Two-loop power spectrum with full time- and scale-dependence and EFT corrections: impact of massive neutrinos and going beyond EdS

We compute the density and velocity power spectra at next-to-next-to-leading order taking into account the effect of time- and scale-dependent growth of massive neutrino perturbations as well as the departure from Einstein-de-Sitter (EdS) dynamics at late times non-linearly. We determine the impact of these effects by comparing to the commonly adopted approximate treatment where they are not included. For the bare cold dark matter (CDM)+baryon spectrum, we find percent deviations for k greater than or similar to 0.17h Mpc(-1), mainly due to the departure from EdS. For the velocity and cross power spectrum the main difference arises due to time- and scale-dependence in presence of massive neutrinos yielding percent deviation above k similar or equal to 0.08, 0.13,0.16h Mpc(-1) for Sigma m(v) = 0.4,0.2,0.1 eV, respectively. We use an effective field theory (EFT) framework at two-loop valid for wavenumbers k >> k(FS), where kFs is the neutrino free-streaming scale. Comparing to Quijote N-body simulations, we find that for the CDM+baryon density power spectrum the effect of neutrino perturbations and exact time-dependent dynamics at late times can be accounted for by a shift in the one-loop EFT counterterm, Delta((gamma) over bar1) similar or equal to -0.2 Mpc(2)/h(2). We find percent agreement between the perturbative and N-body results up to k less than or similar to 0.12h Mpc(-1) and k less than or similar to 0.16h Mpc(-1) at one- and two-loop order, respectively, for all considered neutrino masses Sigma m(v) <= 0.4 eV.

Automated summary

In this study, we computed the density and velocity power spectra, taking into account the effect of time- and scale-dependent growth of massive neutrino perturbations as well as the departure from Einstein-de-Sitter dynamics. We found significant deviations from the commonly adopted approximate treatment, highlighting the importance of including these effects in the analysis.