Structure formation from non-Gaussian initial conditions: Multivariate biasing, statistics, and comparison with N -body simulations

摘要: We study structure formation in the presence of primordial non-Gaussianity local type with parameters ${f}_{\mathrm{NL}}$ and ${g}_{\mathrm{NL}}$. show that distribution dark-matter halos is naturally described by a multivariate bias scheme where halo overdensity depends not only on underlying matter density fluctuation $\ensuremath{\delta}$ but also Gaussian part gravitational potential $\ensuremath{\varphi}$. This corresponds to non-local terms only. derive coefficients expansion as function mass applying peak-background split common parametrizations for non-Gaussian scenario. then compute power spectrum halo-matter cross framework Eulerian perturbation theory up third order. Comparing our results against $N$-body simulations, we find model accurately describes numerical data wave numbers $k\ensuremath{\le}0.1\char21{}0.3h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$ depending redshift mass. In approach, perturbations counts trace $\ensuremath{\varphi}$ large scales, this explains why spectra different asymptotic trends $k\ensuremath{\rightarrow}0$. strongly scale-dependent originates from at leading order expansion. what happens using standard univariate come badly behaved higher-order corrections. On other hand, biasing reduces usual smaller $|\ensuremath{\varphi}|$ typically much than perturbations. finally discuss bispectrum context that, due its strong scale shape dependence, it powerful tool detection future galaxy surveys.