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An Optimally Weighted Estimator of the Linear Power Spectrum Disentangling the Growth of Density Perturbations Across Galaxy Surveys
Cosmology and Nongalactic Astrophysics · Submitted 2 Dec 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim I show that the estimator presented recovers the fiducial linear power spectrum at present time within 5% accuracy up to $k \sim 0.80\;h\,\mathrm{Mpc}^{-1}$ and within 10% up to $k \sim 0.94\;h\,\mathrm{Mpc}^{-1}$, well into the non-linear regime of the growth of density perturbations.
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The abstract, sentence by sentence
Measuring the clustering of galaxies from surveys allows us to estimate the power spectrum of matter density fluctuations, thus constraining cosmological models. This requires careful modelling of observational effects to avoid misinterpretation of data. In particular, signals coming from different distances encode information from different epochs. This is known as "light-cone effect" and is going to have a higher impact as upcoming galaxy surveys probe larger redshift ranges. Generalising the method by Feldman et al. (1994), I define a minimum-variance estimator of the linear power spectrum at a fixed time, properly taking into account the light-cone effect. An analytic expression for the estimator is provided, and that is consistent with the findings of previous works in the literature. I test the method within the context of the halo model, assuming Planck 2014 cosmological parameters. I show that the estimator presented recovers the fiducial linear power spectrum at present time within 5% accuracy up to $k \sim 0.80\;h\,\mathrm{Mpc}^{-1}$ and within 10% up to $k \sim 0.94\;h\,\mathrm{Mpc}^{-1}$, well into the non-linear regime of the growth of density perturbations. As such, the method could be useful in the analysis of the data from future large-scale surveys, like Euclid.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Measuring the clustering of galaxies from surveys allows us to estimate the power spectrum of matter density fluctuations, thus constraining cosmological models. | background 1.00 | 0.08 | 0.03 | asserted 0.84 |
| s1 | This requires careful modelling of observational effects to avoid misinterpretation of data. | background 1.00 | 0.05 | 0.02 | asserted 1.00 |
| s2 | In particular, signals coming from different distances encode information from different epochs. | background 1.00 | 0.06 | 0.02 | asserted 1.00 |
| s3 | This is known as "light-cone effect" and is going to have a higher impact as upcoming galaxy surveys probe larger redshift ranges. | background 0.99 | 0.07 | 0.03 | asserted 0.62 |
| s4 | Generalising the method by Feldman et al. (1994), I define a minimum-variance estimator of the linear power spectrum at a fixed time, properly taking into account the light-cone effect. | contribution 0.78 | 0.95 | 0.13 | asserted 1.00 |
| s5 | An analytic expression for the estimator is provided, and that is consistent with the findings of previous works in the literature. | contribution 0.67 | 0.66 | 0.05 | hedged possibility 0.61 |
| s6 | I test the method within the context of the halo model, assuming Planck 2014 cosmological parameters. | method 0.97 | 0.94 | 0.03 | asserted 0.91 |
| s7 | I show that the estimator presented recovers the fiducial linear power spectrum at present time within 5% accuracy up to $k \sim 0.80\;h\,\mathrm{Mpc}^{-1}$ and within 10% up to $k \sim 0.94\;h\,\mathrm{Mpc}^{-1}$, well into the non-linear regime of the growth of density perturbations. | result 1.00 | 0.96 | 0.77 | asserted 1.00 |
| s8 | As such, the method could be useful in the analysis of the data from future large-scale surveys, like Euclid. | interpretation 0.52 | 0.18 | 0.13 | hedged possibility 1.00 |
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The paper
Original abstract
Measuring the clustering of galaxies from surveys allows us to estimate the power spectrum of matter density fluctuations, thus constraining cosmological models. This requires careful modelling of observational effects to avoid misinterpretation of data. In particular, signals coming from different distances encode information from different epochs. This is known as "light-cone effect" and is going to have a higher impact as upcoming galaxy surveys probe larger redshift ranges. Generalising the method by Feldman et al. (1994), I define a minimum-variance estimator of the linear power spectrum at a fixed time, properly taking into account the light-cone effect. An analytic expression for the estimator is provided, and that is consistent with the findings of previous works in the literature. I test the method within the context of the halo model, assuming Planck 2014 cosmological parameters. I show that the estimator presented recovers the fiducial linear power spectrum at present time within 5% accuracy up to $k \sim 0.80\;h\,\mathrm{Mpc}^{-1}$ and within 10% up to $k \sim 0.94\;h\,\mathrm{Mpc}^{-1}$, well into the non-linear regime of the growth of density perturbations. As such, the method could be useful in the analysis of the data from future large-scale surveys, like Euclid.
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References
How the literature uses it
2 arXiv papers cite this in 3 sentences
Papers citing it
Cites it as background 2 papers
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Almost all current surveys [ref] have opted to measure the galaxy power spectrum, $P()$, using the `FKP' approach, first proposed in Ref. [ref] and generalized to anisotropic spectra in Refs. [ref] , as well as lightcone evolution in Ref. [ref] .
Cosmology Without Windows: Quadratic Estimators for the Galaxy Power Spectrum · Introduction · 0.97
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These include a variety of (quasi-)optimal quadratic power spectrum estimators [ref] (which saw significant application in the early 2000s [ref] ), approximate power spectrum weighting schemes [ref] , sub-optimal but efficient bispectrum estimators [ref] , as well as extension to anisotropy [ref] , and the analogous methods for two-sphere observables (including [ref] for the two-point function and [ref] for higher-point functions).
PolyBin3D: A Suite of Optimal and Efficient Power Spectrum and Bispectrum Estimators for Large-Scale Structure · Introduction · 0.97
What it cites · 36 sentences without a confident label
Builds on 1 paper
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I extended the method by [ref] , incorporating the light-cone effect.
Power Spectrum Analysis of Three-Dimensional Redshift Surveys · Conclusions and Perspectives · 1.00
Uses the method or tool of 3 papers
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Functions $σ^2 (R)$ and $k_σ(r)$ are then computed, as well as all the quantities needed to define the one- and two-halo terms according to [ref] .
Revising the Halofit Model for the Nonlinear Matter Power Spectrum · Implementation of the Method · 1.00
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Within this assumption and the distant observer approximation, one can write [ref] [equation] where $r^*=(r+r')/2$.
Optimal Weighting Scheme in Redshift-space Power Spectrum Analysis and a Prospect for Measuring the Cosmic Equation of State · Computing Weighted Density Fluctuations · 0.94
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The solid red line is the linear power spectrum generated through CAMB ( [ref] ) with the cosmological parameters given by [ref] ($Ω_m=0.315$, $Ω_Λ=1-Ω_m=0.683$, $Ω_b=0.049$, $h=0.673$, $A_s=2.215 ×10^-9$, $n_s=0.96$).
Planck 2013 results. XVI. Cosmological parameters · Revised Halofit Model · 0.80
Uses data or values from 4 papers
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The method has been tested for the $Λ$CDM cosmology with the parameters given by [ref] , assuming the revised halofit model by [ref] and a shape for number density of galaxies as in [ref] .
Revising the Halofit Model for the Nonlinear Matter Power Spectrum · Conclusions and Perspectives · 0.86
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The method has been tested for the $Λ$CDM cosmology with the parameters given by [ref] , assuming the revised halofit model by [ref] and a shape for number density of galaxies as in [ref] .
Planck 2013 results. XVI. Cosmological parameters · Conclusions and Perspectives · 0.86
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The method has been tested for the $Λ$CDM cosmology with the parameters given by [ref] , assuming the revised halofit model by [ref] and a shape for number density of galaxies as in [ref] .
Gravitational Lensing of Distant Field Galaxies by Rich Clusters: I. -- Faint Galaxy Redshift Distributions · Conclusions and Perspectives · 0.86
Compares with 1 paper
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The result presented in this work is formally identical to [ref] , but has a different physical meaning.
Optimal Weighting Scheme in Redshift-space Power Spectrum Analysis and a Prospect for Measuring the Cosmic Equation of State · Conclusions and Perspectives · 0.99
Cites as background 32 papers
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A different idea to address the issue is expressing the non-linear power spectrum (or correlation function) as a function of its linear counterpart, evaluated at a different scale [ref] .
Pattern in Nonlinear Gravatational Clustering: A Numerical Investigation · Growth of Perturbations · 0.90
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A different idea to address the issue is expressing the non-linear power spectrum (or correlation function) as a function of its linear counterpart, evaluated at a different scale [ref] .
Reconstructing the linear power spectrum of cosmological mass fluctuations · Growth of Perturbations · 0.90
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A different idea to address the issue is expressing the non-linear power spectrum (or correlation function) as a function of its linear counterpart, evaluated at a different scale [ref] .
Does Gravitational Clustering Stabilize On Small Scales? · Growth of Perturbations · 0.90
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