N-body simulations with generic non-Gaussian initial conditions I: Power Spectrum and halo mass function

TL;DR

The issue of setting up generic non-Gaussian initial conditions for N-body simulations for inflationary-motivated primordial non- Gaussianity where the perturbations in the Bardeen potential are given by a dominant Gaussian part plus a non-GAussian part specified by its bispectrum is addressed.

Abstract

We address the issue of setting up generic non-Gaussian initial conditions for N-body simulations. We consider inflationary-motivated primordial non-Gaussianity where the perturbations in the Bardeen potential are given by a dominant Gaussian part plus a non-Gaussian part specified by its bispectrum. The approach we explore here is suitable for any bispectrum, i.e. it does not have to be of the so-called separable or factorizable form. The procedure of generating a non-Gaussian field with a given bispectrum (and a given power spectrum for the Gaussian component) is not univocal, and care must be taken so that higher-order corrections do not leave a too large signature on the power spectrum. This is so far a limiting factor of our approach. We then run N-body simulations for the most popular inflationary-motivated non-Gaussian shapes. The halo mass function and the non-linear power spectrum agree with theoretical analytical approximations proposed in the literature, even if they were so far developed and tested only for a particular shape (the local one). We plan to make the simulations outputs available to the community via the non-Gaussian simulations comparison project web site http://icc.ub.edu/~liciaverde/NGSCP.html.

Figures (10)

• Figure 1: Variance of the linear density field at $z=0$ as a function of the smoothing radius $R$. The non-linearity parameter is $f_{\rm NL}=100$. The symbols show the variance derived from the 8 different realizations of each type of non-Gaussianity. The lines depict the theoretical predictions. For clarity, the case "local a)" and "local b)" are slightly shifted horizontally. All other symbols and lines fall on top of each other.
• Figure 2: Skewness of the linear density field at $z=0$ for different types of non-Gaussianity with $f_{\rm NL}=100$. Symbols show the skewness of the 8 different realizations. Note that the skewness of the Gaussian field due to the finite volume and grid size is subtracted from the measured skewness of the non-Gaussian field. Lines show the theoretical predictions. Only the orthogonal case has a negative skewness for positive $f_{\rm NL}$. For clarity, the case "local a)" and "local b)" are slightly shifted horizontally.
• Figure 3: Ratio of the power spectra derived from the particle distributions of the non-Gaussian ($f_{\rm NL}=100$) and Gaussian initial conditions. For $k<0.1\,h/{\rm Mpc}$, individual realizations are shown by symbols. The lines depict the arithmetic mean of the realizations. For clarity, the case "local a)" and "local b)" are slightly shifted horizontally.
• Figure 4: Ratio of the power spectrum of local non-Gaussian ($f_{\rm NL}=100$) and Gaussian simulations at $z=1$ (dashed lines) and $z=0$ (solid lines) for different simulation settings (see Tab. \ref{['tab:sims']}). The dashed and solid black lines show the mean ratio derived from the main set of our simulations of type "local c)".
• Figure 5: Fractional difference in the mass function of local non-Gaussian ($f_{\rm NL}=100$) and Gaussian simulations at $z=0.67$ (filled circles) and $z=1.5$ (open squares) for different simulation settings (see text). Error bars represent Poisson errors. The dashed and solid black lines show the average of the fractional difference derived from the main set of our simulations of type "local c)".