Non-Gaussian gravitational clustering field statistics

Kitaura, Francisco-Shu

doi:10.1111/j.1365-2966.2011.19680.x

Cited by 15 publications

(14 citation statements)

References 68 publications

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“…It is easier to obtain estimates of the linear component than of the full non‐linear density field from observational data. The reason being that modelling the power spectrum (or two‐point correlation function) in the reconstruction method is easier than including higher order correlation functions (see Kitaura ). It was demonstrated in Kitaura et al () how to transform the density field into its linear component to apply a Gaussian prior and determine the power spectrum iteratively.…”

Section: Discussionmentioning

confidence: 99%

Linearization with cosmological perturbation theory

Kitaura¹,

Angulo

2012

Monthly Notices of the Royal Astronomical Society

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We propose a new method to linearize cosmological mass density fields using higher order Lagrangian perturbation theory (LPT). We demonstrate that a given density field can be expressed as the sum of a linear and a non‐linear component which are tightly coupled to each other by the tidal field tensor within the LPT framework. The linear component corresponds to the initial density field in Eulerian coordinates, and its mean relation with the total field can be approximated by a logarithm (giving theoretical support to recent attempts to find such a component). We also propose to use a combination of the linearization method and the continuity equation to find the mapping between Eulerian and Lagrangian coordinates. In addition, we note that this method opens the possibility of using directly higher order LPT on non‐linear fields. We test our linearization scheme by applying it to the z ∼ 0.5 density field from an N‐body simulation. We find that the linearized version of the full density field can be successfully recovered on ≳5 h−1 Mpc, reducing the skewness and kurtosis of the distribution by about one and two orders of magnitude, respectively. This component can also be successfully traced back in time, converging towards the initial unevolved density field at z ∼ 100. We anticipate a number of applications of our results, from predicting velocity fields to estimates of the initial conditions of the Universe, passing by improved constraints on cosmological parameters derived from galaxy clustering via reconstruction methods.

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Section: Discussionmentioning

confidence: 99%

Linearization with cosmological perturbation theory

Kitaura¹,

Angulo

2012

Monthly Notices of the Royal Astronomical Society

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“…The distribution of haloes is statistically determined by all its moments. Nevertheless, a method imposing all the corresponding correlation functions (assuming that they are known) to a distribution of haloes is far from trivial and hardly numerically efficient (see Kitaura 2012). Instead, one tries to encode the physics encapturing all the higher-order statistics in the generation of the halo distribution.…”

Section: Introductionmentioning

confidence: 99%

Constraining the halo bispectrum in real and redshift space from perturbation theory and non-linear stochastic bias

Kitaura¹,

Gil-Marín²,

Scóccola³

et al. 2015

Monthly Notices of the Royal Astronomical Society

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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 underlying dark matter field with a fix halo number density, and accurately matching the power spectrum (within 2%), can lead to very different bispectra depending on the adopted halo bias model. A model ignoring the shape of the halo PDF can lead to deviations up to factors of 2. The catalogues obtained additionally constraining the shape of the halo PDF can significantly lower the discrepancy in the three-point statistics, yielding closely unbiased bispectra both in real and in redshift space; which are in general compatible with those corresponding to an N-body simulation within 10% (deviating at most up to 20%). Our calculations show that the constant linear bias of ∼2 for Luminous Red Galaxy (LRG) like galaxies seen in the power spectrum, mainly comes from sampling halos in high density peaks, choosing a high density threshold rather than from a factor multiplying the dark matter density field. Our method contributes towards an efficient modelling of the halo/galaxy distribution required to estimate uncertainties in the clustering measurements from galaxy redshift surveys. We have also demonstrated that it represents a powerful tool to test various bias models.

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“…We note however, that this prior can be substituted by another one, e.g., based on Lagrangian perturbation theory (see Kitaura (2013) ;Jasche & Wandelt (2013); Wang et al (2013); Heß, Kitaura & Gottlöber (2013)). Alternatively, one can extend the lognormal assumption in an Edgeworth expansion to include higher order correlation functions (Colombi (1994); Kitaura (2012b)). We show in this work that our likelihood model is able of yielding unbiased dark matter field reconstructions on ∼ 6 h −1 Mpc scales based on N -body simulations.…”

Section: Introductionmentioning

confidence: 99%

Bayesian inference of cosmic density fields from non-linear, scale-dependent, and stochastic biased tracers

Ata

Kitaura

Müller

2014

Monthly Notices of the Royal Astronomical Society

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We present a Bayesian reconstruction algorithm to generate unbiased samples of the underlying dark matter field from halo catalogues. Our new contribution consists of implementing a non-Poisson likelihood including a deterministic non-linear and scale-dependent bias. In particular we present the Hamiltonian equations of motions for the negative binomial (NB) probability distribution function. This permits us to efficiently sample the posterior distribution function of density fields given a sample of galaxies using the Hamiltonian Monte Carlo technique implemented in the ARGO code. We have tested our algorithm with the Bolshoi Nbody simulation at redshift z = 0, inferring the underlying dark matter density field from subsamples of the halo catalogue with biases smaller and larger than one. Our method shows that we can draw closely unbiased samples (compatible within 1-σ) from the posterior distribution up to scales of about k ∼1 h Mpc −1 in terms of power-spectra and cell-to-cell correlations. We find that a Poisson likelihood including a scale-dependent non-linear deterministic bias can yield reconstructions with power spectra deviating more than 10% at k = 0.2 h Mpc −1 . Our reconstruction algorithm is especially suited for emission line galaxy data for which a complex non-linear stochastic biasing treatment beyond Poissonity becomes indispensable.

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Non-Gaussian gravitational clustering field statistics

Cited by 15 publications

References 68 publications

Linearization with cosmological perturbation theory

Linearization with cosmological perturbation theory

Constraining the halo bispectrum in real and redshift space from perturbation theory and non-linear stochastic bias

Bayesian inference of cosmic density fields from non-linear, scale-dependent, and stochastic biased tracers

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