The Bispectrum as a Signature of Gravitational Instability in Redshift Space

Scoccimarro, Román; Couchman, H. M. P.; Frieman, Joshua A.

doi:10.1086/307220

Cited by 286 publications

(453 citation statements)

References 35 publications

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“…At large scales, k \ 0.2 h Mpc~1, 2LPT reproduces the suppression of power compared to linear PT ; at smaller scales, the suppression is overestimated, as we approach the cuto † scale of the power spectrum and shell crossing also starts to play a role. The bottom panel of Figure 2 shows a similar comparison for the equilateral bispectrum ; the dotted line now corresponds to the redshift-space prediction at large scales from tree-level PT (Scoccimarro et al 1999a). We see that although tree-level PT breaks down at about k B 0.2 h Mpc~1, 2LPT continues to hold at smaller The dotted line shows the prediction of k 1 k 2 .…”

Section: Galaxy Biasing : Effects Of Stochasticitymentioning

confidence: 56%

“…tree-level PT . As noted before (Scoccimarro et al 1999a), the predictions of tree-level PT in redshift space break down at relatively large scales, due to the nonperturbative nature of the redshift-space mapping. Fortunately, since 2LPT performs the mapping exactly, the agreement with the numerical simulations is very good down to scales of k B 0.4 h Mpc~1.…”

Section: Galaxy Biasing : Effects Of Stochasticitymentioning

confidence: 77%

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The Bispectrum: From Theory to Observations

Scoccimarro¹

2000

ApJ

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216

269

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The bispectrum is the lowest order statistic sensitive to the shape of structures generated by gravitational instability and is a potentially powerful probe of galaxy biasing and the Gaussianity of primordial Ñuctuations. Although the evolution of the bispectrum is well understood theoretically from nonlinear perturbation theory and numerical simulations, applications to galaxy surveys require a number of issues to be addressed. In this paper we consider the e †ect on the bispectrum of stochastic nonlinear biasing, radial redshift distortions, non-Gaussian initial conditions, survey geometry, and sampling. We Ðnd that : (1) Bias stochasticity does not a †ect the use of the bispectrum to recover the mean biasing relation between galaxies and mass, at least for models in which the scatter is uncorrelated at large scales. (2) Radial redshift distortions do not signiÐcantly change the monopole power spectrum and bispectrum compared to their plane-parallel values. (3) Survey geometry leads to Ðnite-volume e †ects, which must be taken into account in current surveys before comparison with theoretical predictions can be made. (4) Sparse sampling and survey geometry correlate di †erent triangles, leading to a breakdown of the Gaussian likelihood approximation. We develop a likelihood analysis using bispectrum eigenmodes, calculated by Monte Carlo realizations of mock surveys generated with second-order Lagrangian perturbation theory and checked against N-body simulations. In a companion paper, we apply these results to the analysis of the bispectrum of IRAS galaxies.

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Section: Galaxy Biasing : Effects Of Stochasticitymentioning

confidence: 56%

Section: Galaxy Biasing : Effects Of Stochasticitymentioning

confidence: 77%

The Bispectrum: From Theory to Observations

Scoccimarro¹

2000

ApJ

Self Cite

216

269

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“…Detailed discussions of the projection effects are beyond the scope of this paper. We refer interested readers to a systematic study of the relativistic projection effects on the galaxy power spectrum [47] and on the squeezed galaxy bispectrum [10,22,48].…”

Section: Squeezed Matter Bispectrum As Measured By a Local Observermentioning

confidence: 99%

On separate universes

Dai

Pajer

Schmidt

2015

J. Cosmol. Astropart. Phys.

188

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Abstract. The separate universe conjecture states that in General Relativity a density perturbation behaves locally (i.e. on scales much smaller than the wavelength of the mode) as a separate universe with different background density and curvature. We prove this conjecture for a spherical compensated tophat density perturbation of arbitrary amplitude and radius in ΛCDM. We then use Conformal Fermi Coordinates to generalize this result to scalar perturbations of arbitrary configuration and scale in a general cosmology with a mixture of fluids, but to linear order in perturbations. In this case, the separate universe conjecture holds for the isotropic part of the perturbations. The anisotropic part on the other hand is exactly captured by a tidal field in the Newtonian form. We show that the separate universe picture is restricted to scales larger than the sound horizons of all fluid components. We then derive an expression for the locally measured matter bispectrum induced by a long-wavelength mode of arbitrary wavelength, a new result which in standard perturbation theory is equivalent to a relativistic second-order calculation. We show that nonlinear gravitational dynamics does not generate observable contributions that scale like local-type non-Gaussianity f loc NL , and hence does not contribute to a scale-dependent galaxy bias ∆b ∝ k −2 on large scales; rather, the locally measurable long-short mode coupling assumes a form essentially identical to subhorizon perturbation theory results, once the long-mode density perturbation is replaced by the synchronous-comoving gauge density perturbation. Apparent f loc NL -type contributions arise through projection effects on photon propagation, which depend on the specific large-scale structure tracer and observable considered, and are in principle distinguishable from the local mode coupling induced by gravity. We conclude that any observation of f loc NL beyond these projection effects signals a departure from standard single-clock inflation.

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“…Assuming the line of sight component is along the z-axis, the fully non-linear relation between the real and redshift space power spectrum can be written as (Scoccimarro et al, 1999) first suggested by Peebles (1980) and modified by Fisher (1995) to take into account the density-velocity coupling. At small scales (as k increases) the exponential component damps the power, representing the impact of randomised velocities inside gravitationally bound structures.…”

Section: Modelling Non-linear Distortions To the Power Spectrum In Rementioning

confidence: 99%

“…The velocity divergence depends on Ω m and Ω Λ , in a standard ΛCDM cosmology, only through the linear growth rate, f (Scoccimarro et al, 1999).…”

Section: Dependence On Cosmological Modelmentioning

confidence: 99%

Simulations of Dark Energy Cosmologies

Jennings

2012

Springer Theses

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The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source• a link is made to the metadata record in Durham E-Theses• the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders. No part of this thesis has been submitted elsewhere for any other degree or qualification.The work of others has been duly acknowledged.The copyright of this thesis rests with the author. No quotations from it should be published without the author's prior written consent and information derived from it should be acknowledged. AbstractFuture galaxy redshift surveys will make high precision measurements of the cosmic expansion history and the growth of structure which will potentially allow us to distinguish between different scenarios for the accelerating expansion of the Universe. In this thesis we study the nonlinear growth of cosmic structure in different dark energy models, using ultra-large volume N-body simulations. We measure key observables such as the growth of large scale structure, the halo mass function and baryonic acoustic oscillations.We study the power spectrum in redshift space in ΛCDM and quintessence dark energy models and test predictions for the form of the redshift space distortions. An improved model for the redshift space power spectrum, including the non-linear velocity divergence power spectrum, is presented. We have found a density-velocity relation which is cosmology independent and which relates the non-linear velocity divergence spectrum to the non-linear matter power spectrum. We provide a formula which generates the non-linear velocity divergence P(k) at any redshift, using only the non-linear matter power spectrum and the linear growth factor at the desired redshift. We also demonstrate for the first time that competing cosmological models with identical expansion histories -one with a scalar field and the other with a time-dependent change to Newton's gravitational constant -can indeed be distinguished by a measurement of the rate at which structures grow.Our calculations show that linear theory models for the power spectrum in redshift space fail to recover the correct growth rate on surprisingly large scales, leading to catastrophic systematic errors. Improved theoretical models, which have been calibrated against simulations, are needed to exploit the exquisitely accurate clustering measurements expected from future surveys.

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The Bispectrum as a Signature of Gravitational Instability in Redshift Space

Cited by 286 publications

References 35 publications

The Bispectrum: From Theory to Observations

The Bispectrum: From Theory to Observations

On separate universes

Simulations of Dark Energy Cosmologies

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