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Going beyond the Kaiser redshift-space distortion formula: a full general relativistic account of the effects and their detectability in galaxy clustering
Cosmology and Nongalactic Astrophysics · Submitted 25 Jun 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that in an all-sky galaxy redshift survey at low redshift the velocity term can be measured at a few sigma if one can utilize halos of mass M>10^12 Msun (this can increase to 10-sigma or more in some more optimistic scenarios), while the gravitational potential term itself can only be marginally detected.
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The abstract, sentence by sentence
Kaiser redshift-space distortion formula describes well the clustering of galaxies in redshift surveys on small scales, but there are numerous additional terms that arise on large scales. Some of these terms can be described using Newtonian dynamics and have been discussed in the literature, while the others require proper general relativistic description that was only recently developed. Accounting for these terms in galaxy clustering is the first step toward tests of general relativity on horizon scales. The effects can be classified as two terms that represent the velocity and the gravitational potential contributions. Their amplitude is determined by effects such as the volume and luminosity distance fluctuation effects and the time evolution of galaxy number density and Hubble parameter. We compare the Newtonian approximation often used in the redshift-space distortion literature to the fully general relativistic equation, and show that Newtonian approximation accounts for most of the terms contributing to velocity effect. We perform a Fisher matrix analysis of detectability of these terms and show that in a single tracer survey they are completely undetectable. To detect these terms one must resort to the recently developed methods to reduce sampling variance and shot noise. We show that in an all-sky galaxy redshift survey at low redshift the velocity term can be measured at a few sigma if one can utilize halos of mass M>10^12 Msun (this can increase to 10-sigma or more in some more optimistic scenarios), while the gravitational potential term itself can only be marginally detected. We also demonstrate that the general relativistic effect is not degenerate with the primordial non-Gaussian signature in galaxy bias, and the ability to detect primordial non-Gaussianity is little compromised.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Kaiser redshift-space distortion formula describes well the clustering of galaxies in redshift surveys on small scales, but there are numerous additional terms that arise on large scales. | background 0.95 | 0.09 | 0.04 | asserted 0.99 |
| s1 | Some of these terms can be described using Newtonian dynamics and have been discussed in the literature, while the others require proper general relativistic description that was only recently developed. | background 0.70 | 0.06 | 0.04 | asserted 0.90 |
| s2 | Accounting for these terms in galaxy clustering is the first step toward tests of general relativity on horizon scales. | interpretation 0.51 | 0.11 | 0.09 | asserted 0.99 |
| s3 | The effects can be classified as two terms that represent the velocity and the gravitational potential contributions. | background 0.43 | 0.30 | 0.05 | asserted 1.00 |
| s4 | Their amplitude is determined by effects such as the volume and luminosity distance fluctuation effects and the time evolution of galaxy number density and Hubble parameter. | background 0.75 | 0.22 | 0.03 | asserted 1.00 |
| s5 | We compare the Newtonian approximation often used in the redshift-space distortion literature to the fully general relativistic equation, and show that Newtonian approximation accounts for most of the terms contributing to velocity effect. | result 0.64 | 0.94 | 0.11 | asserted 1.00 |
| s6 | We perform a Fisher matrix analysis of detectability of these terms and show that in a single tracer survey they are completely undetectable. | result 0.99 | 0.96 | 0.22 | asserted 1.00 |
| s7 | To detect these terms one must resort to the recently developed methods to reduce sampling variance and shot noise. | method 0.32 | 0.33 | 0.09 | asserted 0.98 |
| s8 | We show that in an all-sky galaxy redshift survey at low redshift the velocity term can be measured at a few sigma if one can utilize halos of mass M>10^12 Msun (this can increase to 10-sigma or more in some more optimistic scenarios), while the gravitational potential term itself can only be marginally detected. | result 1.00 | 0.94 | 0.47 | asserted 0.82 |
| s9 | We also demonstrate that the general relativistic effect is not degenerate with the primordial non-Gaussian signature in galaxy bias, and the ability to detect primordial non-Gaussianity is little compromised. | result 0.94 | 0.93 | 0.11 | asserted 1.00 |
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The paper
Original abstract
Kaiser redshift-space distortion formula describes well the clustering of galaxies in redshift surveys on small scales, but there are numerous additional terms that arise on large scales. Some of these terms can be described using Newtonian dynamics and have been discussed in the literature, while the others require proper general relativistic description that was only recently developed. Accounting for these terms in galaxy clustering is the first step toward tests of general relativity on horizon scales. The effects can be classified as two terms that represent the velocity and the gravitational potential contributions. Their amplitude is determined by effects such as the volume and luminosity distance fluctuation effects and the time evolution of galaxy number density and Hubble parameter. We compare the Newtonian approximation often used in the redshift-space distortion literature to the fully general relativistic equation, and show that Newtonian approximation accounts for most of the terms contributing to velocity effect. We perform a Fisher matrix analysis of detectability of these terms and show that in a single tracer survey they are completely undetectable. To detect these terms one must resort to the recently developed methods to reduce sampling variance and shot noise. We show that in an all-sky galaxy redshift survey at low redshift the velocity term can be measured at a few sigma if one can utilize halos of mass M>10^12 Msun (this can increase to 10-sigma or more in some more optimistic scenarios), while the gravitational potential term itself can only be marginally detected. We also demonstrate that the general relativistic effect is not degenerate with the primordial non-Gaussian signature in galaxy bias, and the ability to detect primordial non-Gaussianity is little compromised.
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References
How the literature uses it
57 arXiv papers cite this in 100 sentences
Papers citing it · 73 sentences without a confident label
Contests it 1 paper
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As mentioned above, we show that when all terms are taken into account, the theory power spectrum is devoid of the infrared divergence claimed in previous works [ref] .
Galaxy Power Spectrum in General Relativity · Introduction · contest 0.88
Compares with it 2 papers
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First, we compute the power spectrum $P_s$ of the fluctuation $δ_s$ at the source position and compare it with the result presented in [ref] .
Galaxy Power Spectrum in General Relativity · Individual contributions to the power spectrum · 0.99
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Since observations are done in redshift space, though, care must be taken to disentangle the 3D asymmetries we consider below from the redshift-space asymmetries discussed in Refs. [ref] , and from the angular dependence induced by the 3D RSD operator [ref] .
Antisymmetric galaxy cross-correlations as a cosmological probe · Introduction · 0.83
Cites it as support 2 papers
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Indeed, as was shown in [ref] , combinations of various future data sets can be used to great effect to detect horizon-scale, general relativistic corrections to cosmological observables.
The Observational Future of Cosmological Scalar-Tensor Theories · Introduction · 0.99
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Non-linear effects have also been extensively studied by some of these authors, and they were shown to be negligible on the scales of interest; finally, while general-relativistic effects are present on the largest scales, they are small and do not affect the PNG constraints from the bias [ref] .
Improved Primordial Non-Gaussianity Constraints from Measurements of Galaxy Clustering and the Integrated Sachs-Wolfe Effect · Primordial Non-Gaussianity and the LSS · 0.96
Cites it as background 17 papers
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These are purely general relativistic effects and depends on how the gravitational potential, velocity fields as well as the matter density affect the observed number density of galaxies on large cosmological scales [ref] .
Imprint of thawing scalar fields on large scale galaxy overdensity · The observed galaxy power spectrum · 0.85
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It is well known that standard general relativistic effects in large scale structure give rise to odd CF multiples [ref] (or, in Fourier space, an imaginary part of the power spectrum [ref] ).
Screened fifth forces in parity-breaking correlation functions · Introduction · 0.80
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The relativistic effects at first order in perturbation theory have been derived in [ref] .
Modeling relativistic contributions to the halo power spectrum dipole · Introduction · 0.90
What it cites · 43 sentences without a confident label
Contests 1 paper
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This conclusion is in apparent contradiction with [ref] , where correlation functions are shown with smaller errors than the size of the effects.
Simulating Redshift-Space Distortions for Galaxy Pairs with Wide Angular Separation · Single tracers · contest 0.73
Builds on 1 paper
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This result confirms the prediction in [ref] and extends the predictions to galaxy samples with different number density and bias.
General Relativistic Description of the Observed Galaxy Power Spectrum: Do We Understand What We Measure? · Single tracers · 0.91
Cites as support 1 paper
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Calculations of wide-angle correlation functions [ref] shows that the effects of geometry are negligible, and a similar calculation can be performed for power spectrum measurements (in preparation).
Interpreting large-scale redshift-space distortion measurements · Multiple tracers · 0.97
Cites as background 4 papers
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where $δ_c$ is the linear overdensity for spherical collapse and $T_φ$ is the transfer function of the curvature perturbation (see also [ref] ).
Large-scale clustering of galaxies in general relativity · Primordial non-Gaussianity · 0.87
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where $δ_c$ is the linear overdensity for spherical collapse and $T_φ$ is the transfer function of the curvature perturbation (see also [ref] ).
Disentangling non-Gaussianity, bias and GR effects in the galaxy distribution · Primordial non-Gaussianity · 0.87
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where $δ_c$ is the linear overdensity for spherical collapse and $T_φ$ is the transfer function of the curvature perturbation (see also [ref] ).
Galaxy Bias and non-Linear Structure Formation in General Relativity · Primordial non-Gaussianity · 0.87
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