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Register a new userHalo mass function and scale-dependent bias from N-body simulations with non-Gaussian initial conditions
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Annalisa Pillepich
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We perform a series of high-resolution N-body simulations of cosmological structure formation starting from Gaussian and non-Gaussian initial conditions. We adopt the best-fitting cosmological parameters of WMAP (3rd- and 5th-year) and we consider non-Gaussianity of the local type parameterised by 8 different values of the non-linearity parameter F_NL. Building upon previous work based on the Gaussian case, we show that, expressed in terms of suitable variables, the mass function of friends-of-friends haloes is approximately universal (i.e. independent of redshift, cosmology, and matter transfer function) to good precision (nearly 10 per cent) also in non-Gaussian scenarios. We provide fitting formulae for the high-mass end (M>10^13 M_sol/h) of the universal mass function in terms of F_NL, and we also present a non-universal fit in terms of both F_NL and z to be used for applications requiring higher accuracy. In the Gaussian case, we extend our fit to a wider range of halo masses (M>2.4 x 10^10 M_sol/h) and we also provide a consistent fit of the linear halo bias. We show that, for realistic values of F_NL, the matter power-spectrum in non-Gaussian cosmologies departs from the Gaussian one by up to 2 per cent on the scales where the baryonic- oscillation features are imprinted on the 2-point statistics. We confirm the strong k-dependence of the halo bias on large scales (k<0.05 h Mpc^-1) which was already detected in previous studies. However, we find that commonly used parameterisations based on the peak-background split do not provide an accurate description of our simulations which present extra dependencies on the wavenumber, the non-linearity parameter and, possibly, the clustering strength. We provide an accurate fit of the simulation data that can be used as a benchmark for future determinations of F_NL with galaxy surveys.
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The description of the abundance and clustering of halos for non-Gaussian initial conditions has recently received renewed interest, motivated by the forthcoming large galaxy and cluster surveys, which can potentially yield constraints of order unity on the non-Gaussianity parameter f_{NL}. We present tests on N-body simulations of analytical formulae describing the halo abundance and clustering for non-Gaussian initial conditions. We calibrate the analytic non-Gaussian mass function of Matarrese et al.(2000) and LoVerde et al.(2008) and the analytic description of clustering of halos for non-Gaussian initial conditions on N-body simulations. We find excellent agreement between the simulations and the analytic predictions if we make the corrections delta_c --> delta_c X sqrt{q} and delta_c --> delta_c X q where q ~ 0.75, in the density threshold for gravitational collapse and in the non-Gaussian fractional correction to the halo bias, respectively. We discuss the implications of this correction on present and forecasted primordial non-Gaussianity constraints. We confirm that the non-Gaussian halo bias offers a robust and highly competitive test of primordial non-Gaussianity.
In this paper we present the implementation of an efficient formalism for the generation of arbitrary non-Gaussian initial conditions for use in N-body simulations. The methodology involves the use of a separable modal approach for decomposing a primordial bispectrum or trispectrum. This approach allows for the far more efficient generation of the non-Gaussian initial conditions already described in the literature, as well as the generation for the first time of non-separable bispectra and the special class of diagonal-free trispectra. The modal approach also allows for the reconstruction of the spectra from given realisations, a fact which is exploited to provide an accurate consistency check of the simulations.
We study structure formation in the presence of primordial non-Gaussianity of the local type with parameters f_NL and g_NL. We show that the distribution of dark-matter halos is naturally described by a multivariate bias scheme where the halo overdensity depends not only on the underlying matter density fluctuation delta, but also on the Gaussian part of the primordial gravitational potential phi. This corresponds to a non-local bias scheme in terms of delta only. We derive the coefficients of the bias expansion as a function of the halo mass by applying the peak-background split to common parametrizations for the halo mass function in the non-Gaussian scenario. We then compute the halo power spectrum and halo-matter cross spectrum in the framework of Eulerian perturbation theory up to third order. Comparing our results against N-body simulations, we find that our model accurately describes the numerical data for wavenumbers k < 0.1-0.3 h/Mpc depending on redshift and halo mass. In our multivariate approach, perturbations in the halo counts trace phi on large scales and this explains why the halo and matter power spectra show different asymptotic trends for k -> 0. This strongly scale-dependent bias originates from terms at leading order in our expansion. This is different from what happens using the standard univariate local bias where the scale-dependent terms come from badly behaved higher-order corrections. On the other hand, our biasing scheme reduces to the usual local bias on smaller scales where |phi| is typically much smaller than the density perturbations. We finally discuss the halo bispectrum in the context of multivariate biasing and show that, due to its strong scale and shape dependence, it is a powerful tool for the detection of primordial non-Gaussianity from future galaxy surveys.
We perform for the first time N-body simulations of Interacting Dark Energy assuming non-Gaussian initial conditions, with the aim of investigating possible degeneracies of these two theoretically independent phenomena in different observational probes. We focus on the large-scale matter distribution, as well as on the statistical and structural properties of collapsed halos and cosmic voids. On very large scales, we show that it is possible to choose the Interaction and non-Gaussian parameters such that their effects on the halo power spectrum cancel, and the power spectrum is indistinguishable from a $mathrm{Lambda CDM}$ model. On small scales, measurements of the non-linear matter power spectrum, halo-matter bias, halo and subhalo mass function and cosmic void number function validate the degeneracy determined on large scales. However, the internal structural properties of halos and cosmic voids, namely halo concentration-mass relation and void density profile, are very different from those measured in the $mathrm{Lambda CDM}$ model, thereby breaking the degeneracy. In practice, the values of $mathrm{f_{NL}}$ required to cancel the effect of interaction are already ruled by observations. Our results show in principle that the combination of large- and small-scale probes is needed to constrain Interacting Dark Energy and Primordial non-Gaussianity separately.
Initial conditions for (Newtonian) cosmological N-body simulations are usually set by re-scaling the present-day power spectrum obtained from linear (relativistic) Boltzmann codes to the desired initial redshift of the simulation. This back-scaling method can account for the effect of inhomogeneous residual thermal radiation at early times, which is absent in the Newtonian simulations. We analyse this procedure from a fully relativistic perspective, employing the recently-proposed Newtonian motion gauge framework. We find that N-body simulations for LambdaCDM cosmology starting from back-scaled initial conditions can be self-consistently embedded in a relativistic space-time with first-order metric potentials calculated using a linear Boltzmann code. This space-time coincides with a simple N-body gauge for z<50 for all observable modes. Care must be taken, however, when simulating non-standard cosmologies. As an example, we analyse the back-scaling method in a cosmology with decaying dark matter, and show that metric perturbations become large at early times in the back-scaling approach, indicating a breakdown of the perturbative description. We suggest a suitable forwards approach for such cases.
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