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Efficient exploration of cosmology dependence in the EFT of LSS
Cosmology and Nongalactic Astrophysics · Submitted 11 Jun 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim When applied to cosmologies that are within 3$\sigma$ of the Planck best-fit model, the first method evaluates the power spectrum in a few minutes on a laptop, with results that have 1\% or better precision, while with the Taylor expansion the same quantity is instantly generated with similar precision.
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The abstract, sentence by sentence
The most effective use of data from current and upcoming large scale structure~(LSS) and CMB observations requires the ability to predict the clustering of LSS with very high precision. The Effective Field Theory of Large Scale Structure (EFTofLSS) provides an instrument for performing analytical computations of LSS observables with the required precision in the mildly nonlinear regime. In this paper, we develop efficient implementations of these computations that allow for an exploration of their dependence on cosmological parameters. They are based on two ideas. First, once an observable has been computed with high precision for a reference cosmology, for a new cosmology the same can be easily obtained with comparable precision just by adding the difference in that observable, evaluated with much less precision. Second, most cosmologies of interest are sufficiently close to the Planck best-fit cosmology that observables can be obtained from a Taylor expansion around the reference cosmology. These ideas are implemented for the matter power spectrum at two loops and are released as public codes. When applied to cosmologies that are within 3$\sigma$ of the Planck best-fit model, the first method evaluates the power spectrum in a few minutes on a laptop, with results that have 1\% or better precision, while with the Taylor expansion the same quantity is instantly generated with similar precision. The ideas and codes we present may easily be extended for other applications or higher-precision results.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The most effective use of data from current and upcoming large scale structure~(LSS) and CMB observations requires the ability to predict the clustering of LSS with very high precision. | background 1.00 | 0.06 | 0.03 | asserted 1.00 |
| s1 | The Effective Field Theory of Large Scale Structure (EFTofLSS) provides an instrument for performing analytical computations of LSS observables with the required precision in the mildly nonlinear regime. | background 0.99 | 0.07 | 0.03 | asserted 1.00 |
| s2 | In this paper, we develop efficient implementations of these computations that allow for an exploration of their dependence on cosmological parameters. | contribution 1.00 | 0.95 | 0.15 | asserted 1.00 |
| s3 | They are based on two ideas. | method 0.90 | 0.34 | 0.02 | asserted 0.77 |
| s4 | First, once an observable has been computed with high precision for a reference cosmology, for a new cosmology the same can be easily obtained with comparable precision just by adding the difference in that observable, evaluated with much less precision. | method 0.98 | 0.59 | 0.12 | asserted 0.94 |
| s5 | Second, most cosmologies of interest are sufficiently close to the Planck best-fit cosmology that observables can be obtained from a Taylor expansion around the reference cosmology. | method 0.96 | 0.26 | 0.07 | asserted 0.77 |
| s6 | These ideas are implemented for the matter power spectrum at two loops and are released as public codes. | contribution 0.92 | 0.94 | 0.14 | asserted 1.00 |
| s7 | When applied to cosmologies that are within 3$\sigma$ of the Planck best-fit model, the first method evaluates the power spectrum in a few minutes on a laptop, with results that have 1\% or better precision, while with the Taylor expansion the same quantity is instantly generated with similar precision. | result 1.00 | 0.94 | 0.45 | asserted 1.00 |
| s8 | The ideas and codes we present may easily be extended for other applications or higher-precision results. | future work 0.97 | 0.34 | 0.12 | hedged possibility 1.00 |
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The paper
Original abstract
The most effective use of data from current and upcoming large scale structure~(LSS) and CMB observations requires the ability to predict the clustering of LSS with very high precision. The Effective Field Theory of Large Scale Structure (EFTofLSS) provides an instrument for performing analytical computations of LSS observables with the required precision in the mildly nonlinear regime. In this paper, we develop efficient implementations of these computations that allow for an exploration of their dependence on cosmological parameters. They are based on two ideas. First, once an observable has been computed with high precision for a reference cosmology, for a new cosmology the same can be easily obtained with comparable precision just by adding the difference in that observable, evaluated with much less precision. Second, most cosmologies of interest are sufficiently close to the Planck best-fit cosmology that observables can be obtained from a Taylor expansion around the reference cosmology. These ideas are implemented for the matter power spectrum at two loops and are released as public codes. When applied to cosmologies that are within 3$\sigma$ of the Planck best-fit model, the first method evaluates the power spectrum in a few minutes on a laptop, with results that have 1\% or better precision, while with the Taylor expansion the same quantity is instantly generated with similar precision. The ideas and codes we present may easily be extended for other applications or higher-precision results.
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References
How the literature uses it
30 arXiv papers cite this in 48 sentences
Papers citing it · 15 sentences without a confident label
Uses its method or tool 6 papers
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In order to do this in an effective way, following the idea initially developed in [ref] , we have used the fact that the range of parameter space that is consistent with the observational data is small enough to approximate the dependence of the EFTofLSS power spectrum on cosmological parameters with a Taylor expansion around a reference cosmology.
Efficient Cosmological Analysis of the SDSS/BOSS data from the Effective Field Theory of Large-Scale Structure · Conclusions · 0.99
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We include the IR-resummation of [ref] , which removes large oscillations in the power spectrum.
The Effective Field Theory of Large Scale Structure at Three Loops · Introduction · 1.00
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For both the Taylor-$A$PT and EoM-$A$PT models, we implemented the resummation scheme presented in [ref] [equation] in which $P_X_j(k)||_1-j$ states for each one of the loop terms of order $j$ that appear in the final EFT calculation Eq. ([ref]) and are resummed at order $1-j$.
The Effective Field Theory and Perturbative Analysis for Log-Density Fields · Effect of the IR resummation · 0.99
Compares with it 2 papers
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Finally, we compare our MLP surrogate model to a Taylor series expansion, a common alternative for approximating EFT models for redshift space power spectra [ref] .
Neural Network Acceleration of Large-scale Structure Theory Calculations · Comparison with Taylor Expansions · 0.87
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Although we share the same motivation and goals with Refs. [ref] , our exact method is technically completely different and therefore complementary in practice, providing a useful path for cross-checks.
FFT-PT: Reducing the two-loop large-scale structure power spectrum to low-dimensional radial integrals · Introduction · 0.93
Cites it as background 22 papers
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This very objective, restricted to the context of analytic predictions, is approached by the research program called the Effective Field Theory of Large-Scale Structure (EFTofLSS) [ref] : the idea is to study LSS in the mildly non-linear regime by correctly describing the effect of ultraviolet (UV) modes on long-wavelength observables.
Baryonic effects in the Effective Field Theory of Large-Scale Structure and an analytic recipe for lensing in CMB-S4 · Introduction · 0.83
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While in the last couple of decades numerical simulations have been the main tool to predict the clustering of large scale structures, in the last few years the advent of the so-called Effective Field Theory of Large Scale Structures (EFTofLSS) [ref] has allowed the development of an analytic approach that is able to predict the Large Scale Structure (LSS) correlation functions with exquisite precision in the so-called mildly non-linear regime, where density fluctuations are still safely smaller than one [ref] .
Very Massive Tracers and Higher Derivative Biases · Introduction and main ideas · 0.90
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In recent years, a large activity has occurred in this small field, see for example [ref] .
An effective description of dark matter and dark energy in the mildly non-linear regime · Introduction · 0.83
What it cites · 93 sentences without a confident label
Uses the method or tool of 14 papers
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In a separate step, the output files from , along with $Ω_m$ and desired redshift, are then used as input for the IR-resummation code [], also released with this work. implements the IR-resummation technique developed in [ref] to incorporate the leading effect of large-scale displacements on the perturbative predictions of the EFTofLSS.
The IR-resummed Effective Field Theory of Large Scale Structures · ResumEFT · 0.99
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In a separate step, the output files from , along with $Ω_m$ and desired redshift, are then used as input for the IR-resummation code [], also released with this work. implements the IR-resummation technique developed in [ref] to incorporate the leading effect of large-scale displacements on the perturbative predictions of the EFTofLSS.
The One-Loop Matter Bispectrum in the Effective Field Theory of Large Scale Structures · ResumEFT · 0.99
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Similarly to [ref] , in this work we express the EFTofLSS parameters $c_s(1)^2$, $c_1$ in units of $(k_NL/2 hMpc^-1)^2$ and $c_4$ in units of $(k_NL/2 hMpc^-1)^4$, and determine $c_s(2)^2$ by matching the one-loop and two-loop EFTofLSS matter power spectrum at the renormalization scale $k_ren = 0.02$.
Precision Comparison of the Power Spectrum in the EFTofLSS with Simulations · The two-loop power spectrum · 0.96
Uses data or values from 1 paper
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More formally, the point $θ$ defines an $nσ$-cosmology if it is contained in a thin shell around the 5-dimensional hyper-ellipsoid defined by [equation] Here, $Σ_5^-1$ represents the inverse of the $5 ×5$ covariance submatrix obtained by selecting the appropriate rows and columns from the covariance matrix for the combination “TT+TE+EE+lowP” in [ref] , giving a reasonable account for the covariances between our 5 chosen parameters when all others are marginalized over [For easy reference, $1σ$ marginalized uncertainties on each parameter from Eq. [ref] are given below: [equation] ]: [equation] In Eq. [ref], $χ_5^2(p)$ is the quantile function for probability $p$ of the chi-squared distribution with 5 degrees of freedom.
Planck 2015 results. XIII. Cosmological parameters · Tests and performance · 0.95
Compares with 1 paper
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We anticipate here that in order to obtain $P_EFT-2-loop$ within 1% of the nonlinear power spectrum obtained from the emulator code [ref] [<http://www.hep.anl.gov/cosmology/CosmicEmu/emu.html>.
The Coyote Universe Extended: Precision Emulation of the Matter Power Spectrum · Tests · 0.83
Cites as background 29 papers
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Several ways to make the integration more efficient have been proposed [ref] .
FAST-PT: a novel algorithm to calculate convolution integrals in cosmological perturbation theory · : Efficient exploration of cosmology-dependence in the EFTofLSS · 0.82
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Several ways to make the integration more efficient have been proposed [ref] .
RegPT: Direct and fast calculation of regularized cosmological power spectrum at two-loop order · : Efficient exploration of cosmology-dependence in the EFTofLSS · 0.82
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Several ways to make the integration more efficient have been proposed [ref] .
Cosmological perturbation theory at three-loop order · : Efficient exploration of cosmology-dependence in the EFTofLSS · 0.82
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