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Register a new userMatter bispectrum of large-scale structure with Gaussian and non-Gaussian initial conditions: Halo models, perturbation theory, and a three-shape model
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We study the matter bispectrum of large-scale structure by comparing the predictions of different perturbative and phenomenological models with the full three-dimensional bispectrum from $N$-body simulations estimated using modal methods. We show that among the perturbative approaches, effective field theory succeeds in extending the range of validity furthest on intermediate scales, at the cost of free additional parameters. By studying the halo model, we show that although it is satisfactory in the deeply non-linear regime, it predicts a deficit of power on intermediate scales, worsening at redshifts $z>0$. By comparison with the $N$-body bispectrum on those scales, we show that there is a significant squeezed component underestimated in the halo model. On the basis of these results, we propose a new three-shape model, based on the tree-level, squeezed and constant bispectrum shapes we identified in the halo model; after calibration this fits the simulations on all scales and redshifts of interest. We extend this model further to primordial non-Gaussianity of the local and equilateral types by showing that the same shapes can be used to describe the additional non-Gaussian component in the matter bispectrum. This method provides a HALOFIT-like prototype of the bispectrum that could be used to describe and test parameter dependencies and should be relevant for the bispectrum of weak gravitational lensing and wider applications.
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We study the matter bispectrum of the large-scale structure by comparing different perturbative and phenomenological models with measurements from $N$-body simulations obtained with a modal bispectrum estimator. Using shape and amplitude correlators, we directly compare simulated data with theoretical models over the full three-dimensional domain of the bispectrum, for different redshifts and scales. We review and investigate the main perturbative methods in the literature that predict the one-loop bispectrum: standard perturbation theory, effective field theory, resummed Lagrangian and renormalised perturbation theory, calculating the latter also at two loops for some triangle configurations. We find that effective field theory (EFT) succeeds in extending the range of validity furthest into the mildly nonlinear regime, albeit at the price of free extra parameters requiring calibration on simulations. For the more phenomenological halo model, we confirm that despite its validity in the deeply nonlinear regime it has a deficit of power on intermediate scales, which worsens at higher redshifts; this issue is ameliorated, but not solved, by combined halo-perturbative models. We show from simulations that in this transition region there is a strong squeezed bispectrum component that is significantly underestimated in the halo model at earlier redshifts. We thus propose a phenomenological method for alleviating this deficit, which we develop into a simple phenomenological three-shape benchmark model based on the three fundamental shapes we have obtained from studying the halo model. When calibrated on the simulations, this three-shape benchmark model accurately describes the bispectrum on all scales and redshifts considered, providing a prototype bispectrum HALOFIT-like methodology that could be used to describe and test parameter dependencies.
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.
We show here how Renormalized Perturbation Theory (RPT) calculations applied to the quasi-linear growth of the large-scale structure can be carried on in presence of primordial non-Gaussian (PNG) initial conditions. It is explicitly demonstrated that the series reordering scheme proposed in Bernardeau, Crocce and Scoccimarro (2008) is preserved for non-Gaussian initial conditions. This scheme applies to the power spectrum and higher order spectra and is based on a reorganization of the contributing terms into sum of products of multi-point propagators. In case of PNG new contributing terms appear, the importance of which is discussed in the context of current PNG models. The properties of the building blocks of such resummation schemes, the multi-point propagators, are then investigated. It is first remarked that their expressions are left unchanged at one-loop order irrespectively of statistical properties of the initial field. We furthermore show that the high-momemtum limit of each of these propagators can be explicitly computed even for arbitrary initial conditions. They are found to be damped by an exponential cutoff whose expression is directly related to the moment generating function of the one-dimensional displacement field. This extends what had been established for multi-point propagators for Gaussian initial conditions. Numerical forms of the cut-off are shown for the so-called local model of PNG.
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.
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.
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