Non-local bias contribution to third-order galaxy correlations

Bel, J.; Hoffmann, Kai; Gaztañaga, E.

doi:10.1093/mnras/stv1600

Cited by 27 publications

(33 citation statements)

References 54 publications

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“…We recognize that the first of these corresponds to a linear bias renormalization byb 2 , leading tob 1 → b 1 =b 1 + (34b 2 /21 +b 3 /2) σ 2 in Eq. (23), which is consistent with the result found for the one-point propagator in Eq. (21).…”

Section: Renormalized Bias Expansion With Nonlinear Evolutionsupporting

confidence: 92%

Bias loop corrections to the galaxy bispectrum

2019

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Combination of the power spectrum and bispectrum is a powerful way of breaking degeneracies between galaxy bias and cosmological parameters, enabling us to maximize the constraining power from galaxy surveys. Recent cosmological constraints treat the power spectrum and bispectrum on an uneven footing: they include one-loop bias corrections for the power spectrum but not the bispectrum. To bridge this gap, we develop the galaxy bias description up to fourth order in perturbation theory, conveniently expressed through a basis of Galilean invariants that clearly split contributions that are local and nonlocal in the second derivatives of the linear gravitational potential. In addition, we consider relevant contributions from short-range nonlocality (higher-derivative terms), stress-tensor corrections and stochasticity. To sidestep the usual renormalization of bias parameters that complicates predictions beyond leading order, we recast the bias expansion in terms of multipoint propagators, which take a simple form in our split-basis with loop corrections depending only on bias parameters corresponding to nonlocal operators. We show how to take advantage of Galilean invariance to compute the time evolution of bias and present results for the fourth-order parameters for the first time. We also discuss the possibilities of reducing the bias parameter space by using the evolution of bias and exploiting degeneracies between various bias contributions in the large-scale limit. Our baseline model allows to verify these simplifications for any application to large-scale structure data sets.

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Section: Renormalized Bias Expansion With Nonlinear Evolutionsupporting

confidence: 92%

Bias loop corrections to the galaxy bispectrum

2019

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“…Equation (17) extends the local bias model introduced by Fry & Gaztanaga (1993) to account for the anisotropy and environmental dependence of gravitational collapse (Catelan et al 1998). The tidal-bias term alters the dependence of the galaxy bispectrum on the triangular configurations of the wavevectors (Catelan et al 2000) and a non-vanishing b s 2 has been measured for dark-matter haloes extracted from cosmological simulations (Baldauf et al 2012;Chan et al 2012;Saito et al 2014;Bel et al 2015). The tidal bias is also required to ensure a proper renormalization (in the fieldtheory sense) of the quadratic local bias that is otherwise sensitive to short-wavelength modes of the density field that are not suitable for a perturbative analysis (McDonald & Roy 2009;Assassi et al 2014;Desjacques et al 2018).…”

Section: Galaxy Biasingmentioning

confidence: 99%

Cosmological information in the redshift-space bispectrum

Yankelevich

Porciani

2018

Monthly Notices of the Royal Astronomical Society

136

209

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We use the Fisher-matrix formalism to investigate whether the galaxy bispectrum in redshift space, B, contains additional cosmological information with respect to the power spectrum, P. We focus on a Euclid -like survey and consider cosmological models dominated by dark energy and cold dark matter with Gaussian primordial perturbations. After discussing the phenomenology of redshift-space distortions for the bispectrum, we derive an expression for the cross-covariance between B and P at leading order in perturbation theory. Our equation generalizes previous results that did not consider binning in the orientation of wavevector triangles with respect to the line of sight. By considering Fourier modes with wavenumber k < 0.15 h Mpc −1 , we find that B and P set similar constraints on the cosmological parameters. Generally, error bars moderately improve when the two probes are combined together. For instance, the joint 68.3 per cent credible region for the parameters that describe a dynamical dark-energy equation of state shrinks by a factor of 2.6 with respect to only using the power spectrum. Regrettably, this improvement is cancelled out when the clustering analysis is combined with priors based on current studies of the cosmic microwave background. In this case, combining B and P does not give any appreciable benefit other than allowing a precise determination of galaxy bias. Finally, we discuss how results depend on the binning strategy for the clustering statistics as well as on the maximum wavenumber. We also show that only considering the bispectrum monopole leads to a significant loss of information.the nature of dark energy and dark matter, (ii) the neutrino masses, (iii) the statistical properties of primordial density fluctuations. These are the main science drivers of the planned next generation of surveys that will be conducted, for instance, with the Dark Energy Spectroscopic Instrument (DESI, DESI Collaboration et al. 2016a,b), the Euclid satellite (Laureijs et al. 2011) and the Square Kilometre Array (SKA, Maartens et al. 2015).It is customary to extract cosmological information from galaxy catalogues using the two-point correlation function or its Fourier transform, the power spectrum. Either of these functions fully characterize a zero-mean Gaussian random field. However, the galaxy distribution displays complex patterns characterized by elongated filaments, compact clusters, and volume-filling underdense regions. These features are not captured by two-point statistics that do not retain information on the phases of the Fourier modes of the galaxy distribution. Therefore, if measured with sufficient accuracy and precision, higher-order statistics like the n-point correlation functions (with n > 2) and their Fourier transforms, the polyspectra, should contain additional information.Until recently, galaxy redshift surveys could only pro-

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“…For the quadratic tidal bias (b K 2 ), we obtain a significant detection of a negative Lagrangian tidal bias.as well, as we will see). The parameter b K 2 has also been measured from the tree-level bispectrum in [10,16,27,28], the Lagrangian bispectrum [29], the 3-point function [30], and from Lagrangian moments-based measurements [23,31]. Some disagreement has been found between [16] and [31] in the results for b K 2 .…”

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confidence: 99%

Beyond LIMD bias: a measurement of the complete set of third-order halo bias parameters

Lazeyras

Schmidt

2018

J. Cosmol. Astropart. Phys.

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We present direct measurements of cubic bias parameters of dark matter halos from the halo-matter-matter-matter trispectrum. We measure this statistic efficiently by cross-correlating the halo field measured in N-body simulations with specific third-order nonlocal transformations of the initial density field in the same simulation. Together with the recent Ref.[1], these are the first measurements of halo bias using the four-point function that have been reported to date. We also obtain constraints on the quadratic bias parameters. For all individual cubic parameters involving the tidal field K ij , we find broad consistency with the prediction of the Lagrangian local-in-matter-density ansatz, with some indications of a positive Lagrangian coefficient b L td multiplying the time derivative of K ij . For the quadratic tidal bias (b K 2 ), we obtain a significant detection of a negative Lagrangian tidal bias.as well, as we will see). The parameter b K 2 has also been measured from the tree-level bispectrum in [10,16,27,28], the Lagrangian bispectrum [29], the 3-point function [30], and from Lagrangian moments-based measurements [23,31]. Some disagreement has been found between [16] and [31] in the results for b K 2 . Finally, the parameter b 3nl , a certain combination of quadratic and cubic tidal biases, has also been constrained from the 1-loop halo-matter power spectrum in [16], but, following our discussion, it is degenerate with the higher-derivative bias, which was set to zero in that reference.The goal of the present paper is to measure all the cubic bias terms, which are: b 3 = 6b δ 3 , b td , b K 3 , and b δK 2 . The leading statistic to which these contribute is the four-point function (trispectrum). In order to measure them, we generalize a technique proposed by Ref.[26] to measure the relevant trispectrum contributions efficiently. This technique allows us to measure all the cubic bias parameters at once. Together with the recent Ref.[1], these are the first measurements of halo bias using the four-point function that have been reported to date. We further use the analogous technique for the bispectrum to measure b 1 , b 2 and b K 2 , to cross-check our results obtained from the trispectrum, and to compare with previous measurements.The very similar study of [1] came out shortly after this paper appeared on the arXiv preprint server. While they use the same technique to obtain cubic order bias parameters from the trispectrum, some details such as higher-order corrections are treated differently. Overall, our results are in good agreement with theirs.This paper is organised as follows: in section 2 we present our estimator for the trispectrum and show how to obtain the bias parameters from it. Section 3 describes our set of simulations, shortly explains the halo finding procedure, and gives details on the actual procedure to measure the bias parameters. Section 4 reviews previous measurements and theoretical predictions for the parameters. Finally, section 5 presents and discusses our results. We conclu...

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Non-local bias contribution to third-order galaxy correlations

Cited by 27 publications

References 54 publications

Bias loop corrections to the galaxy bispectrum

Bias loop corrections to the galaxy bispectrum

Cosmological information in the redshift-space bispectrum

Beyond LIMD bias: a measurement of the complete set of third-order halo bias parameters

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