3\%-accurate predictions for the clustering of dark matter, haloes and subhaloes, over a wide range of cosmologies and scales

Predicting the spatial distribution of objects as a function of cosmology is an essential ingredient for the exploitation of future galaxy surveys. In this paper we show that a specially-designed suite of gravity-only simulations together with cosmology-rescaling algorithms can provide the clustering of dark matter, haloes, and subhaloes with high precision. Specifically, with only 3 $N$-body simulations we obtain the power spectrum of dark matter at $z=0$ and $z=1$ to better than 3\% precision for essentially all currently viable values of 8 cosmological parameters, including massive neutrinos and dynamical dark energy, and over the whole range of scales explored, 0.03 < $k/h^{-1}Mpc$ < 5. This precision holds at the same level for mass-selected haloes and for subhaloes selected according to their peak maximum circular velocity. As an initial application of these predictions, we successfully constrain $\Omega_{\rm m}$, $\sigma_8$, and the scatter in subhalo-abundance-matching employing the projected correlation function of mock SDSS galaxies.