Flowing with time: a new approach to non-linear cosmological perturbations

Pietroni, Massimo

doi:10.1088/1475-7516/2008/10/036

Cited by 229 publications

(383 citation statements)

References 45 publications

(222 reference statements)

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“…As discussed in [14], the above approximation is accurate at better than 1% level in the whole range of redshifts and scales we are interested in. If we consider the linear equations (obtained in the e η γ abc → 0 limit) we can define the linear retarded propagator as the operator giving the evolution of the field ϕ a from η in to η,…”

Section: Nonlinear Power Spectrum From Resummed Perturbation Theory: mentioning

confidence: 79%

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

Anselmi

Pietroni

2012

J. Cosmol. Astropart. Phys.

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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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Section: Nonlinear Power Spectrum From Resummed Perturbation Theory: mentioning

confidence: 79%

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

Anselmi

Pietroni

2012

J. Cosmol. Astropart. Phys.

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108

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“…This might be achievable using either standard perturbation theory (e.g., Saito et al 2008) or a resummation scheme (see e.g., Crocce & Scoccimarro 2006;Pietroni 2008). It will be interesting, eventually, to investigate the degeneracy with the low-redshift physics (z < ∼ 20), such as reionization and dark energy, relevant if m ν < ∼ 0.01 eV.…”

Section: Discussionmentioning

confidence: 99%

CFHTLS weak-lensing constraints on the neutrino masses

Tereno

Schimd

Uzan

et al. 2009

A&A

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Context. Oscillation experiments yield strong evidence that at least some neutrinos are massive. As a hot dark-matter component, massive neutrinos should modify the expansion history of the Universe as well as the evolution of cosmological perturbations, in a different way from cold dark matter or dark energy. Aims. We use the latest release of CFHTLS cosmic-shear data to constrain the sum of the masses m ν of neutrinos, assuming three degenerate mass states. We also consider a joint analysis including other cosmological observables, notably CMB anisotropies, baryonic acoustic oscillations, and distance modulus from type Ia supernovae. Methods. Combining CAMB with a lensing code, we compute the aperture mass variance using a suitable recipe to deal with matter perturbations in the non-linear regime. The statistical analysis is performed by sampling an 8-dimensional likelihood on a regular grid as well as using the importance sampling technique. Results. We obtain the first constraint on neutrino masses based on cosmic-shear data, and combine CFHTLS with WMAP, SDSS, 2dFGRS, Gold-set, and SNLS data. The joint analysis yields 0.03 eV < m ν < 0.54 eV at the 95% confidence level. The preference for massive neutrinos vanishes when systematics are included.

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“…This has led to tremendous progress in structure formation theory in the last several decades. In particular, nonlinear perturbation theory (PT), both Eulerian and Lagrangian (Bernardeau et al 2002), has evolved into sophisticated forms (Crocce & Scoccimarro 2006a, 2006bBernardeau et al 2008;Matsubara 2008;Pietroni 2008;Taruya & Hiramatsu 2008) that could provide a very accurate estimation of the matter clustering in the weakly nonlinear regime. In the deeply nonlinear region, however, PT performs poorly.…”

Section: Introductionmentioning

confidence: 99%

Statistical Decoupling of a Lagrangian Fluid Parcel in Newtonian Cosmology

Wang

Szalay

2016

ApJ

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The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differential equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Consequently it is guaranteed that the one-point ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, and the dynamical system would recover the prediction of the Zel'dovich approximation (ZA) with the further assumption of the linearized continuity equation. For a weakly non-Gaussian field, the averaged tidal tensor could be expanded perturbatively as a function of all relevant dynamical variables whose coefficients are determined by the statistics of the field.

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Flowing with time: a new approach to non-linear cosmological perturbations

Cited by 229 publications

References 45 publications

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

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

CFHTLS weak-lensing constraints on the neutrino masses

Statistical Decoupling of a Lagrangian Fluid Parcel in Newtonian Cosmology

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