We study the impact of setting initial conditions in numerical simulations using the standard procedure based on the Zel'dovich approximation (ZA). As it is well known from the perturbation theory, ZA initial conditions have incorrect second-and higher-order growth and therefore excite long-lived transients in the evolution of the statistical properties of density and velocity fields. We also study the improvement brought by using more accurate initial conditions based on second-order Lagrangian perturbation theory (2LPT). We show that 2LPT initial conditions reduce transients significantly and thus are much more appropriate for numerical simulations devoted to precision cosmology. Using controlled numerical experiments with ZA and 2LPT initial conditions, we show that simulations started at redshift z i = 49 using the ZA underestimate the power spectrum in the non-linear regime by about 2, 4 and 8 per cent at z = 0, 1, and 3, respectively, whereas the mass function of dark matter haloes is underestimated by 5 per cent at m = 10 15 M h −1 (z = 0) and 10 per cent at m = 2 × 10 14 M h −1 (z = 1). The clustering of haloes is also affected to the few per cent level at z = 0. These systematics effects are typically larger than statistical uncertainties in recent mass function and power spectrum fitting formulae extracted from numerical simulations. At large scales, the measured transients in higher-order correlations can be understood from first principle calculations based on perturbation theory.
The present spatial distribution of galaxies in the Universe is non-Gaussian, with 40% skewness in 50 h −1 Mpc spheres, and remarkably little is known about the information encoded in it about cosmological parameters beyond the power spectrum. In this work we present an attempt to bridge this gap by studying the bispectrum, paying particular attention to a joint analysis with the power spectrum and their combination with CMB data. We address the covariance properties of the power spectrum and bispectrum including the effects of beat coupling that lead to interesting cross-correlations, and discuss how baryon acoustic oscillations break degeneracies. We show that the bispectrum has significant information on cosmological parameters well beyond its power in constraining galaxy bias, and when combined with the power spectrum is more complementary than combining power spectra of different samples of galaxies, since non-Gaussianity provides a somewhat different direction in parameter space. In the framework of flat cosmological models we show that most of the improvement of adding bispectrum information corresponds to parameters related to the amplitude and effective spectral index of perturbations, which can be improved by almost a factor of two. Moreover, we demonstrate that the expected statistical uncertainties in σ8 of a few percent are robust to relaxing the dark energy beyond a cosmological constant.
We study the generation of vorticity and velocity dispersion by orbit crossing using cosmological numerical simulations, and calculate the backreaction of these effects on the evolution of large-scale density and velocity divergence power spectra. We use Delaunay tessellations to define the velocity field, showing that the power spectra of velocity divergence and vorticity measured in this way are unbiased and have better noise properties than for standard interpolation methods that deal with mass weighted velocities. We show that high resolution simulations are required to recover the correct large-scale vorticity power spectrum, while poor resolution can spuriously amplify its amplitude by more than one order of magnitude. We measure the scalar and vector modes of the stress tensor induced by orbit crossing using an adaptive technique, showing that its vector modes lead, when input into the vorticity evolution equation, to the same vorticity power spectrum obtained from the Delaunay method. We incorporate orbit crossing corrections to the evolution of large scale density and velocity fields in perturbation theory by using the measured stress tensor modes. We find that at large scales (k ≃ 0.1 h Mpc −1 ) vector modes have very little effect in the density power spectrum, while scalar modes (velocity dispersion) can induce percent level corrections at z = 0, particularly in the velocity divergence power spectrum. In addition, we show that the velocity power spectrum is smaller than predicted by linear theory until well into the nonlinear regime, with little contribution from virial velocities.
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