Fully relativistic treatment of light neutrinos in N-body simulations

Abstract

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.

Fully relativistic treatment of decaying cold dark matter in N-body simulations

“…In the models studied here the separation between small k where GR and radiation effects must be taken into account, and large k where structures are non-linear is almost absent, contrary to e.g. models with massive neutrinos [21] or time-varying dark energy equation of state [27]. However, since Fig.…”

“…The correction potential γ Nb in (2.4) originates in perturbed non-dust components such as relativistic species. We refer the reader to [21] for details on how to compute this quantity. The only difference here is that dark radiation contribute to the total pressure perturbation, total shear and the time derivative of the total background pressure, all of which γ Nb depends upon.…”

“…When writing the equations of motion using a globally defined clock (here τ ), a correction term is needed, which is exactly the origin of the source term in the continuity equation (2.3). We wish to reuse the numerical machinery of [21] where the lapse potential γ lapse is a new general relativistic correction potential, given in N -body gauge as…”

“…We will approach point 2) by solving the full Einstein-Boltzmann equations in linear perturbation theory and subsequently add perturbations from all species which are not dark matter or baryons to the simulation using the prescription outlined in [21]. Point 3) can be treated using the same formalism because the potential governing the correction to the decay rate can be realised in the simulation.…”

“…Point 3) can be treated using the same formalism because the potential governing the correction to the decay rate can be realised in the simulation. Using the formalism from [21] also automatically takes into account general relativistic corrections to the equations of motion of particles in the simulation and the whole framework is thus fully compatible with general relativity.…”