Abstract
We revisit the case of fast Monte Carlo simulations of galaxy positions for a non-Gaussian field. More precisely, we address the question of generating a 3D field with a given one-point function (e.g. log-normal) and some power spectrum fixed by cosmology. We highlight and investigate a problem that occurs in the log-normal case when the field is filtered, and we identify a regime where this approximation still holds. However, we show that the filtering is unnecessary if aliasing effects are taken into account and the discrete sampling step is carefully controlled. In this way we demonstrate a sub-percent precision of all our spectra up to the Nyquist frequency. We extend the method to generate a full light cone evolution, comparing two methods for this process, and validate our method with a tomographic analysis. We analytically and numerically investigate the structure of the covariance matrices obtained with such simulations which may be useful for future large and deep surveys.
Highlights
Fast Monte Carlo methods are essential tools to design analyses over large datasets
We first pointed out the current main mathematical issue arising when we want to generate a density field with a cut-off scale by filtering its power spectrum
We demonstrated that the power spectrum of the Gaussian field that will eventually be transformed into a non-Gaussian is likely to be undefined on some bandwidth
Summary
Fast Monte Carlo methods are essential tools to design analyses over large datasets. Widely used in the cosmic microwave background (CMB) community, thanks to the high-quality Healpix software (Górski et al 2005), they are less frequently used in galactic surveys where analyses often rely on mock catalogues following a complicated and heavy process chain. A more physical description may be preferred, like the one based on a large deviation principle and spherical infall model (Uhlemann et al 2016) that provides a fully deterministic formula for the probability distribution function (PDF) in the mildly non-linear regime (Codis et al 2016) Boltzmann codes such as CLASS (Blas et al 2011), by numerically solving the perturbation equations in the linear regime and adding some contributions describing small scales, predict the matter power spectrum for a given cosmology. For any field, this quantity is always defined as the Fourier transform of the auto-correlation function. Throughout the paper we target a sub-percent precision of all our spectra up to the Nyquist frequency
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