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Ringing the initial Universe: the response of overdensity and transformed-density power spectra to initial spikes
Cosmology and Nongalactic Astrophysics · Submitted 7 May 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim These power spectra show much greater sensitivity to small-scale initial features.
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The abstract, sentence by sentence
We present an experiment in which we 'ring' a set of cosmological N-body-simulation initial conditions, placing spikes in the initial power spectrum at different wavenumber bins. We then measure where these spikes end up in the final conditions. In the usual overdensity power spectrum, most sensitive to contracting and collapsing dense regions, initial power on slightly non-linear scales (k ~ 0.3 h/Mpc) smears to smaller scales, coming to dominate the initial power once there. Log-density and Gaussianized-density power spectra, sensitive to low-density (expanding) and high-density regions, respond differently: initial spikes spread symmetrically in scale, both upward and downward. In fact, in the power spectrum of 1/(1 + {\delta}), spikes migrate to larger scales, showing the magnifying effect of voids on small-scale modes. These power spectra show much greater sensitivity to small-scale initial features. We also test the difference between an approximation of the Ly-{\alpha} flux field, and its Gaussianized form, and give a toy model that qualitatively explains the symmetric power spreading in Gaussianized-density power spectra. Also, we discuss how to use this framework to estimate power-spectrum covariance matrices. This can be used to track the fate of information in the Universe, that takes the form of initial degrees of freedom, one random spike per initial mode.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present an experiment in which we 'ring' a set of cosmological N-body-simulation initial conditions, placing spikes in the initial power spectrum at different wavenumber bins. | method 0.60 | 0.96 | 0.04 | asserted 0.98 |
| s1 | We then measure where these spikes end up in the final conditions. | method 0.93 | 0.97 | 0.03 | asserted 0.98 |
| s2 | In the usual overdensity power spectrum, most sensitive to contracting and collapsing dense regions, initial power on slightly non-linear scales (k ~ 0.3 h/Mpc) smears to smaller scales, coming to dominate the initial power once there. | result 1.00 | 0.92 | 0.22 | asserted 1.00 |
| s3 | Log-density and Gaussianized-density power spectra, sensitive to low-density (expanding) and high-density regions, respond differently: initial spikes spread symmetrically in scale, both upward and downward. | result 1.00 | 0.93 | 0.25 | asserted 1.00 |
| s4 | In fact, in the power spectrum of 1/(1 + {\delta}), spikes migrate to larger scales, showing the magnifying effect of voids on small-scale modes. | result 0.94 | 0.91 | 0.10 | asserted 1.00 |
| s5 | These power spectra show much greater sensitivity to small-scale initial features. | result 0.86 | 0.88 | 0.17 | asserted 1.00 |
| s6 | We also test the difference between an approximation of the Ly-{\alpha} flux field, and its Gaussianized form, and give a toy model that qualitatively explains the symmetric power spreading in Gaussianized-density power spectra. | contribution 0.70 | 0.94 | 0.06 | asserted 0.94 |
| s7 | Also, we discuss how to use this framework to estimate power-spectrum covariance matrices. | contribution 0.72 | 0.80 | 0.03 | asserted 0.79 |
| s8 | This can be used to track the fate of information in the Universe, that takes the form of initial degrees of freedom, one random spike per initial mode. | interpretation 0.97 | 0.45 | 0.18 | asserted 0.76 |
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The paper
Original abstract
We present an experiment in which we 'ring' a set of cosmological N-body-simulation initial conditions, placing spikes in the initial power spectrum at different wavenumber bins. We then measure where these spikes end up in the final conditions. In the usual overdensity power spectrum, most sensitive to contracting and collapsing dense regions, initial power on slightly non-linear scales (k ~ 0.3 h/Mpc) smears to smaller scales, coming to dominate the initial power once there. Log-density and Gaussianized-density power spectra, sensitive to low-density (expanding) and high-density regions, respond differently: initial spikes spread symmetrically in scale, both upward and downward. In fact, in the power spectrum of 1/(1 + {\delta}), spikes migrate to larger scales, showing the magnifying effect of voids on small-scale modes. These power spectra show much greater sensitivity to small-scale initial features. We also test the difference between an approximation of the Ly-{\alpha} flux field, and its Gaussianized form, and give a toy model that qualitatively explains the symmetric power spreading in Gaussianized-density power spectra. Also, we discuss how to use this framework to estimate power-spectrum covariance matrices. This can be used to track the fate of information in the Universe, that takes the form of initial degrees of freedom, one random spike per initial mode.
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References
How the literature uses it
11 arXiv papers cite this in 13 sentences
Papers citing it · 12 sentences without a confident label
Cites it as support 1 paper
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This was further confirmed by the numerical experiments in [ref] based on an ensemble of simulations with slightly different linear power spectra [See also [ref] for earlier numerical studies on the mode transfer in the context of large-scale structure cosmology.].
Moving around the cosmological parameter space: a nonlinear power spectrum reconstruction based on high-resolution cosmic responses · Introduction · 0.99
What it cites · 3 sentences without a confident label
Uses the method or tool of 4 papers
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Alternatively, a spherical-collapse approximation can be used for the behavior of $ψ$, where $ψ_z$ is its ZA value [ref] , [equation] This uses an approximation for the evolution of a volume element found by [ref] , valid in the limit of low matter density.
Reconstruction of primordial density fields · Toy model for power spreading · 0.98
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Alternatively, a spherical-collapse approximation can be used for the behavior of $ψ$, where $ψ_z$ is its ZA value [ref] , [equation] This uses an approximation for the evolution of a volume element found by [ref] , valid in the limit of low matter density.
The Nonlinear Evolution of Rare Events · Toy model for power spreading · 0.98
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We use what we call the Lagrangian Tessellation Field Estimator [ref] , referencing the Delaunay and Voronoi Tessellation Field Estimators [ref] , which use Eulerian tessellations.
Continuous Fields and Discrete Samples: Reconstruction through Delaunay Tessellations · Methods · 0.88
Compares with 1 paper
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In $δ$, the migration of power is qualitatively as in [ref] and [ref] : power moves from large to small scales.
Nonlinear evolution of cosmological power spectra · Results · 0.94
Cites as support 2 papers
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This covariance greatly reduces the Fisher information, i.e. increases error bars on cosmological parameters observable in principle [ref] .
Information content in the halo-model dark-matter power spectrum · Introduction · 0.96
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This covariance greatly reduces the Fisher information, i.e. increases error bars on cosmological parameters observable in principle [ref] .
Information content of the non-linear power spectrum: the effect of beat-coupling to large scales · Introduction · 0.96
Cites as background 2 papers
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It is of interest in the study of density transforms, since Gaussianization [ref] was tried in Ly-$α$-forest studies [ref] , but later works skipped that step [ref] .
Towards a Precise Measurement of Matter Clustering: Lyman-alpha Forest Data at Redshifts 2-4 · Introduction · 0.87
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It is of interest in the study of density transforms, since Gaussianization [ref] was tried in Ly-$α$-forest studies [ref] , but later works skipped that step [ref] .
Recovery of the Power Spectrum of Mass Fluctuations from Observations of the Lyman-alpha Forest · Introduction · 0.87
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