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Next-to-leading resummations in cosmological perturbation theory
Cosmology and Nongalactic Astrophysics · Submitted 19 Nov 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Using an exact evolution equation, we generalize this result, by showing that a class of next-to-leading corrections can also be resummed at all orders in perturbation theory.
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The abstract, sentence by sentence
One of the nicest results in cosmological perturbation theory is the analytical resummaton of the leading corrections at large momentum, which was obtained by Crocce and Scoccimarro for the propagator. Using an exact evolution equation, we generalize this result, by showing that a class of next-to-leading corrections can also be resummed at all orders in perturbation theory. The new corrections modify the propagator by a few percent in the Baryonic Acoustic Oscillation range of scales, and therefore cannot be neglected in resummation schemes aiming at an accuracy compatible with future generation galaxy surveys. Similar tools can be employed to derive improved approximations for the Power Spectrum.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | One of the nicest results in cosmological perturbation theory is the analytical resummaton of the leading corrections at large momentum, which was obtained by Crocce and Scoccimarro for the propagator. | background 1.00 | 0.03 | 0.04 | asserted 1.00 |
| s1 | Using an exact evolution equation, we generalize this result, by showing that a class of next-to-leading corrections can also be resummed at all orders in perturbation theory. | contribution 0.89 | 0.96 | 0.67 | asserted 1.00 |
| s2 | The new corrections modify the propagator by a few percent in the Baryonic Acoustic Oscillation range of scales, and therefore cannot be neglected in resummation schemes aiming at an accuracy compatible with future generation galaxy surveys. | interpretation 0.61 | 0.86 | 0.45 | asserted 1.00 |
| s3 | Similar tools can be employed to derive improved approximations for the Power Spectrum. | future work 0.83 | 0.42 | 0.05 | hedged possibility 0.87 |
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The paper
Original abstract
One of the nicest results in cosmological perturbation theory is the analytical resummaton of the leading corrections at large momentum, which was obtained by Crocce and Scoccimarro for the propagator. Using an exact evolution equation, we generalize this result, by showing that a class of next-to-leading corrections can also be resummed at all orders in perturbation theory. The new corrections modify the propagator by a few percent in the Baryonic Acoustic Oscillation range of scales, and therefore cannot be neglected in resummation schemes aiming at an accuracy compatible with future generation galaxy surveys. Similar tools can be employed to derive improved approximations for the Power Spectrum.
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References
How the literature uses it
18 arXiv papers cite this in 42 sentences
Papers citing it · 28 sentences without a confident label
Builds on it 1 paper
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[ref] for the function $Σ_ab(k;η,)$ to the mode-coupling function, $Φ_ac(k;η,)$.
Nonlinear Power Spectrum from Resummed Perturbation Theory: a Leap Beyond the BAO Scale · The eikonal limit · 1.00
Uses its method or tool 2 papers
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To this end we use of the resummation scheme proposed in [ref] .
Nonlinear effects of dark energy clustering beyond the acoustic scales · The power spectrum in the mildly nonlinear regime · 0.99
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In order to recover the proper momentum dependence for the nonlinear propagator at lower k, in [ref] we used the 1-loop expression for $H_ a$ in the evolution equation dgtot.
Nonlinear Power Spectrum from Resummed Perturbation Theory: a Leap Beyond the BAO Scale · The intermediate $k$ regime · 0.94
Cites it as background 8 papers
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[ref] we recall the main equations, introduce our formalism, and clarify the relation between the TRG approach of [ref] and the time-flow equations of [ref] , in Sect.
Galilean invariant resummation schemes of cosmological perturbations · Introduction · 0.88
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The propagator has been studied thoroughly in the recent literature [ref] .
The effect of massive neutrinos on the BAO peak · Nonlinear evolution of the BAO peak · 0.95
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After [ref] first presented their resummation scheme, a lot of progress has been made towards a better understanding of how long-wavelength modes effect smaller scales [ref] , but also different resummation schemes have been explored [ref] .
Renormalizing a Viscous Fluid Model for Large Scale Structure Formation · Introduction · 0.92
What it cites · 49 sentences without a confident label
Contests 1 paper
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As a result, the procedure illustrated in [ref] leads to a wrong prediction on the sign of the corrections to the CS propagator induced by the subleading corrections.
Nonlinear Evolution of Baryon Acoustic Oscillations · Discussion and conclusions · contest 0.93
Builds on 3 papers
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To extend the validity of this approach to $Λ$CDM, we will reinterpret the variable $η$ as the logarithm of the linear growth factor of the growing mode, i.e. [ref] , η=ln(D/D_in) , and we redefine the field in Eq. ([ref]) as ([ φ_1 ( k, η); φ_2 ( k, η) ]) ≡e^-η ( [ δ_m ( k, η); -θ( k, η)/H f ]) ,
Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations · Nonlinear fluid equations and the Propagator · 0.83
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To extend the validity of this approach to $Λ$CDM, we will reinterpret the variable $η$ as the logarithm of the linear growth factor of the growing mode, i.e. [ref] , η=ln(D/D_in) , and we redefine the field in Eq. ([ref]) as ([ φ_1 ( k, η); φ_2 ( k, η) ]) ≡e^-η ( [ δ_m ( k, η); -θ( k, η)/H f ]) ,
Large-Scale Structure of the Universe and Cosmological Perturbation Theory · Nonlinear fluid equations and the Propagator · 0.83
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To extend the validity of this approach to $Λ$CDM, we will reinterpret the variable $η$ as the logarithm of the linear growth factor of the growing mode, i.e. [ref] , η=ln(D/D_in) , and we redefine the field in Eq. ([ref]) as ([ φ_1 ( k, η); φ_2 ( k, η) ]) ≡e^-η ( [ δ_m ( k, η); -θ( k, η)/H f ]) ,
Memory of Initial Conditions in Gravitational Clustering · Nonlinear fluid equations and the Propagator · 0.83
Uses the method or tool of 4 papers
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Following the path-integral formulation of cosmological perturbation theory introduced in [ref] we can derive exact evolution equations for the propagator and for the PS.
Resumming Cosmic Perturbations · The non-linear propagator and its evolution · 0.91
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One can write Eqs. ([ref]) in a compact form [ref] .
Memory of Initial Conditions in Gravitational Clustering · Nonlinear fluid equations and the Propagator · 0.86
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We have tested two different approximations for the non-linear PS: the 1-loop approximation, and the result of the TRG evolution [ref] .
Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations · Discussion and conclusions · 0.87
Compares with 5 papers
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We stress again that the difference between the propagator computed along the lines described in this section and the one in [ref] is entirely due to the different interpolation procedures, while the classes of diagrams resummed are exactly the same.
Memory of Initial Conditions in Gravitational Clustering · Factorization and the Crocce-Scoccimarro propagator · 0.99
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Should the discrepancy mentioned in [ref] persist, it would imply that other effects should be taken into account.
Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations · Discussion and conclusions · 0.88
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Should the discrepancy mentioned in [ref] persist, it would imply that other effects should be taken into account.
Nonlinear Evolution of Baryon Acoustic Oscillations · Discussion and conclusions · 0.88
Cites as support 2 papers
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Different choices for the latter may give different results on the size of these corrections, but the sign is only determined by the assumption that the non-linear velocity PS is smaller than the linear one, which is verified in all consistent approximations (see, for instance, [ref] )
Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations · Discussion and conclusions · 1.00
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Different choices for the latter may give different results on the size of these corrections, but the sign is only determined by the assumption that the non-linear velocity PS is smaller than the linear one, which is verified in all consistent approximations (see, for instance, [ref] )
Chasing the non-linear evolution of matter power spectrum with numerical resummation method: solution of closure equations · Discussion and conclusions · 1.00
Cites as background 3 papers
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In this section we will give a short review of the formalism introduced and discussed in [ref] , and we will obtain the exact evolution equation for the propagator, which will be solved in various approximations in the remaining sections.
Resumming Cosmic Perturbations · The non-linear propagator and its evolution · 0.80
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In this Appendix we briefly review the Time-Remornalization Group approach (TRG) introduced in [ref] to compute the non linear PS.
Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations · Time-Remornalization Group equations for the non linear PS · 0.85
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Cosmological perturbation theory (hereafter, PT, for a review, see [ref] ) has attracted a renewed interest in the recent literature.
Large-Scale Structure of the Universe and Cosmological Perturbation Theory · Introduction · 1.00
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