On the road to percent accuracy III: non-linear reaction of the matter power spectrum to massive neutrinos

We analytically model the non-linear effects induced by massive neutrinos on the total matter power spectrum using the halo model reaction framework of Cataneo et al. 2019. In this approach the halo model is used to determine the relative change to the matter power spectrum caused by new physics beyond the concordance cosmology. Using standard fitting functions for the halo abundance and the halo mass-concentration relation, the total matter power spectrum in the presence of massive neutrinos is predicted to percent-level accuracy, out to $k=10 \, h \, {\rm Mpc}^{-1}$. We find that refining the prescriptions for the halo properties using $N$-body simulations improves the recovered accuracy to better than 1%. This paper serves as another demonstration for how the halo model reaction framework, in combination with a single suite of standard $\Lambda$CDM simulations, can recover percent-level accurate predictions for beyond-$\Lambda$CDM matter power spectra, well into the non-linear regime.