DEMNUni: comparing nonlinear power spectra prescriptions in the presence of massive neutrinos and dynamical dark energy

We provide an accurate comparison, against large cosmological N-body simulations, of different prescriptions for modelling nonlinear matter power spectra in the presence of massive neutrinos and dynamical dark energy. We test the current most widely used approaches: fitting functions (HALOFIT and HMcode), the halo-model reaction (ReACT) and emulators (baccoemu and EuclidEmulator2). Focussing on redshifts z <= 2 and scales k less than or similar to 1 h/Mpc (where the simulation mass resolution provides similar to 1% accuracy), we find that HMcode and ReACT considerably improve over the HALOFIT prescriptions of Smith and Takahashi (both combined with the Bird correction), with an overall agreement of 2% for all the cosmological scenarios considered. Concerning emulators, we find that, especially at low redshifts, EuclidEmulator2 remarkably agrees with the simulated spectra at. 1% level in scenarios with dynamical dark energy and massless neutrinos, reaching a maximum difference of similar to 2% at z = 2. baccoemu has a similar behaviour as EuclidEmulator2, except for a couple of dark energy models. In cosmologies with massive neutrinos, at z = 0 all the nonlinear prescriptions improve their agreement with respect to the massless neutrino case, except for the Bird and TakaBird models which, however, are not tailored to w(0)-w(a) models. At z > 0 we do not find a similar improvement when including massive neutrinos, probably due to the lower impact of neutrino free-streaming at higher redshifts; rather at z = 2 EuclidEmulator2 exceeds 2% agreement for some dark energy equation of state. When considering ratios between the matter power spectrum computed in a given cosmological model and its Lambda CDM counterpart, all the tested prescriptions agree with simulated data, at sub-percent or percent level, depending on z. Finally, we also test how nonlinear prescriptions compare against simulations when computing cosmic shear and angular galaxy clustering spectra. For the former, we find a 2-3% agreement for HMcode, baccoemu, EuclidEmulator2 and ReACT; for the latter, due to the minimum stellar mass of the simulated galaxies, shot noise highly affects the signal and makes the discrepancies as high as 5%.