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Evolution Equation for Non-linear Cosmological Perturbations
Cosmology and Nongalactic Astrophysics · Submitted 23 May 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our approach can therefore reproduce the main features of the renormalized perturbation theory and (time)-renormalization group approaches to the study of non-linear cosmological perturbations.
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The abstract, sentence by sentence
We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations. Starting from the perturbed Einstein equations, we integrate out the non-relativistic degrees of freedom of the cosmic fluid and obtain a single closed equation for the gravitational potential. We then verify the validity of the new equation by comparing its approximate solutions to known results in the theory of non-linear cosmological perturbations. First, we show explicitly that the perturbative solution of our equation matches the standard perturbative solutions. Next, using the mean field approximation to the equation, we show that its solution reproduces in a simple way the exponential suppression of the non-linear propagator on small scales due to the velocity dispersion. Our approach can therefore reproduce the main features of the renormalized perturbation theory and (time)-renormalization group approaches to the study of non-linear cosmological perturbations. We conclude by a preliminary discussion of the nature of the full solutions of the equation and their significance.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations. | contribution 1.00 | 0.94 | 0.11 | asserted 1.00 |
| s1 | Starting from the perturbed Einstein equations, we integrate out the non-relativistic degrees of freedom of the cosmic fluid and obtain a single closed equation for the gravitational potential. | method 0.96 | 0.96 | 0.07 | asserted 1.00 |
| s2 | We then verify the validity of the new equation by comparing its approximate solutions to known results in the theory of non-linear cosmological perturbations. | method 0.82 | 0.95 | 0.08 | asserted 0.98 |
| s3 | First, we show explicitly that the perturbative solution of our equation matches the standard perturbative solutions. | result 0.76 | 0.94 | 0.07 | asserted 1.00 |
| s4 | Next, using the mean field approximation to the equation, we show that its solution reproduces in a simple way the exponential suppression of the non-linear propagator on small scales due to the velocity dispersion. | result 0.95 | 0.95 | 0.12 | asserted 1.00 |
| s5 | Our approach can therefore reproduce the main features of the renormalized perturbation theory and (time)-renormalization group approaches to the study of non-linear cosmological perturbations. | interpretation 0.85 | 0.80 | 0.47 | hedged possibility 0.64 |
| s6 | We conclude by a preliminary discussion of the nature of the full solutions of the equation and their significance. | future work 0.77 | 0.69 | 0.16 | unclear 0.79 |
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The paper
Original abstract
We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations. Starting from the perturbed Einstein equations, we integrate out the non-relativistic degrees of freedom of the cosmic fluid and obtain a single closed equation for the gravitational potential. We then verify the validity of the new equation by comparing its approximate solutions to known results in the theory of non-linear cosmological perturbations. First, we show explicitly that the perturbative solution of our equation matches the standard perturbative solutions. Next, using the mean field approximation to the equation, we show that its solution reproduces in a simple way the exponential suppression of the non-linear propagator on small scales due to the velocity dispersion. Our approach can therefore reproduce the main features of the renormalized perturbation theory and (time)-renormalization group approaches to the study of non-linear cosmological perturbations. We conclude by a preliminary discussion of the nature of the full solutions of the equation and their significance.
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References
How the literature uses it
8 arXiv papers cite this in 9 sentences
Papers citing it · 5 sentences without a confident label
Uses its method or tool 1 paper
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We thus adopt the so-called weak-field approximation [ref] , which allows us to probe structures even at very non-linear scales, provided that velocities are still small [ref] .
Structure formation in an anisotropic universe: Eulerian perturbation theory · Newtonian limit and perturbed variables · 0.90
Compares with it 2 papers
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Our weak-field expansion scheme is in agreement with the one of [ref] , whereas it differs in subleading terms from the schemes of [ref] .
A new approach to cosmological structure formation with massive neutrinos · Definitions and weak-field expansion · 1.00
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Our double expansion scheme is in agreement with the one as employed in [ref] , whereas it differs in the treatment of subleading terms (according to our counting) from the one of [ref] .
General relativistic weak-field limit and Newtonian N-body simulations · Weak-field expansion scheme · 1.00
Cites it as background 1 paper
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Other methods have been proposed in Refs. [ref] .
Symmetries and Consistency Relations in the Large Scale Structure of the Universe · Introduction · 0.90
What it cites · 2 sentences without a confident label
Compares with 1 paper
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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] .
Multi-Point Propagators for Non-Gaussian Initial Conditions · Comparison to the RPT and RG methods · 1.00
Cites as background 1 paper
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With these assumptions, the relevant Einstein equations are (see, for instance, Ref. [ref] ) (00): 3^̋2+ 2∇^2 Ψ= ρ u_0^2 , (i0): ∇_i Ψ'+ ∇̋_iΨ= 1/2 ρ u_0 u_i , (ij): (2 Ψ”+6Ψ̋' -2 (^̋2-2 a”/a)Ψ+ (∇Ψ)^2-∇^2(Ψ-Φ))δ_ij +∇_i∇_j(Ψ-Φ)-2∇_iΨ∇_jΨ= ρ u_i u_j .
Non-Gaussianity and the Cosmic Microwave Background Anisotropies · The non-perturbative equation for the gravitational potential · 0.87
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