non-Gaussian Initial Conditions Research Articles

Galaxy bias and primordial non-Gaussianity

We present a systematic study of galaxy biasing in the presence of primordial non-Gaussianity. For a large class of non-Gaussian initial conditions, we define a general bias expansion and prove that it is closed under renormalization, thereby showing that the basis of operators in the expansion is complete. We then study the effects of primordial non-Gaussianity on the statistics of galaxies. We show that the equivalence principle enforces a relation between the scale-dependent bias in the galaxy power spectrum and that in the dipolar part of the bispectrum. This provides a powerful consistency check to confirm the primordial origin of any observed scale-dependent bias. Finally, we also discuss the imprints of anisotropic non-Gaussianity as motivated by recent studies of higher-spin fields during inflation.

Effective theory of large-scale structure with primordial non-Gaussianity

We develop the effective theory of large-scale structure for non-Gaussian initial conditions. The effective stress tensor in the dark matter equations of motion contains new operators, which originate from the squeezed limit of the primordial bispectrum. Parameterizing the squeezed limit by a scaling and an angular dependence, captures large classes of primordial non-Gaussianity. Within this parameterization, we classify the possible contributions to the effective theory. We show explicitly how all terms consistent with the symmetries arise from coarse graining the dark matter equations of motion and its initial conditions. We also demonstrate that the system is closed under renormalization and that the basis of correction terms is therefore complete. The relevant corrections to the matter power spectrum and bispectrum are computed numerically and their relative importance is discussed.

Effect of primordial non-Gaussianities on the far-UV luminosity function of high-redshift galaxies: implications for cosmic reionization

[Abridged] Understanding how the intergalactic medium (IGM) was reionized at z > 6 is one of the big challenges of current high redshift astronomy. It requires modelling the collapse of the first astrophysical objects (Pop III stars, first galaxies) and their interaction with the IGM, while at the same time pushing current observational facilities to their limits. The observational and theoretical progress of the last few years have led to the emergence of a coherent picture in which the budget of hydrogen-ionizing photons is dominated by low-mass star-forming galaxies, with little contribution from Pop III stars and quasars. The reionization history of the Universe therefore critically depends on the number density of low-mass galaxies at high redshift. In this work, we explore how changes in the statistical properties of initial density fluctuations affect the formation of early galaxies. Following Habouzit et al. (2014), we run 5 N-body simulations with Gaussian and (scale-dependent) non-Gaussian initial conditions, all consistent with Planck constraints. By appealing to a galaxy formation model and to a population synthesis code, we compute the far-UV galaxy luminosity function down to M_UV = -14 at redshift 7 < z < 15. We find that models with strong primordial non-Gaussianities on < Mpc scales show a far-UV luminosity function significantly enhanced in low-mass galaxies. We adopt a reionization model calibrated from state-of-the-art hydrodynamical simulations and show that such non-Gaussianities leave a clear imprint on the Universe reionization history and electron Thomson scattering optical depth tau_E. Although current uncertainties in the physics of reionization and on the determination of tau_E still dominate the signatures of non-Gaussianities, our results suggest that tau_E could ultimately be used to constrain the statistical properties of initial density fluctuations.

Testing primordial non-Gaussianities on galactic scales at high redshift

Abstract Primordial non-Gaussianities provide an important test of inflationary models. Although the Planck cosmic microwave background experiment has produced strong limits on non-Gaussianity on scales of clusters, there is still room for considerable non-Gaussianity on galactic scales. We have tested the effect of local non-Gaussianity on the high-redshift galaxy population by running five cosmological N-body simulations down to z = 6.5. For these simulations, we adopt the same initial phases, and either Gaussian or scale-dependent non-Gaussian primordial fluctuations, all consistent with the constraints set by Planck on cluster scales. We then assign stellar masses to each halo using the halo–stellar mass empirical relation of Behroozi et al. Our simulations with non-Gaussian initial conditions produce halo mass functions that show clear departures from those obtained from the analogous simulations with Gaussian initial conditions at z ≳ 10. We observe a &amp;gt;0.3 dex enhancement of the low end of the halo mass function, which leads to a similar effect on the galaxy stellar mass function, which should be testable with future galaxy surveys at z &amp;gt; 10. As cosmic reionization is thought to be driven by dwarf galaxies at high redshift, our findings may have implications for the reionization history of the Universe.

Constraining primordial non-Gaussianity with moments of the large-scale density field

We use cosmological N-body simulations to investigate whether measurements of the moments of large-scale structure can yield constraints on primordial non-Gaussianity. We measure the variance, skewness, and kurtosis of the evolved density field from simulations with Gaussian and three different non-Gaussian initial conditions: a local model with fNL = 100, an equilateral model with fNL = −400, and an orthogonal model with fNL = −400. We show that the moments of the dark matter density field differ significantly between Gaussian and non-Gaussian models. We also make the measurements on mock galaxy catalogues that contain galaxies with clustering properties similar to those of luminous red galaxies. We find that, in the case of skewness and kurtosis, galaxy bias reduces the detectability of non-Gaussianity. However, in the case of the variance, galaxy bias greatly amplifies the detectability of non-Gaussianity. In all cases, we find that redshift distortions do not significantly affect the detectability. When we restrict our measurements to volumes equivalent to the Sloan Digital Sky Survey II or Baryon Oscillation Spectroscopic Survey samples, the probability of detecting a departure from the Gaussian model is high by using measurements of the variance, but very low by using only skewness and kurtosis. We estimate that in order to detect an amount of non-Gaussianity that is consistent with recent cosmic microwave background constraints using skewness or kurtosis, we would need a galaxy survey that is much larger than any planned future survey. However, future surveys should be large enough to place meaningful constraints using galaxy variance measurements.

Higher moments of primordial non-Gaussianity and N-bodysimulations

We perform cosmological N-body simulations with non-Gaussian initial conditions generated from two independent fields. The dominant contribution to the perturbations comes from a purely Gaussian field, but we allow the second field to have local non-Gaussianity that need not be weak. This scenario allows us to adjust the relative importance of non-Gaussian contributions beyond the skewness, producing a scaling of the higher moments different from (and stronger than) the scaling in the usual single field local ansatz. We compare semi-analytic prescriptions for the non-Gaussian mass function, large scale halo bias, and stochastic bias against the simulation results. We discuss applications of this work to large scale structure measurements that can test a wider range of models for the primordial fluctuations than is usually explored.

Large-scale structure non-Gaussianities with modal methods

AbstractRelying on a separable modal expansion of the bispectrum, the implementation of a fast estimator for the full bispectrum of a 3d particle distribution is presented. The computational cost of accurate bispectrum estimation is negligible relative to simulation evolution, so the bispectrum can be used as a standard diagnostic whenever the power spectrum is evaluated. As an application, the time evolution of gravitational and primordial dark matter bispectra was measured in a large suite of N-body simulations. The bispectrum shape changes characteristically when the cosmic web becomes dominated by filaments and halos, therefore providing a quantitative probe of 3d structure formation. Our measured bispectra are determined by ∼ 50 coefficients, which can be used as fitting formulae in the nonlinear regime and for non-Gaussian initial conditions. We also compare the measured bispectra with predictions from the Effective Field Theory of Large Scale Structures (EFTofLSS).

Kinematic consistency relations of large-scale structures

We describe how the kinematic consistency relations satisfied by density correlations of the large-scale structures of the Universe can be derived within the usual Newtonian framework. These relations express a kinematic effect and show how the $(\ell+n)$-density correlation factors in terms of the $n$-point correlation and $\ell$ linear power spectrum factors, in the limit where the $\ell$ soft wave numbers become linear and much smaller than the $n$ other wave numbers. We describe how these relations extend to multifluid cases. In the standard cosmology, these consistency relations derive from the equivalence principle. A detection of their violation would indicate non-Gaussian initial conditions, non-negligible decaying modes, or a modification of gravity that does not converge to General Relativity on large scales.

High-performance P3M N-body code: CUBEP3M

This paper presents CUBEP3M, a publicly-available high performance cosmological N-body code and describes many utilities and extensions that have been added to the standard package. These include a memory-light runtime SO halo finder, a non-Gaussian initial conditions generator, and a system of unique particle identification. CUBEP3M is fast, its accuracy is tuneable to optimize speed or memory, and has been run on more than 27,000 cores, achieving within a factor of two of ideal weak scaling even at this problem size. The code can be run in an extra-lean mode where the peak memory imprint for large runs is as low as 37 bytes per particles, which is almost two times leaner than other widely used N-body codes. However, load imbalances can increase this requirement by a factor of two, such that fast configurations with all the utilities enabled and load imbalances factored in require between 70 and 120 bytes per particles. CUBEP3M is well designed to study large scales cosmological systems, where imbalances are not too large and adaptive time-stepping not essential. It has already been used for a broad number of science applications that require either large samples of non-linear realizations or very large dark matter N-body simulations, including cosmological reionization, halo formation, baryonic acoustic oscillations, weak lensing or non-Gaussian statistics. We discuss the structure, the accuracy, known systematic effects and the scaling performance of the code and its utilities, when applicable.

Fast estimation of gravitational and primordial bispectra in large scale structures

We present the implementation of a fast estimator for the full dark matter bispectrum of a three-dimensional particle distribution relying on a separable modal expansion of the bispectrum. The computational cost of accurate bispectrum estimation is negligible relative to simulation evolution, so the isotropic bispectrum can be used as a standard diagnostic whenever the power spectrum is evaluated. As an application we measure the evolution of gravitational and primordial dark matter bispectra in $N$-body simulations with Gaussian and non-Gaussian initial conditions of the local, equilateral, orthogonal and flattened shape. The results are compared to theoretical models using a 3D visualisation, 3D shape correlations and the cumulative bispectrum signal-to-noise, all of which can be evaluated extremely quickly. Our measured bispectra are determined by $\mathcal{O}(50)$ coefficients, which can be used as fitting formulae in the nonlinear regime and for non-Gaussian initial conditions. In the nonlinear regime with $k<2h\,\mathrm{Mpc}^{-1}$, we find an excellent correlation between the measured dark matter bispectrum and a simple model based on a `constant' bispectrum plus a (nonlinear) tree-level gravitational bispectrum. In the same range for non-Gaussian simulations, we find an excellent correlation between the measured additional bispectrum and a constant model plus a (nonlinear) tree-level primordial bispectrum. We demonstrate that the constant contribution to the non-Gaussian bispectrum can be understood as a time-shift of the constant mode in the gravitational bispectrum, which is motivated by the one-halo model. The final amplitude of this extra non-Gaussian constant contribution is directly related to the initial amplitude of the constant mode in the primordial bispectrum. We also comment on the effects of regular grid and glass initial conditions on the bispectrum.

Non-gaussian mode coupling and the statistical cosmological principle

Local-type primordial non-Gaussianity couples statistics of the curvature perturbation ζ on vastly different physical scales. Because of this coupling, statistics (i.e. the polyspectra) of ζ in our Hubble volume may not be representative of those in the larger universe — that is, they may be biased. The bias depends on the local background value of ζ, which includes contributions from all modes with wavelength k≲H0 and is therefore enhanced if the entire post-inflationary patch is large compared with our Hubble volume. We study the bias to locally-measured statistics for general local-type non-Gaussianity. We consider three examples in detail: (i) the usual fNL, gNL model, (ii) a strongly non-Gaussian model with ζ ∼ ζGp, and (iii) two-field non-Gaussian initial conditions. In each scenario one may generate statistics in a Hubble-size patch that are weakly Gaussian and consistent with observations despite the fact that the statistics in the larger, post-inflationary patch look very different.

Stochastic bias from non-Gaussian initial conditions

In this article, we show that a stochastic form of scale-dependent halo bias arises in multi-source inflationary models, where multiple fields determine the initial curvature perturbation.We derive this effect for general non-Gaussian initial conditions and study various examples, such as curvaton models and quasi-single field inflation. We present a general formula for both the stochastic and the non-stochastic parts of the halo bias, in terms of the N-point cumulants of the curvatureperturbation at the end of inflation. At lowest order, the stochasticity arises if the collapsed limit of the four-point function is boosted relative to the square of the three-point function in the squeezed limit.We derive all our results in two ways, using the barrier crossing formalism and the peak-background split method. In a companion paper [1], we prove that these two approaches are mathematically equivalent.

Revisiting the angular momentum growth of protostructures evolved from non-Gaussian initial conditions

Abstract I adopt a formalism previously developed by Catelan and Theuns (CT) in order to estimate the impact of primordial non-Gaussianity on the quasi-linear spin growth of cold dark matter protostructures. A variety of bispectrum shapes are considered, spanning the currently most popular early Universe models for the occurrence of non-Gaussian density fluctuations. In their original work, CT considered several other shapes, and suggested that only for one of those does the impact of non-Gaussianity seem to be perturbatively tractable. For that model, and on galactic scales, the next-to-linear non-Gaussian contribution to the angular momentum variance has an upper limit of ∼10 per cent with respect to the linear one. I find that all the new models considered in this work can also be seemingly described via perturbation theory. Considering current bounds on fNL for inflationary non-Gaussianity leads to the quasi-linear contribution being ∼10–20 per cent of the linear one. This result motivates the systematic study of higher order non-Gaussian corrections, in order to attain a comprehensive picture of how structure gravitational dynamics descends from the physics of the primordial Universe.

Universal non-Gaussian initial conditions forN-body simulations

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.

Rapid separable analysis of higher order correlators in large-scale structure

We present an efficient separable approach to the estimation and reconstruction of the bispectrum and the trispectrum from observational (or simulated) large scale structure data. This is developed from general CMB (poly-)spectra methods which exploit the fact that the bispectrum and trispectrum in the literature can be represented by a separable mode expansion which converges rapidly (with $n_\textrm{max}={\cal{O}}(30)$ terms). With an effective grid resolution $l_\textrm{max}$ (number of particles/grid points $N=l_\textrm{max}^3$), we present a bispectrum estimator which requires only ${\cal O}(n_\textrm{max} \times l_\textrm{max}^3)$ operations, along with a corresponding method for direct bispectrum reconstruction. This method is extended to the trispectrum revealing an estimator which requires only ${\cal O}(n_\textrm{max}^{4/3} \times l_\textrm{max}^3)$ operations. The complexity in calculating the trispectrum in this method is now involved in the original decomposition and orthogonalisation process which need only be performed once for each model. However, for non-diagonal trispectra these processes present little extra difficulty and may be performed in ${\cal O}(l_\textrm{max}^4)$ operations. A discussion of how the methodology may be applied to the quadspectrum is also given. An efficient algorithm for the generation of arbitrary nonGaussian initial conditions for use in N-body codes using this separable approach is described. This prescription allows for the production of nonGaussian initial conditions for arbitrary bispectra and trispectra. A brief outline of the key issues involved in parameter estimation, particularly in the non-linear regime, is also given.

The halo bispectrum in N-body simulations with non-Gaussian initial conditions

We present measurements of the bispectrum of dark matter halos in numerical simulations with non-Gaussian initial conditions of the local type. We show, in the first place, that the overall effect of primordial non-Gaussianity on the halo bispectrum is larger than on the halo power spectrum when all measurable configurations are taken into account. We then compare our measurements with a tree-level perturbative prediction finding good agreement at large scale when the constant Gaussian bias parameter, both linear and quadratic, and their constant non-Gaussian corrections are fitted for. The best-fit values of the Gaussian bias factors and their non-Gaussian, scale-independent corrections are in qualitative agreement with the peak-background split expectations. In particular, we show that the effect of non-Gaussian initial conditions on squeezed configurations is fairly large (up to 30% for f_NL=100 at redshift z=0.5) and results from contributions of similar amplitude induced by the initial matter bispectrum, scale-dependent bias corrections as well as from nonlinear matter bispectrum corrections. We show, in addition, that effects at second order in f_NL are irrelevant for the range of values allowed by CMB and galaxy power spectrum measurements, at least on the scales probed by our simulations. Finally, we present a Fisher matrix analysis to assess the possibility of constraining primordial non-Gaussianity with future measurements of the galaxy bispectrum. We find that a survey with a volume of about 10 cubic Gpc at mean redshift z ~ 1 could provide an error on f_NL of the order of a few. This shows the relevance of a joint analysis of galaxy power spectrum and bispectrum in future redshift surveys.

Effects and detectability of quasi-single field inflation in the large-scale structure and cosmic microwave background

Quasi-single field inflation predicts a peculiar momentum dependence in the squeezed limit of the primordial bispectrum which smoothly interpolates between the local and equilateral models. This dependence is directly related to the mass of the isocurvatons in the theory which is determined by the supersymmetry. Therefore, in the event of detection of a non-zero primordial bispectrum, additional constraints on the parameter controlling the momentum-dependence in the squeezed limit becomes an important question. We explore the effects of these non-Gaussian initial conditions on large-scale structure and the cosmic microwave background, with particular attention to the galaxy power spectrum at large scales and scale-dependence corrections to galaxy bias. We determine the simultaneous constraints on the two parameters describing the QSF bispectrum that we can expect from upcoming large-scale structure and cosmic microwave background observations. We find that for relatively large values of the non-Gaussian amplitude parameters, but still well within current uncertainties, galaxy power spectrum measurements will be able to distinguish the QSF scenario from the predictions of the local model. A CMB likelihood analysis, as well as Fisher matrix analysis, shows that there is also a range of parameter values for which Planck data may be able distinguish between QSF models and the related local and equilateral shapes. Given the different observational weightings of the CMB and LSS results, degeneracies can be significantly reduced in a joint analysis.

The effect of local non-Gaussianity on the matter bispectrum at small scales

We compute the matter bispectrum in the presence of primordial local non-Gaussianity over a wide range of scales, including the very small nonlinear ones. We use the Halo Model approach, considering non-Gaussian corrections to the halo profiles, the halo mass function and the bias functions. We compare our results in the linear and mildly nonlinear scales to a large ensemble of Gaussian and non-Gaussian numerical simulations. We consider both squeezed and equilateral configurations, at redshift z = 0 and z = 1. For z = 0, the deviations between the Halo Model and the simulations are smaller than 10% in the squeezed limit, both in the Gaussian and non-Gaussian cases. The Halo Model allows to make predictions on scales much smaller than those reached by numerical simulations. For local non-Gaussian initial conditions with a parameter fNL = 100, we find an enhancement of the bispectrum in the squeezed configuration k = k3 = k2 >> k1 ∼ 0.01h−1Mpc, of ∼ 15% and ∼ 25% on scales k ∼ 1h−1Mpc, at z = 0 and z = 1 respectively. This is mainly due to the non-Gaussian corrections in the linear bias. Finally we provide a very simple expression valid for any scenario, i.e. for any choice of the halo profile, mass and bias functions, which allow for a fast evaluation of the bispectrum on squeezed configurations.

Constructing regularized cosmic propagators

We present a new scheme for the general computation of cosmic propagators that allow to interpolate between standard perturbative results at low-k and their expected large-k resummed behavior. This scheme is applicable to any multi-point propagator and allows the matching of perturbative low-k calculations to any number of loops to their large-k behavior, and can potentially be applied in case of non-standard cosmological scenarios such as those with non-Gaussian initial conditions. The validity of our proposal is checked against previous prescriptions and measurements in numerical simulations showing a remarkably good agreement. Such a generic prescription for multi-point propagators provides the necessary building blocks for the computation of polyspectra in the context of the so-called Gamma-expansion introduced by Bernardeau et al. (2008). As a concrete application we present a consistent calculation of the matter bispectrum at one-loop order.

Lagrangian perturbations and the matter bispectrum II: the resummed one-loop correction to the matter bispectrum

This is part two in a series of papers in which we investigate an approach based on Lagrangian perturbation theory (LPT) to study the non-linear evolution of the large-scale structure distribution in the universe.Firstly, we compute the matter bispectrum in real space using LPT up one-loop order, for both Gaussian and non-Gaussian initial conditions. In the initial position limit, we find that the one-loop bispectrum computed in this manner is identical to its counterpartobtained from standard Eulerian perturbation theory (SPT). Furthermore, the LPT formalism allows for a simple reorganisation of the perturbative series corresponding to the resummation of an infinite series of perturbations in SPT. Applying this method, we finda resummed one-loop bispectrum that compares favourably with results from N-body simulations.We generalise the resummation method also to the computation of the redshift-space bispectrum up to one loop.