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Multi-Point Propagators for Non-Gaussian Initial Conditions
Cosmology and Nongalactic Astrophysics · Submitted 23 Jun 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show here how Renormalized Perturbation Theory (RPT) calculations applied to the quasi-linear growth of the large-scale structure can be carried on in presence of primordial non-Gaussian (PNG) initial conditions.
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The abstract, sentence by sentence
We show here how Renormalized Perturbation Theory (RPT) calculations applied to the quasi-linear growth of the large-scale structure can be carried on in presence of primordial non-Gaussian (PNG) initial conditions. It is explicitly demonstrated that the series reordering scheme proposed in Bernardeau, Crocce and Scoccimarro (2008) is preserved for non-Gaussian initial conditions. This scheme applies to the power spectrum and higher order spectra and is based on a reorganization of the contributing terms into sum of products of multi-point propagators. In case of PNG new contributing terms appear, the importance of which is discussed in the context of current PNG models. The properties of the building blocks of such resummation schemes, the multi-point propagators, are then investigated. It is first remarked that their expressions are left unchanged at one-loop order irrespectively of statistical properties of the initial field. We furthermore show that the high-momemtum limit of each of these propagators can be explicitly computed even for arbitrary initial conditions. They are found to be damped by an exponential cutoff whose expression is directly related to the moment generating function of the one-dimensional displacement field. This extends what had been established for multi-point propagators for Gaussian initial conditions. Numerical forms of the cut-off are shown for the so-called local model of PNG.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We show here how Renormalized Perturbation Theory (RPT) calculations applied to the quasi-linear growth of the large-scale structure can be carried on in presence of primordial non-Gaussian (PNG) initial conditions. | contribution 0.99 | 0.92 | 0.30 | asserted 1.00 |
| s1 | It is explicitly demonstrated that the series reordering scheme proposed in Bernardeau, Crocce and Scoccimarro (2008) is preserved for non-Gaussian initial conditions. | result 0.94 | 0.81 | 0.30 | asserted 1.00 |
| s2 | This scheme applies to the power spectrum and higher order spectra and is based on a reorganization of the contributing terms into sum of products of multi-point propagators. | method 0.55 | 0.20 | 0.11 | asserted 1.00 |
| s3 | In case of PNG new contributing terms appear, the importance of which is discussed in the context of current PNG models. | contribution 0.46 | 0.72 | 0.11 | asserted 0.70 |
| s4 | The properties of the building blocks of such resummation schemes, the multi-point propagators, are then investigated. | contribution 0.92 | 0.78 | 0.07 | asserted 0.74 |
| s5 | It is first remarked that their expressions are left unchanged at one-loop order irrespectively of statistical properties of the initial field. | result 0.99 | 0.57 | 0.10 | asserted 1.00 |
| s6 | We furthermore show that the high-momemtum limit of each of these propagators can be explicitly computed even for arbitrary initial conditions. | result 0.57 | 0.93 | 0.12 | asserted 1.00 |
| s7 | They are found to be damped by an exponential cutoff whose expression is directly related to the moment generating function of the one-dimensional displacement field. | result 1.00 | 0.92 | 0.17 | asserted 1.00 |
| s8 | This extends what had been established for multi-point propagators for Gaussian initial conditions. | interpretation 0.56 | 0.43 | 0.11 | asserted 0.99 |
| s9 | Numerical forms of the cut-off are shown for the so-called local model of PNG. | result 0.82 | 0.89 | 0.06 | asserted 1.00 |
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The paper
Original abstract
We show here how Renormalized Perturbation Theory (RPT) calculations applied to the quasi-linear growth of the large-scale structure can be carried on in presence of primordial non-Gaussian (PNG) initial conditions. It is explicitly demonstrated that the series reordering scheme proposed in Bernardeau, Crocce and Scoccimarro (2008) is preserved for non-Gaussian initial conditions. This scheme applies to the power spectrum and higher order spectra and is based on a reorganization of the contributing terms into sum of products of multi-point propagators. In case of PNG new contributing terms appear, the importance of which is discussed in the context of current PNG models. The properties of the building blocks of such resummation schemes, the multi-point propagators, are then investigated. It is first remarked that their expressions are left unchanged at one-loop order irrespectively of statistical properties of the initial field. We furthermore show that the high-momemtum limit of each of these propagators can be explicitly computed even for arbitrary initial conditions. They are found to be damped by an exponential cutoff whose expression is directly related to the moment generating function of the one-dimensional displacement field. This extends what had been established for multi-point propagators for Gaussian initial conditions. Numerical forms of the cut-off are shown for the so-called local model of PNG.
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References
How the literature uses it
14 arXiv papers cite this in 29 sentences
Papers citing it · 23 sentences without a confident label
Compares with it 2 papers
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We have reproduced the results of [ref] in the case of Gaussian initial conditions and [ref] in the presence of initial non–Gaussianities for the special class of $n$–point propagators that was introduced in [ref] .
Large-k Limit of Multi-Point Propagators in the RG Formalism · Conclusions · 0.85
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In the RPT method the order is different, as is made particulary clear when using the so-called $α$ method [ref] .
Evolution Equation for Non-linear Cosmological Perturbations · Comparison to the RPT and RG methods · 1.00
Cites it as support 1 paper
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Recent developments in the description of matter nonlinearities in Perturbation Theory (see [ref] ) can justify even our more optimistic choice of $k_max=0.15$ at $z=0$, also in the case of non-Gaussian initial conditions [ref] .
Effects and Detectability of Quasi-Single Field Inflation in the Large-Scale Structure and Cosmic Microwave Background · Fisher matrix · 0.96
Cites it as background 3 papers
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Simulations and perturbation theory calculations show that there are interesting PNG corrections for the mass power spectrum and bispectrum (see [ref] and Fig. [ref]), and even down to the nonlinear regime [ref] , but we won't explore those here.
Large-scale Bias and Efficient Generation of Initial Conditions for Non-Local Primordial Non-Gaussianity · Comparison with Simulations · 0.84
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Further modification have been considered, such as, e.g., the “Closure Theory” [ref] , the “Time Renormalization Group” approach [ref] , and the “$Γ$-expansion approach” using Multi-Point Propagators [ref] .
An Application of Wiener Hermite Expansion to Non-linear Evolution of Dark Matter · Introduction · 0.97
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In Refs. [ref] , the bispectrum has been studied within the context of RPT.
The Bispectrum in the Effective Field Theory of Large Scale Structure · Conclusions · 0.97
What it cites · 61 sentences without a confident label
Builds on 2 papers
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This is a remarkable result that extends in a concrete and simple way the findings of [ref] for Gaussian initial conditions.
Multi-Point Propagators in Cosmological Gravitational Instability · The $α$-method · 1.00
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This is a remarkable result that extends in a concrete and simple way the findings of [ref] for Gaussian initial conditions.
Memory of Initial Conditions in Gravitational Clustering · The $α$-method · 1.00
Uses the method or tool of 2 papers
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A perturbative solution to Eq. ([ref]) can be obtained by expanding the fields in terms of the initial ones, [equation] such that, [equation] where we adopt the notation $_1…n≡_1+…+_n$ for vectors sums and where $^(n)$ are fully symmetric functions of the wave-vectors that can be obtained recursively in terms of $g_ij$ and $γ_ijk$ [ref] .
Large-Scale Structure of the Universe and Cosmological Perturbation Theory · The $Γ-$expansion · 0.86
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Following [ref] , the equations of motion can be written in a compact form with the use of the two component quantity $Ψ_i(,τ)$, defined as [equation] where the index $i=1,2$ selects the density or velocity components and which makes explicit use of the growing solution.
Transients from Initial Conditions: A Perturbative Analysis · The equations of motion · 0.93
Uses data or values from 1 paper
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This can be summarized as $h=0.7$, $Ω_m=0.279$, $Ω_b=0.0462$, $n_s=0.96$ and $σ_8≃0.81$ (see Sec. 3 in [ref] for more detail)
The Matter Bispectrum in N-body Simulations with non-Gaussian Initial Conditions · Predictions for the local model of PNG · 0.81
Compares with 2 papers
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In dashed line we show the result of standard perturbation theory at one-loop from [ref] .
The Matter Bispectrum in N-body Simulations with non-Gaussian Initial Conditions · Predictions for the local model of PNG · 0.98
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Comparing with the standard perturbative approach up to one-loop given in [ref] we see that his terms $B^I_112$, $B_111$, $B^I_222$, $B^I_123$, $B^I_122$, $B^II_122$, $B^II_113$, $B^II_112$ correspond to those in Eq. ([ref]) when the $Γ^(p)$ functions are taken at their lowest or “bare” order in Eq. ([ref]) (i.e. prior to any resummation).
1-loop Perturbative Corrections to the Matter and Galaxy Bispectrum with non-Gaussian Initial Conditions · The $Γ-$expansion · 1.00
Cites as background 9 papers
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Various resummation schemes have been proposed over the last few years to overcome those difficulties while aiming at providing tools for performing such calculations in a systematic way [ref] .
Renormalized Cosmological Perturbation Theory · Introduction · 0.87
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Various resummation schemes have been proposed over the last few years to overcome those difficulties while aiming at providing tools for performing such calculations in a systematic way [ref] .
Memory of Initial Conditions in Gravitational Clustering · Introduction · 0.87
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Various resummation schemes have been proposed over the last few years to overcome those difficulties while aiming at providing tools for performing such calculations in a systematic way [ref] .
Multi-Point Propagators in Cosmological Gravitational Instability · Introduction · 0.87
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