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 ≲ 1 h/Mpc (where the
simulation mass resolution provides ∼ 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 ∼ 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–wa
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 ΛCDM 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%.