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.
Modeling the nonlinearity of the halo bispectrum remains a major challenge in modern cosmology, in particular for ongoing and upcoming large-scale structure observations that are performed to study the inflationary physics. The "power spectrum response" offers a solution for bispectrum in the so-called squeezed limit, in which one wavenumber is much smaller than the other two. As a first step, we demonstrate that the halo squeezed-limit bispectrum computed from the second-order standard perturbation theory agrees precisely with the responses of linear halo power spectrum to large-scale density…
We study the halo bispectrum from non-Gaussian initial conditions. Based on a set of large $N$-body simulations starting from initial density fields with local type non-Gaussianity, we find that the halo bispectrum exhibits a strong dependence on the shape and scale of Fourier space triangles near squeezed configurations at large scales. The amplitude of the halo bispectrum roughly scales as $f_nl^2$. The resultant scaling on the triangular shape is consistent with that predicted by Jeong & Komatsu based on perturbation theory. We systematically investigate this dependence with varying redshif…
We study the halo-matter cross bispectrum in the presence of primordial non-Gaussianity of the local type. We restrict ourselves to the squeezed limit, for which the calculation are straightforward, and perform the measurements in the initial conditions of N-body simulations, to mitigate the contamination induced by nonlinear gravitational evolution. Interestingly, the halo-matter cross bispectrum is not trivial even in this simple limit as it is strongly sensitive to the scale-dependence of the quadratic and third-order halo bias. Therefore, it can be used to test biasing prescriptions. We co…
We present an analytic formula for the galaxy bispectrum in redshift space on the basis of the halo approach description with the halo occupation distribution of central galaxies and satellite galaxies. This work is an extension of a previous work on the galaxy power spectrum, which illuminated the significant contribution of satellite galaxies to the higher multipole spectrum through the non-linear redshift space distortions of their random motions. Behaviors of the multipoles of the bispectrum are compared with results of numerical simulations assuming a halo occupation distribution of the L…
The bispectrum vanishes for linear Gaussian fields and is thus a sensitive probe of non-linearities and non-Gaussianities in the cosmic density field. Hence, a detection of the bispectrum in the halo density field would enable tight constraints on non-Gaussian processes in the early Universe and allow inference of the dynamics driving inflation. We present a tree level derivation of the halo bispectrum arising from non-linear clustering, non-linear biasing and primordial non-Gaussianity. A diagrammatic description is developed to provide an intuitive understanding of the contributing terms and…
We derive a formula for the halo/galaxy bispectrum on the basis of the integrated Perturbation Theory (iPT). In addition to the gravity-induced non-Gaussianity, we consider the non-Gaussianity of the primordial curvature perturbations, and investigate in detail the effect of such primordial non-Gaussianity on the large-scale halo/galaxy bispectrum. In iPT, the effects of primordial non-Gaussianity are wholly encapsulated in the linear (primordial) polyspectra, and we systematically calculate the contributions to the large-scale behaviors arising from the three types of primordial bispectrum (l…
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 …
We investigate how much can be learnt about four types of primordial non-Gaussianity (PNG) from small-scale measurements of the halo field. Using the QUIJOTE-PNG simulations, we quantify the information content accessible with measurements of the halo power spectrum monopole and quadrupole, the matter power spectrum, the halo-matter cross spectrum and the halo bispectrum monopole. This analysis is the first to include small, non-linear scales, up to $k_\mathrm{max}=0.5 \mathrm{h/Mpc}$, and to explore whether these scales can break degeneracies with cosmological and nuisance parameters making u…
We investigate various phenomenological schemes for the rapid generation of 3D mock galaxy catalogues with a given power spectrum and bispectrum. We apply the fast bispectrum estimator \MODALLSS{} to these mock galaxy catalogues and compare to $N$-body simulation data analysed with the halo-finder \texttt{ROCKSTAR} (our benchmark data). We propose an assembly bias model for populating parent halos with subhalos by using a joint lognormal-Gaussian probability distribution for the subhalo occupation number and the halo concentration. This prescription enabled us to recover the benchmark power sp…
We use a set of numerical N-body simulations to study the large-scale behavior of the reduced bispectrum of dark matter and compare the results with the second-order perturbation theory and the halo models for different halo mass functions. We find that the second-order perturbation theory (PT2) agrees with the simulations fairly well on large scales of k<0.05 h/Mpc, but it shows a signature of deviation as the scale goes down. Even on the largest scale where the bispectrum can be measured reasonably well in our simulations, the inconsistency between PT2 and the simulations appears for the col…
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 th…
We investigate how unified models should be built to be able to predict the matter-density bispectrum (and power spectrum) from very large to small scales and that are at the same time consistent with perturbation theory at low $k$ and with halo models at high $k$. We use a Lagrangian framework to decompose the bispectrum into "3-halo", "2-halo", and "1-halo" contributions, related to "perturbative" and "non-perturbative" terms. We describe a simple implementation of this approach and present a detailed comparison with numerical simulations. We show that the 1-halo and 2-halo contributions con…
We investigate the effect of equilateral-type primordial trispectrum on the halo/galaxy bispectrum. We consider three types of equilateral primordial trispectra which are generated by quartic operators naturally appeared in the effective field theory of inflation and can be characterized by three non-linearity parameters, $g_{\rm NL} ^{\dotσ^4}$, $g_{\rm NL} ^{\dotσ^2 (\partial σ)^2}$, and $g_{\rm NL} ^{(\partial σ)^4}$. Recently, constraints on these parameters have been investigated from CMB observations by using WMAP9 data. In order to consider the halo/galaxy bispectrum with the equilatera…
The covariance matrix of the matter and halo power spectrum and bispectrum are studied. Using a large suite of simulations, we find that the non-Gaussianity in the covariance is significant already at mildly nonlinear scales. We compute the leading disconnected non-Gaussian correction to the matter bispectrum covariance using perturbation theory, and find that the corrections result in good agreement in the mildly nonlinear regime. The shot noise contribution to the halo power spectrum and bispectrum covariance is computed using the Poisson model, and the model yields decent agreement with sim…
Higher-order clustering statistics, like the galaxy bispectrum, can add complementary cosmological information to what is accessible with two-point statistics, like the power spectrum. While the standard way of measuring the bispectrum involves estimating a bispectrum value in a large number of Fourier triangle bins, the compressed modal bispectrum approximates the bispectrum as a linear combination of basis functions and estimates the expansion coefficients on the chosen basis. In this work, we compare the two estimators by using parallel pipelines to analyze the real-space halo bispectrum me…
The high-mass end of the halo mass function is a sensitive probe of primordial non-Gaussianity (NG). In a recent study [9] we have computed the NG halo mass function in the context of the Excursion Set theory and shown that the primordial NG imprint is coupled to that induced by the non-linear collapse of dark matter halos. We also found an excellent agreement with N-body simulation results. Here, we perform a more accurate computation which accounts for the interval validity of the bispectrum expansion to next-to-leading order and extend the calculation to the case of a non-vanishing primordi…
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 renorm…
Using a full analytical computation of the bispectrum based on the halo model together with the halo occupation number, we derive the bispectrum of the cos- mic infrared background (CIB) anisotropies that trace the clustering of dusty-star- forming galaxies. We focus our analysis on wavelengths in the far-infrared and the sub-millimeter typical of the Planck/HFI and Herschel/SPIRE instruments, 350, 550, 850, and 1380 um. We explore the bispectrum behaviour as a function of several models of evolution of galaxies and show that it is strongly sensitive to that ingredient. Contrary to the power s…
Primordial non-Gaussianity can lead to a scale-dependent bias in the density of collapsed halos relative to the underlying matter density. The galaxy power spectrum already provides constraints on local-type primordial non-Gaussianity complementary those from the cosmic microwave background (CMB), while the bispectrum contains additional shape information and has the potential to outperform CMB constraints in future. We develop the bias model for the halo density contrast in the presence of local-type primordial non-Gaussianity, deriving a bivariate expansion up to second order in terms of the…
We investigate the gravitational effect of large-scale radiation perturbations on small-scale structure formation. In addition to making the growth of matter perturbations scale dependent, the free-streaming of radiation also affects the coupling between structure formation at small and large scales. We study this using Separate Universe N-body simulations to compute the (isotropized) squeezed-limit matter bispectrum and the linear halo bias. Our results show that the scale dependence in the growth of long-wavelength matter perturbations, caused by radiation, translates into these quantities a…
Clustering of large-scale structure provides significant cosmological information through the power spectrum of density perturbations. Additional information can be gained from higher-order statistics like the bispectrum, especially to break the degeneracy between the linear halo bias $b_1$ and the amplitude of fluctuations $σ_8$. We propose new simple, computationally inexpensive bispectrum statistics that are near optimal for the specific applications like bias determination. Corresponding to the Legendre decomposition of nonlinear halo bias and gravitational coupling at second order, these …
We present a phenomenological modification of the standard perturbation theory prediction for the bispectrum in redshift space that allows us to extend the model to mildly non-linear scales over a wide range of redshifts, $z\leq1.5$. We find that we can describe the bispectrum of dark matter particles with $\sim5%$ accuracy for $k_i\lesssim0.10\,h/{\rm Mpc}$ at $z=0$, for $k_i\lesssim0.15\,h/{\rm Mpc}$ at $z=0.5$, for $k_i\lesssim0.17\,h/{\rm Mpc}$ at $z=1.0$ and for $k_i\lesssim0.20\,h/{\rm Mpc}$ at $z=1.5$. We also test that the fitting formula is able to describe with similar accuracy the b…
We compare the efficiency of weak lensing-selected galaxy clusters counts and of the weak lensing bispectrum at capturing non-Gaussian features in the dark matter distribution. We use the halo model to compute the weak lensing power spectrum, the bispectrum and the expected number of detected clusters, and derive constraints on cosmological parameters for a large, low systematic weak lensing survey, by focusing on the $Ω_m$-$σ_8$ plane and on the dark energy equation of state. We separate the power spectrum into the resolved and the unresolved parts of the data, the resolved part being defined…
We measure the halo bispectrum covariance in a large set of N-body simulations and compare it with theoretical expectations. We find a large correlation among (even mildly) squeezed halo bispectrum configurations. A similarly large correlation can be found between squeezed triangles and the long-wavelength halo power spectrum. This shows that the diagonal Gaussian contribution fails to describe, even approximately, the full covariance in these cases. We compare our numerical estimate with a model that includes, in addition to the Gaussian one, only the non-Gaussian terms that are large for squ…
Understanding the relation between underlying matter distribution and biased tracers such as galaxy or dark matter halo is essential to extract cosmological information from ongoing or future galaxy redshift surveys. At sufficiently large scales such as the BAO scale, a standard approach for the bias problem on the basis of the perturbation theory (PT) is to assume the `local bias' model in which the density field of biased tracers is deterministically expanded in terms of matter density field at the same position. The higher-order bias parameters are then determined by combining the power spe…
We study constraints on primordial mode-coupling from the power spectrum, squeezed-limit bispectrum and collapsed trispectrum of matter and halos. We describe these statistics in terms of long-wavelength $2$-point functions involving the matter/halo density and position-dependent power spectrum. This allows us to derive simple, analytic expression for the information content, treating constraints from scale-dependent bias in the halo power spectrum on the same footing as those from higher order statistics. In particular, we include non-Gaussian covariance due to long-short mode-coupling from n…
We study the matter bispectrum of large structure by comparing theoretical models (perturbation theories and halo models) to numerical simulations using shape and amplitude correlators. We show that among the perturbation theories at one loop the effective field theory of large scale structure extends the furthest into the non-linear regime. We analyse the one and two-loop bispectra in the renormalised perturbation theory and we show that there is a significant extension in the range where results are accurate when going to two loops. In the case of the halo model, we show that there are defic…
The relation between the clustering properties of luminous matter in the form of galaxies and the underlying dark matter distribution is of fundamental importance for the interpretation of ongoing and upcoming galaxy surveys. The so called local bias model, where galaxy density is a function of local matter density, is frequently discussed as a means to infer the matter power spectrum or correlation function from the measured galaxy correlation. However, gravitational evolution generates a term quadratic in the tidal tensor and thus non-local in the density field, even if this term is absent i…
We study whether the bias factors of galaxies can be unbiasedly recovered from their power spectra and bispectra. We use a set of numerical N-body simulations and construct large mock galaxy catalogs based upon the semi-analytical model of Croton et al. (2006). We measure the reduced bispectra for galaxies of different luminosity, and determine the linear and first nonlinear bias factors from their bispectra. We find that on large scales down to that of the wavenumber k=0.1h/Mpc, the bias factors b1 and b2 are nearly constant, and b1 obtained with the bispectrum method agrees very well with th…
We study the relation between the halo and matter density fields -- commonly termed bias -- in the LCDM framework. In particular, we examine the local model of biasing at quadratic order in the matter density. This model is characterized by parameters b_1 and b_2. Using an ensemble of N-body simulations, we apply several statistical methods to estimate the parameters. We measure halo and matter fluctuations smoothed on various scales and find that the parameters vary with smoothing scale. We argue that, for real-space measurements, owing to the mixing of wavemodes, no scale can be found for wh…
We investigate the performance of an analytic model of the 3D matter distribution, which combines perturbation theory with halo models, for weak-lensing statistics. We compare our predictions for the weak-lensing convergence power spectrum and bispectrum with numerical simulations and fitting formulas proposed in previous works. We find that this model provides better agreement with simulations than published fitting formulas. This shows that building on systematic and physically motivated models is a promising approach. Moreover, this makes explicit the link between the weak-lensing statistic…
We provide a new fitting formula of the matter bispectrum in the nonlinear regime calibrated by high-resolution cosmological $N$-body simulations of $41$ cold dark matter ($w$CDM, $w=$ constant) models around the Planck 2015 best-fit parameters. As the parameterization in our fitting function is similar to that in Halofit, our fitting is named BiHalofit. The simulation volume is sufficiently large ($> 10 \, {\rm Gpc}^3$) to cover almost all measurable triangle bispectrum configurations in the universe. The function is also calibrated using one-loop perturbation theory at large scales ($k<0.3 \…
Cosmic background neutrinos have a large velocity dispersion, which causes the evolution of long-wavelength density perturbations to depend on scale. This scale-dependent growth leads to the well-known suppression in the linear theory matter power spectrum that is used to probe neutrino mass. In this paper, we study the impact of long-wavelength density perturbations on small-scale structure formation. By performing separate universe simulations where the long-wavelength mode is absorbed into the local expansion, we measure the responses of the cold dark matter (CDM) power spectrum and halo ma…
We present the analysis of the halo bispectrum in redshift-space in terms of its multipoles, monopole, quadrupole and hexadecapole, measured from a large set of simulations. We fit such measurements with a tree-level model in perturbation theory that depends on linear and nonlinear bias parameters as well as on the growth rate $f$ of density fluctuations. The likelihood analysis takes advantage of a very large set of mock catalogs, enabling a robust estimation of the covariance properties for all multipoles. We compare the numerical estimate of the covariance matrix to its Gaussian prediction …
We present the first halo model based description of the Cosmic Infrared Background (CIB) non-Gaussianity (NG) that is fully parametric. To this end, we introduce, for the first time, a diagrammatic method to compute high order polyspectra of the 3D galaxy density field. It allows an easy derivation and visualisation of the different terms of the polyspectrum. We apply this framework to the power spectrum and bispectrum, and we show how to project them on the celestial sphere in the purpose of the application to the CIB angular anisotropies. Furthermore, we show how to take into account the pa…
With the advent of large scale galaxy surveys, constraints on primordial non-Gaussianity (PNG) are expected to reach ${\cal O}(f_\text{NL}) \sim 1$. In order to fully exploit the potential of these future surveys, a deep theoretical understanding of the signatures imprinted by PNG on the large scale structure of the Universe is necessary. In this paper, we explore the effect of a stochastic moving barrier on the amplitude of the non-Gaussian bias induced by local quadratic PNG. We show that, in the peak approach to halo clustering, the amplitude of the non-Gaussian bias will generally differ f…
We present a method to produce mock galaxy catalogues with efficient perturbation theory schemes, which match the number density, power spectra and bispectra in real and in redshift space from N-body simulations. The essential contribution of this work is the way in which we constrain the bias parameters in the PATCHY-code. In addition of aiming at reproducing the two-point statistics, we seek the set of bias parameters, which constrain the univariate halo probability distribution function (PDF) encoding higher-order correlation functions. We demonstrate that halo catalogues based on the same …
Accurate modeling of nonlinearities in the galaxy bispectrum, the Fourier transform of the galaxy three-point correlation function, is essential to fully exploit it as a cosmological probe. In this paper, we present numerical and theoretical challenges in modeling the nonlinear bispectrum. First, we test the robustness of the matter bispectrum measured from N-body simulations using different initial conditions generators. We run a suite of N-body simulations using the Zel'dovich approximation and second-order Lagrangian perturbation theory (2LPT) at different starting redshifts, and find that …
We address the amount of information in the non-Gaussian regime of weak lensing surveys by modelling all relevant covariances of the power spectra and bispectra, using 1000 ray-tracing simulation realizations for a Lambda-CDM model and an analytical halo model. We develop a formalism to describe the covariance matrices of power spectra and bispectra of all triangle configurations. In addition to the known contributions which extend up to six-point correlation functions, we propose a new contribution `the halo sample variance (HSV)' arising from the coupling of the lensing Fourier modes with la…
We perform for the first time a joint analysis of the monopole and quadrupoles for power spectrum, bispectrum and integrated trispectrum (i-trispectrum) from the redshift space matter field in N-body simulations. With a full Markov Chain Monte Carlo exploration of the posterior distribution, we quantify the constraints on cosmological parameters for an object density of $n_\mathrm{p}=5\times10^{-4} (h\,\mathrm{Mpc}^{-1})^{3}$, redshift $z=0.5$, and a covariance corresponding to a survey volume of $V_\mathrm{survey} =25\,(h^{-1}\mathrm{Gpc})^3$, a set up which is representative of forthcoming g…
We study the bispectrum of large-scale structure in the EFTofLSS including corrections up to two-loop. We derive an analytic result for the double-hard limit of the two-loop correction, and show that the UV-sensitivity can be absorbed by the same four EFT operators that renormalize the one-loop bispectrum. For the single-hard region, we employ a simplified treatment, introducing one extra EFT parameter. We compare our results to N-body simulations, and show that going from one- to two-loop extends the wavenumber range with percent-level agreement from $k \simeq 0.08$ to $0.15~h/\mathrm{Mpc}$.
Future large-scale structure surveys will measure three-point statistics with high statistical significance. This will offer significant improvements on our understanding of gravity, provided we can model these statistics accurately. We assess the performance of several schemes for theoretical modelling of the matter bispectrum, including halo-model based approaches and fitting formulae. We compare the model predictions against N-body simulations, considering scales up to $k_{\rm max} = 4 h/{\rm Mpc}$, well into non-linear regime of structure formation. Focusing on the equilateral configuratio…
Dark matter evolution during the process of cosmological structure formation can be described in terms of a one-particle irreducible effective action at a characteristic scale $k_m$ and a loop expansion below this scale, based on the effective propagators and vertices. We calculate the form of the effective vertices and compute the bispectrum of density perturbations within a one-loop approximation. We find that the effective vertices play a subdominant role as compared to the effective viscosity and sound velocity that modify the (inverse) propagators. For the bispectrum we reproduce the resu…
We re-examine a genuine power of weak lensing bispectrum tomography for constraining cosmological parameters, when combined with the power spectrum tomography, based on the Fisher information matrix formalism. To account for the full information at two- and three-point levels, we include all the power spectrum and bispectrum information built from all-available combinations of tomographic redshift bins, multipole bins and different triangle configurations over a range of angular scales (up to lmax=2000 as our fiducial choice). For the parameter forecast, we use the halo model approach in Kayo,…
The main effect of massive neutrinos on the large-scale structure consists in a few percent suppression of matter perturbations on all scales below their free-streaming scale. Such effect is of particular importance as it allows to constraint the value of the sum of neutrino masses from measurements of the galaxy power spectrum. In this work, we present the first measurements of the next higher-order correlation function, the bispectrum, from N-body simulations that include massive neutrinos as particles. This is the simplest statistics characterising the non-Gaussian properties of the matter …
We present measurements of the dark matter bispectrum in N-body simulations with non-Gaussian initial conditions of the local kind for a large variety of triangular configurations and compare them with predictions from Eulerian Perturbation Theory up to one-loop corrections. We find that the effects of primordial non-Gaussianity at large scales, when compared to Perturbation Theory, are well described by the initial component of the matter bispectrum, linearly extrapolated at the redshift of interest. In addition, we find that, for f_NL=100, the nonlinear corrections due to non-Gaussian initia…
Upcoming galaxy redshift surveys promise to significantly improve current limits on primordial non-Gaussianity (PNG) through measurements of 2- and 3-point correlation functions in Fourier space. However, realizing the full potential of this dataset is contingent upon having both accurate theoretical models and optimized analysis methods. Focusing on the local model of PNG, parameterized by $f_{\rm NL}$, we perform a Monte-Carlo Markov Chain analysis to confront perturbation theory predictions of the halo power spectrum and bispectrum in real space against a suite of N-body simulations. We mod…
Halo models and halo occupation distributions (HODs) are important tools to model the galaxy and matter distribution. We present and assess a new method for constraining the parameters of HODs using the gravitational lensing shear around galaxy pairs, galaxy-galaxy-galaxy-lensing (G3L). In contrast to galaxy-galaxy-lensing, G3L is sensitive to correlations between the per-halo numbers of galaxies from different populations. We use G3L to probe these correlations and test the default hypothesis that they are negligible. We derive a halo model for G3L and validate it with realistic mock data fro…
[Abridged] This PhD thesis was defended in September 2013 at Université Paris-Sud, France. It studies the non-Gaussianity (NG) of extragalactic foregrounds to the Cosmic Microwave Background (CMB). This is particularly important for the analysis of CMB data from the Planck satellite, in which I was involved. I studied in particular the extragalactic foregrounds tracing the Large Scale Structure (LSS) of the universe : radio and infrared point-sources and the thermal Sunyaev-Zel'dovich effect (tSZ). The motivations and summary of this thesis cannot be shortened into the length constraints of th…
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 …
We present a joint likelihood analysis of the halo power spectrum and bispectrum in real space. We take advantage of a large set of numerical simulations and of an even larger set of halo mock catalogs to provide a robust estimate of the covariance properties. We derive constraints on bias and cosmological parameters assuming a theoretical model from perturbation theory at one-loop for the power spectrum and tree-level for the bispectrum. By means of the Deviance Information Criterion, we select a reference bias model dependent on seven parameters that can describe the data up to $k_{\rm max,P…
We compare the measurements of the bispectrum and the estimate of its covariance obtained from a set of different methods for the efficient generation of approximate dark matter halo catalogs to the same quantities obtained from full N-body simulations. To this purpose we employ a large set of three-hundred realisations of the same cosmology for each method, run with matching initial conditions in order to reduce the contribution of cosmic variance to the comparison. In addition, we compare how the error on cosmological parameters such as linear and nonlinear bias parameters depends on the app…
We derive the expressions for the 1-loop corrections in cosmological, Eulerian, perturbation theory to the matter bispectrum and to the galaxy bispectrum, assuming local galaxy bias, in presence of non-Gaussian initial conditions. We compute them explicitly for the particular case of non-vanishing initial bispectrum and trispectrum in the local model and for a non-vanishing initial bispectrum alone for the equilateral model of primordial non-Gaussianity. While the primordial contribution to the matter bispectrum for values compatible with CMB observations is dominant over the component due to …
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 counterpart obtained from standard Eulerian perturbation theory (SPT). Furthermore, the LPT formalism allows for a simple reorganisati…
