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Flat to nonflat: Calculating nonlinear power spectra of biased tracers for nonflat $\Lambda$CDM model
Cosmology and Nongalactic Astrophysics · Submitted 20 Oct 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We use $N$-body simulations to show that the estimator can provide the halo-matter (halo-auto) power spectrum at $\sim 1\%$ ($\sim 2\%$ ) accuracy up to $k \simeq 3 (1) \, h {\rm Mpc}^{-1}$ even for a model with large curvature $\Omega_K = \pm 0.1$.
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The abstract, sentence by sentence
The growth of large-scale structure, together with the geometrical information of cosmic expansion history and cosmological distances, can be used to obtain constraints on the spatial curvature of the universe that probes the early universe physics, whereas modeling the nonlinear growth in a nonflat universe is still challenging due to computational expense of simulations in a high-dimensional cosmological parameter space. In this paper, we develop an approximate method to compute the halo-matter and halo-auto power spectra for nonflat $\Lambda$CDM model, from quantities representing the nonlinear evolution of the corresponding flat $\Lambda$CDM model, based on the separate universe (SU) method. By utilizing the fact that the growth response to long-wavelength fluctuations (equivalently the curvature), $T_{\delta_{\rm b}}(k)$, is approximated by the response to the Hubble parameter, $T_h(k)$, our method allows one to estimate the nonlinear power spectra in a nonflat universe efficiently from the power spectra of the flat universe. We use $N$-body simulations to show that the estimator can provide the halo-matter (halo-auto) power spectrum at $\sim 1\%$ ($\sim 2\%$ ) accuracy up to $k \simeq 3 (1) \, h {\rm Mpc}^{-1}$ even for a model with large curvature $\Omega_K = \pm 0.1$. Using the estimator we can extend the prediction of the existing emulators such as Dark Emulator to nonflat models without degrading their accuracy. Since the response to long-wavelength fluctuations is also a key quantity for estimating the super sample covariance (SSC), we discuss that the approximate identity $T_{\delta_{\rm b}}(k) \approx T_h(k)$ can be used to calculate the SSC terms analytically.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The growth of large-scale structure, together with the geometrical information of cosmic expansion history and cosmological distances, can be used to obtain constraints on the spatial curvature of the universe that probes the early universe physics, whereas modeling the nonlinear growth in a nonflat universe is still challenging due to computational expense of simulations in a high-dimensional cosmological parameter space. | background 0.85 | 0.05 | 0.04 | asserted 0.97 |
| s1 | In this paper, we develop an approximate method to compute the halo-matter and halo-auto power spectra for nonflat $\Lambda$CDM model, from quantities representing the nonlinear evolution of the corresponding flat $\Lambda$CDM model, based on the separate universe (SU) method. | contribution 0.93 | 0.96 | 0.21 | asserted 1.00 |
| s2 | By utilizing the fact that the growth response to long-wavelength fluctuations (equivalently the curvature), $T_{\delta_{\rm b}}(k)$, is approximated by the response to the Hubble parameter, $T_h(k)$, our method allows one to estimate the nonlinear power spectra in a nonflat universe efficiently from the power spectra of the flat universe. | method 0.99 | 0.71 | 0.22 | asserted 0.70 |
| s3 | We use $N$-body simulations to show that the estimator can provide the halo-matter (halo-auto) power spectrum at $\sim 1\%$ ($\sim 2\%$ ) accuracy up to $k \simeq 3 (1) \, h {\rm Mpc}^{-1}$ even for a model with large curvature $\Omega_K = \pm 0.1$. | result 1.00 | 0.96 | 0.44 | asserted 0.99 |
| s4 | Using the estimator we can extend the prediction of the existing emulators such as Dark Emulator to nonflat models without degrading their accuracy. | result 0.47 | 0.85 | 0.20 | asserted 0.63 |
| s5 | Since the response to long-wavelength fluctuations is also a key quantity for estimating the super sample covariance (SSC), we discuss that the approximate identity $T_{\delta_{\rm b}}(k) \approx T_h(k)$ can be used to calculate the SSC terms analytically. | contribution 0.50 | 0.62 | 0.07 | hedged possibility 0.72 |
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The paper
Original abstract
The growth of large-scale structure, together with the geometrical information of cosmic expansion history and cosmological distances, can be used to obtain constraints on the spatial curvature of the universe that probes the early universe physics, whereas modeling the nonlinear growth in a nonflat universe is still challenging due to computational expense of simulations in a high-dimensional cosmological parameter space. In this paper, we develop an approximate method to compute the halo-matter and halo-auto power spectra for nonflat $\Lambda$CDM model, from quantities representing the nonlinear evolution of the corresponding flat $\Lambda$CDM model, based on the separate universe (SU) method. By utilizing the fact that the growth response to long-wavelength fluctuations (equivalently the curvature), $T_{\delta_{\rm b}}(k)$, is approximated by the response to the Hubble parameter, $T_h(k)$, our method allows one to estimate the nonlinear power spectra in a nonflat universe efficiently from the power spectra of the flat universe. We use $N$-body simulations to show that the estimator can provide the halo-matter (halo-auto) power spectrum at $\sim 1\%$ ($\sim 2\%$ ) accuracy up to $k \simeq 3 (1) \, h {\rm Mpc}^{-1}$ even for a model with large curvature $\Omega_K = \pm 0.1$. Using the estimator we can extend the prediction of the existing emulators such as Dark Emulator to nonflat models without degrading their accuracy. Since the response to long-wavelength fluctuations is also a key quantity for estimating the super sample covariance (SSC), we discuss that the approximate identity $T_{\delta_{\rm b}}(k) \approx T_h(k)$ can be used to calculate the SSC terms analytically.
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How the literature uses it
1 arXiv paper cite this in 1 sentence
What it cites · 49 sentences without a confident label
Contests 1 paper
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We stress that we included the terms proportional to $I_X^2(k)$ in the parentheses of Eq. ([ref]), which were missing in Ref. [ref] .
CosmoLike - Cosmological Likelihood Analyses for Photometric Galaxy Surveys · Preliminary · contest 0.84
Builds on 1 paper
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This work is a sequel of our previous research [ref] , in which we proposed the approximate method for predicting the nonlinear matter power spectrum for nonflat model.
Separate universe approach to evaluate nonlinear matter power spectrum for non-flat $\Lambda$CDM model · conclusion · 0.96
Uses the method or tool of 16 papers
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We use Halofit in Smith et al. (Smith+03) [ref] and Takahashi et al. (Takahashi+12) [ref] to compute $T_h^mm(k)$ and $P_mm(k)$ in Eq. ([ref]), respectively.
Stable clustering, the halo model and nonlinear cosmological power spectra · Total response · 0.98
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We use Halofit in Smith et al. (Smith+03) [ref] and Takahashi et al. (Takahashi+12) [ref] to compute $T_h^mm(k)$ and $P_mm(k)$ in Eq. ([ref]), respectively.
Revising the Halofit Model for the Nonlinear Matter Power Spectrum · Total response · 0.98
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Our simulations follow the method in [ref] .
1981.09504 · $N$-body simulations · 1.00
Uses data or values from 13 papers
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and $1501/1323$ is the linear limit of $G_2(k)/2$ for the matter power spectrum [ref] , derived in an Einstein-de Sitter cosmology.
The angle-averaged squeezed limit of nonlinear matter N-point functions · SU approach for $P_mm(k;Ω_K)$ · 0.81
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Here the cosmological parameters for the “fiducial” model are chosen to be consistent with those for the Planck 2015 best-fit cosmology [ref] .
Planck 2015 results. XIII. Cosmological parameters · $N$-body simulations · 0.98
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These values correspond to the fiducial vaules of SDSS “CMASS1” sample in Ref. [ref] except for $σ_logM$, for which we use $σ_logM = 0.5$ instead of the fiducial value $σ_logM = 0.7919$.
Cosmological inference from emulator based halo model I: Validation tests with HSC and SDSS mock catalogs · Mock catalogs of galaxies in simulations · 0.96
Cites as support 3 papers
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As shown numerically in Refs. [ref] (also as will be shown in Fig. [ref]), these two responses agree well even in the nonlinear regime: $T_^mm(k) ≃T_h^mm(k)$.
Separate universe approach to evaluate nonlinear matter power spectrum for non-flat $\Lambda$CDM model · SU approach for $P_mm(k;Ω_K)$ · 0.98
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As shown numerically in Refs. [ref] (also as will be shown in Fig. [ref]), these two responses agree well even in the nonlinear regime: $T_^mm(k) ≃T_h^mm(k)$.
Super-Sample Signal · SU approach for $P_mm(k;Ω_K)$ · 0.98
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Assuming that the cosmological dependence is fully encoded in $𝒫_gm$ and that the galaxy profile around halos in physical scale and the mean HOD are given irrespective of the cosmological model, which is partly validated in Ref [ref] , one can trivially derive
Responses of Halo Occupation Distributions: a new ingredient in the halo model & the impact on galaxy bias · The response of galaxy-matter power spectrum · 0.99
Cites as background 20 papers
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The effect of curvature on structure formation can be identified with the very long-wavelength density fluctuations in the model based on the separate universe (SU) approach [ref] .
Power Spectrum Super-Sample Covariance · Introduction · 0.84
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The effect of curvature on structure formation can be identified with the very long-wavelength density fluctuations in the model based on the separate universe (SU) approach [ref] .
Super-Sample Covariance in Simulations · Introduction · 0.84
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The effect of curvature on structure formation can be identified with the very long-wavelength density fluctuations in the model based on the separate universe (SU) approach [ref] .
Super-Sample Signal · Introduction · 0.84
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