Next-to-leading resummations in cosmological perturbation theory

Anselmi, Stefano; Matarrese, S.; Pietroni, Massimo

doi:10.1088/1475-7516/2011/06/015

Cited by 39 publications

(81 citation statements)

References 29 publications

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“…This ensures a good behavior of this quantity in the nonlinear regime, which has been checked against numerical simulations (Crocce & Scoccimarro 2006a;, and expresses a well-understood "sweeping effect" associated with the random transport of density structures by largescale velocity flows (Valageas 2007b;Bernardeau & Valageas 2008. Another advantage of this approach is that its extensions to high-order quantities , to non-Gaussian initial conditions , and to higher perturbative orders (Anselmi et al 2011), have already been studied.…”

Section: Dependence On the Perturbative Schemementioning

confidence: 82%

Combining perturbation theories with halo models for the matter bispectrum

Valageas

Nishimichi

2011

A&A

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Aims. We investigate how unified models should be built to be able to predict the matter-density bispectrum (and power spectrum) from very large to small scales and that are at the same time consistent with perturbation theory at low k and with halo models at high k. Methods. We use a Lagrangian framework to decompose the bispectrum into "3-halo", "2-halo", and "1-halo" contributions, related to "perturbative" and "non-perturbative" terms. We describe a simple implementation of this approach and present a detailed comparison with numerical simulations. Results. We show that the 1-halo and 2-halo contributions contain counterterms that ensure their decay at low k, as required by physical constraints, and allow a better match to simulations. Contrary to the power spectrum, the standard 1-loop perturbation theory can be used for the perturbative 3-halo contribution because it does not grow too fast at high k. Moreover, it is much simpler and more accurate than two resummation schemes investigated in this paper. We obtain a good agreement with numerical simulations on both large and small scales, but the transition scales are poorly described by the simplest implementation. This cannot be amended by simple modifications to the halo parameters, but we show how it can be corrected for the power spectrum and the bispectrum through a simple interpolation scheme that is restricted to this intermediate regime. Then, we reach an accuracy on the order of 10% on mildly and highly nonlinear scales, while an accuracy on the order of 1% is obtained on larger weakly nonlinear scales. This also holds for the real-space two-point correlation function.

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Section: Dependence On the Perturbative Schemementioning

confidence: 82%

Combining perturbation theories with halo models for the matter bispectrum

Valageas

Nishimichi

2011

A&A

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“…(25) with the approximation (28) asḠ ab (k; η, η ), which we will use in (27). As it was discussed thoroughly in [22], the solutionḠ ab (k; η, η ) is exact both in the low and in the large k limits. At low k it reproduces the 1-loop propagatorḠ…”

Section: The Evolution Equationsmentioning

confidence: 99%

“…Notice that the terms containing the Dirac delta in (24) and (25) where not written in [22], because in that paper we always considered propagators at different times. Here, on the other hand, those terms are important when the propagator is inside a time integral, as in the second line of eq.…”

Section: The Evolution Equationsmentioning

confidence: 99%

“…A similar approach was already presented in ref. [22] for the propagator, where it was used to reproduce the CS result, and also to include next-to-leading corrections. Here we derive the relevant equation for the PS and, after implementing an approximation analogous to the one leading to the CS result, we derive its behavior in the large k or, better, large y, limit.…”

Section: Introductionmentioning

confidence: 99%

“…One is the same entering the equation for the propagator, and was already discussed in ref. [22]. A computation of this kernel function at 1-loop provides, by virtue of our evolution equation, the CS propagator at all loop order, as well as part of the leading corrections to the PS.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear power spectrum from resummed perturbation theory: a leap beyond the BAO scale

Anselmi

Pietroni

2012

J. Cosmol. Astropart. Phys.

Self Cite

108

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Abstract. A new computational scheme for the nonlinear cosmological matter power spectrum (PS) is presented. Our method is based on evolution equations in time, which can be cast in a form extremely convenient for fast numerical evaluations. A nonlinear PS is obtained in a time comparable to that needed for a simple 1-loop computation, and the numerical implementation is very simple. Our results agree with N-body simulations at the percent level in the BAO range of scales, and at the few-percent level up to k 1 h/Mpc at z > ∼ 0.5, thereby opening the possibility of applying this tool to scales interesting for weak lensing. We clarify the approximations inherent to this approach as well as its relations to previous ones, such as the Time Renormalization Group, and the multi-point propagator expansion. We discuss possible lines of improvements of the method and its intrinsic limitations by multi streaming at small scales and low redshifts.

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Cosmic Structure Formation with Kinetic Field Theory

et al. 2019

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Kinetic Field Theory (KFT) is a statistical field theory for an ensemble of point-like classical particles in or out of equilibrium. We review its application to cosmological structure formation. Beginning with the construction of the generating functional of the theory, we describe in detail how the theory needs to be adapted to reflect the expanding spatial background and the homogeneous and isotropic, correlated initial conditions for cosmic structures. Based on the generating functional, we develop three main approaches to non-linear, late-time cosmic structures, which rest either on the Taylor expansion of an interaction operator, suitable averaging procedures for the interaction term, or a resummation of perturbation terms. We show how an analytic, parameterfree equation for the non-linear cosmic power spectrum can be derived.We explain how the theory can be used to derive the density profile of gravitationally bound structures and use it to derive power spectra of cosmic velocity densities. We further clarify how KFT relates to the BBGKY hierarchy. We then proceed to apply kinetic field theory to fluids, introduce a reformulation of KFT in terms of macroscopic quantities which leads to a resummation scheme, and use this to describe mixtures of gas and dark matter. We discuss how KFT can be applied to study cosmic structure formation with modified theories of gravity. As an example for an application to a noncosmological particle ensemble, we show results on the spatial correlation function of cold Rydberg atoms derived from KFT.

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Next-to-leading resummations in cosmological perturbation theory

Cited by 39 publications

References 29 publications

Combining perturbation theories with halo models for the matter bispectrum

Combining perturbation theories with halo models for the matter bispectrum

Nonlinear power spectrum from resummed perturbation theory: a leap beyond the BAO scale

Cosmic Structure Formation with Kinetic Field Theory

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