One simulation to have them all: performance of the Bias Assignment Method against N-body simulations

In this paper, we demonstrate that the information encoded in one single (sufficiently large) N-body simulation can be used to reproduce arbitrary numbers of halo catalogues, using approximated realizations of dark matter density fields with different initial conditions. To this end, we use as a reference one realization (from an ensemble of 300) of the Minerva N-body simulations and the recently published Bias Assignment Method to extract the local and non-local bias linking the halo to the dark matter distribution. We use an approximate (and fast) gravity solver to generate 300 dark matter density fields from the down-sampled initial conditions of the reference simulation and sample each of these fields using the halo-bias and a kernel, both calibrated from the arbitrarily chosen realization of the reference simulation. We show that the power spectrum, its variance, and the three-point statistics are reproduced within similar to 2 per cent (up to k similar to 1.0 h Mpc(-1)), similar to 5 - 10 per cent, and similar to 10 per cent, respectively. Using a model for the real space power spectrum (with three free bias parameters), we show that the covariance matrices obtained from our procedure lead to parameter uncertainties that are compatible within similar to 10 per cent with respect to those derived from the reference covariance matrix, and motivate approaches that can help to reduce these differences to similar to 1 per cent. Our method has the potential to learn from one simulation with moderate volumes and high-mass resolution and extrapolate the information of the bias and the kernel to larger volumes, making it ideal for the construction of mock catalogues for present and forthcoming observational campaigns such as Euclid or DESI.