a new, updated version of the EuclidEmulator (called EuclidEmulator2), a fast and accurate predictor for the nonlinear correction of the matter power spectrum. 2 per cent-level accurate emulation is now supported in the eight-dimensional parameter space of w0waCDM+∑mν models between redshift z = 0 and z = 3 for spatial scales within the range 0.01 h Mpc−1 ≤ k ≤ 10 h Mpc−1. In order to achieve this level of accuracy, we have had to improve the quality of the underlying N-body simulations used as training data: (i) we use self-consistent linear evolution of non-dark matter species such as massive neutrinos, photons, dark energy and the metric field, (ii) we perform the simulations in the so-called N-body gauge, which allows one to interpret the results in the framework of general relativity, (iii) we run over 250 high-resolution simulations with 30003 particles in boxes of 1(h−1 Gpc)3 volumes based on paired-and-fixed initial conditions and (iv) we provide a resolution correction that can be applied to emulated results as a post-processing step in order to drastically reduce systematic biases on small scales due to residual resolution effects in the simulations. We find that the inclusion of the dynamical dark energy parameter wa significantly increases the complexity and expense of creating the emulator. The high fidelity of EuclidEmulator2 is tested in various comparisons against N-body simulations as well as alternative fast predictors like HALOFIT, HMCode and CosmicEmu. A blind test is successfully performed against the Euclid Flagship v2.0 simulation. Nonlinear correction factors emulated with EuclidEmulator2 are accurate at the level of $1{{\ \rm per\ cent}}$ or better for 0.01 h Mpc−1 ≤ k ≤ 10 h Mpc−1 and z ≤ 3 compared to high-resolution dark matter only simulations. EuclidEmulator2 is publicly available at https://github.com/miknab/EuclidEmulator2.

We present N -body simulations which are fully compatible with general relativity, with dark energy consistently included at both the background and perturbation level. We test our approach for dark energy parameterised as both a fluid, and using the parameterised post-Friedmann (PPF) formalism. In most cases, dark energy is very smooth relative to dark matter so that its leading effect on structure formation is the change to the background expansion rate. This can be easily incorporated into Newtonian N -body simulations by changing the Friedmann equation. However, dark energy perturbations and relativistic corrections can lead to differences relative to Newtonian N -body simulations at the tens of percent level for scales k < (10 −3 -10 −2 ) Mpc −1 , and given the accuracy of upcoming large scale structure surveys such effects must be included. In this paper we will study both effects in detail and highlight the conditions under which they are important. We also show that our N -body simulations exactly reproduce the results of the Boltzmann solver class for all scales which remain linear. arXiv:1904.05210v1 [astro-ph.CO]

We present N -body simulations in which either all, or a fraction of, the cold dark matter decays non-relativistically to a relativistic, non-interacting dark radiation component. All effects from radiation and general relativity are self-consistently included at the level of linear perturbation theory, and our simulation results therefore match those from linear Einstein-Boltzmann codes such as class in the appropriate large-scale limit. We also find that standard, Newtonian N -body simulations adequately describe the non-linear evolution at smaller scales (k 0.1 h/Mpc) in this type of model, provided that the mass of the decaying component is modified correctly, and that the background evolution is correctly treated. That is, for studies of small scales, effects from general relativity and radiation can be safely neglected.