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Title: The bispectrum of galaxies from high-redshift galaxy surveys: Primordial non-Gaussianity and non-linear galaxy bias

Abstract

The greatest challenge in the interpretation of galaxy clustering data from any surveys is galaxy bias. Using a simple Fisher matrix analysis, we show that the bispectrum provides an excellent determination of linear and non-linear bias parameters of intermediate and high-z galaxies, when all measurable triangle configurations down to mildly non-linear scales, where perturbation theory is still valid, are included. The bispectrum is also a powerful probe of primordial non-Gaussianity. The planned galaxy surveys at z {approx}> 2 should yield constraints on non-Gaussian parameters, f{sub NL}{sup loc.} and f{sub NL}{sup eq.}, that are comparable to, or even better than, those from CMB experiments. We study how these constraints improve with volume, redshift range, as well as the number density of galaxies. Finally we show that a halo occupation distribution may be used to improve these constraints further by lifting degeneracies between gravity, bias, and primordial non-Gaussianity.

Authors:
; ; ;
Publication Date:
Research Org.:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
918733
Report Number(s):
FERMILAB-PUB-07-107-A
arXiv eprint number arXiv:0705.0343; TRN: US200819%%437
DOE Contract Number:
AC02-07CH11359
Resource Type:
Journal Article
Resource Relation:
Journal Name: Phys.Rev.D76:083004,2007
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DISTRIBUTION; GALAXIES; OCCUPATIONS; PERTURBATION THEORY; PROBES; RED SHIFT; Astrophysics

Citation Formats

Sefusatti, Emiliano, /Fermilab, Komatsu, Eiichiro, and /Texas U., Astron. Dept.. The bispectrum of galaxies from high-redshift galaxy surveys: Primordial non-Gaussianity and non-linear galaxy bias. United States: N. p., 2007. Web. doi:10.1103/PhysRevD.76.083004.
Sefusatti, Emiliano, /Fermilab, Komatsu, Eiichiro, & /Texas U., Astron. Dept.. The bispectrum of galaxies from high-redshift galaxy surveys: Primordial non-Gaussianity and non-linear galaxy bias. United States. doi:10.1103/PhysRevD.76.083004.
Sefusatti, Emiliano, /Fermilab, Komatsu, Eiichiro, and /Texas U., Astron. Dept.. Tue . "The bispectrum of galaxies from high-redshift galaxy surveys: Primordial non-Gaussianity and non-linear galaxy bias". United States. doi:10.1103/PhysRevD.76.083004. https://www.osti.gov/servlets/purl/918733.
@article{osti_918733,
title = {The bispectrum of galaxies from high-redshift galaxy surveys: Primordial non-Gaussianity and non-linear galaxy bias},
author = {Sefusatti, Emiliano and /Fermilab and Komatsu, Eiichiro and /Texas U., Astron. Dept.},
abstractNote = {The greatest challenge in the interpretation of galaxy clustering data from any surveys is galaxy bias. Using a simple Fisher matrix analysis, we show that the bispectrum provides an excellent determination of linear and non-linear bias parameters of intermediate and high-z galaxies, when all measurable triangle configurations down to mildly non-linear scales, where perturbation theory is still valid, are included. The bispectrum is also a powerful probe of primordial non-Gaussianity. The planned galaxy surveys at z {approx}> 2 should yield constraints on non-Gaussian parameters, f{sub NL}{sup loc.} and f{sub NL}{sup eq.}, that are comparable to, or even better than, those from CMB experiments. We study how these constraints improve with volume, redshift range, as well as the number density of galaxies. Finally we show that a halo occupation distribution may be used to improve these constraints further by lifting degeneracies between gravity, bias, and primordial non-Gaussianity.},
doi = {10.1103/PhysRevD.76.083004},
journal = {Phys.Rev.D76:083004,2007},
number = ,
volume = ,
place = {United States},
year = {Tue May 01 00:00:00 EDT 2007},
month = {Tue May 01 00:00:00 EDT 2007}
}
  • The greatest challenge in the interpretation of galaxy clustering data from any surveys is galaxy bias. Using a simple Fisher matrix analysis, we show that the bispectrum provides an excellent determination of linear and nonlinear bias parameters of intermediate and high-z galaxies, when all measurable triangle configurations down to mildly nonlinear scales, where perturbation theory is still valid, are included. The bispectrum is also a powerful probe of primordial non-Gaussianity. The planned galaxy surveys at z > or approx. 2 should yield constraints on non-Gaussian parameters, f{sub NL}{sup loc.} and f{sub NL}{sup eq.}, that are comparable to, or even bettermore » than, those from cosmic microwave background experiments. We study how these constraints improve with volume and redshift range, as well as the number density of galaxies. Finally, we show that a halo occupation distribution may be used to improve these constraints further by lifting degeneracies between gravity, bias, and primordial non-Gaussianity.« less
  • The three-point correlation function of cosmological fluctuations is a sensitive probe of the physics of inflation. We calculate the bispectrum, B{sub g} (k{sub 1}, k{sub 2}, k{sub 3}), Fourier transform of the three-point function of density peaks (e.g., galaxies), using two different methods: the Matarrese-Lucchin-Bonometto formula and the locality of galaxy bias. The bispectrum of peaks is not only sensitive to that of the underlying matter density fluctuations, but also to the four-point function. For a physically motivated, local form of primordial non-Gaussianity in the curvature perturbation, PHI = phi + f{sub NL}phi{sup 2} + g{sub NL}phi{sup 3}, where phimore » is a Gaussian field, we show that the galaxy bispectrum contains five physically distinct pieces: (1) non-linear gravitational evolution, (2) non-linear galaxy bias, (3) f{sub NL}, (4) f{sup 2}{sub NL}, and (5) g{sub NL}. While (1), (2), and a part of (3) have been derived in the literature, (4) and (5) are derived in this paper for the first time. We also find that, in the high-density peak limit, (3) receives an enhancement of a factor of {approx}15 relative to the previous calculation for the squeezed triangles (k{sub 1} {approx} k{sub 2} >> k{sub 3}). Our finding suggests that the galaxy bispectrum is more sensitive to f {sub NL} than previously recognized, and is also sensitive to a new term, g{sub NL}. For a more general form of local-type non-Gaussianity, the coefficient f{sup 2}{sub NL} can be interpreted as tau{sub NL}, which allows us to test multi-field inflation models using the relation between the three- and four-point functions. The usual terms from Gaussian initial conditions, (1) and (2), have the smallest signals in the squeezed configurations, while the others have the largest signals; thus, we can distinguish them easily. We cannot interpret the effects of f{sub NL} on B{sub g} (k{sub 1}, k{sub 2}, k{sub 3}) as a scale-dependent bias, and thus replacing the linear bias in the galaxy bispectrum with the scale-dependent bias known for the power spectrum results in an incorrect prediction. As the importance of primordial non-Gaussianity relative to the non-linear gravity evolution and galaxy bias increases toward higher redshifts, galaxy surveys probing a high-redshift universe are particularly useful for probing the primordial non-Gaussianity.« less
  • 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 local linear matter density contrast and the local gravitational potential in Lagrangian coordinates. Nonlinear evolutionmore » of the matter density introduces a non-local tidal term in the halo model. Furthermore, the presence of local-type non-Gaussianity in the Lagrangian frame leads to a novel non-local convective term in the Eulerian frame, that is proportional to the displacement field when going beyond the spherical collapse approximation. We use an extended Press-Schechter approach to evaluate the halo mass function and thus the halo bispectrum. We show that including these non-local terms in the halo bispectra can lead to corrections of up to 25% for some configurations, on large scales or at high redshift.« less
  • We place new constraints on the primordial local non-Gaussianity parameter f{sub NL} using recent cosmic microwave background anisotropy and galaxy clustering data. We model the galaxy power spectrum according to the halo model, accounting for a scale-dependent bias correction proportional to f{sub NL}/k{sup 2}. We first constrain f{sub NL} in a full 13 parameters analysis that includes 5 parameters of the halo model and 7 cosmological parameters. Using the WMAP7 CMB data and the SDSS DR4 galaxy power spectrum, we find f{sub NL}=171{sub -139}{sup +140} at 68% C.L. and -69<f{sub NL}<+492 at 95% C.L. We discuss the degeneracies between f{submore » NL} and other cosmological parameters. Including SN-Ia data and priors on H{sub 0} from Hubble Space Telescope observations we find a stronger bound: -35<f{sub NL}<+479 at 95%. We also fit the more recent SDSS DR7 halo power spectrum data finding, for a {Lambda}CDM+f{sub NL} model, f{sub NL}=-93{+-}128 at 68% C.L. and -327<f{sub NL}<+177 at 95% C.L. We finally forecast the constraints on f{sub NL} from future surveys as EUCLID and from CMB missions as Planck showing that their combined analysis could detect f{sub NL{approx}}5.« less
  • The standard nonlinear perturbation theory of the gravitational instability is extended to incorporate the nonlocal bias, redshift-space distortions, and primordial non-Gaussianity. We show that local Eulerian bias is not generally compatible with local Lagrangian bias in the nonlinear regime. The Eulerian and Lagrangian biases are nonlocally related order by order in the general perturbation theory. The relation between Eulerian and Lagrangian kernels of density perturbations with biasing is derived. The effects of primordial non-Gaussianity and redshift-space distortions are also incorporated in our general formalism, and diagrammatic methods are introduced. Vertex resummations of higher-order perturbations in the presence of bias aremore » considered. Resummations of Lagrangian bias are shown to be essential to handle biasing schemes in a general framework.« less