The nonlinear evolution of rare events

Bernardeau, Francis

doi:10.1086/174121

Cited by 241 publications

(371 citation statements)

References 1 publication

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“…2 therein for a comparison of the Lagrangian and Eulerian definitions for the environment and implications for the structures inferred from that for chameleon theories. The Eulerian overdensity at time t is [46,47] …”

Section: Environmentmentioning

confidence: 99%

Modeling halo mass functions in chameleonf(R)gravity

et al. 2013

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On cosmological scales, observations of the cluster abundance currently place the strongest constraints on f (R) gravity. These constraints lie in the large-field limit, where the modifications of general relativity can correctly be modeled by setting the Compton wavelength of the scalar field to its background value. These bounds are, however, at the verge of penetrating into a regime where the modifications become nonlinearly suppressed due to the chameleon mechanism and cannot be described by this linearized approximation. For future constraints based on observations subjected to cluster abundance, it is therefore essential to consistently model the chameleon effect. We analyze descriptions of the halo mass function in chameleon f (R) gravity using a mass-and environmentdependent spherical collapse model in combination with excursion set theory and phenomenological fits to N -body simulations in the ΛCDM and f (R) gravity scenarios. Our halo mass functions consistently incorporate the chameleon suppression and cosmological parameter dependencies, improving upon previous formalisms and providing an important extension to N -body simulations for the application in consistent tests of gravity with observables sensitive to the abundance of clusters.

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Section: Environmentmentioning

confidence: 99%

Modeling halo mass functions in chameleonf(R)gravity

et al. 2013

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“…For instance, one finds that, for ambient field points, the probability of all three eigenvalues being positive is P (+ + +) = 0.08, and that of the configurations (+ + −) and (+ − −) is 0.84. Note, however, that these values depend strongly on the peak height, ν = δ/σ, of the region under consideration, the highest density peaks being predominantly spherical [29,30].…”

Section: Shearmentioning

confidence: 99%

Statistical properties of the linear tidal shear

2008

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Large-scale structures originate from coherent motions induced by inhomogeneities in the primeval gravitational potential. Here, we investigate the two-point statistics of the second derivative of the potential, the tidal shear, under the assumption of Gaussianity. We derive an exact closed form expression for the angular averaged, two-point distribution of the shear components which is valid for an arbitrary Lagrangian separation. This result is used to write down the two-point statistics of the shear eigenvalues in compact form. Next, we examine the large-scale asymptotics of the correlation of the shear eigenvalues and the alignment of the principal axes. The analytic results are in good agreement with measurements obtained from random realizations of the gravitational potential. Finally, we show that a number of two-point distributions of the shear eigenvalues are well approximated by Gaussian bivariates over a wide range of separation and smoothing scales. We speculate that the Gaussian approximation also holds for multiple point distributions of the shear eigenvalues. It is hoped that these results will be relevant for studies aimed at describing the properties of the (evolved) matter distribution in terms of the statistics of the primordial shear field.

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“…Our goal here is to show that weak-lensing surveys can also provide valuable information in this direction, in addition to constraining the matter power-spectra and background geometry of the universe. We will use the model proposed by Bernardeau & Schaeffer (1992) and its generalization to the quasi-linear regime by Bernardeau (1992Bernardeau ( , 1994 to construct the PDF of the weak lensing field κ (i) . We express the one-point cumulants as:…”

Section: Hierarchical Ansatzementioning

confidence: 99%

“…In this regime the scaling parameters ω and ka can be expressed in terms of the initial power spectral index n. In general the numerical values of the parameters ka or ω characterizing VPF or CPDF are different from there highly non-linear values. The PDF and bias now can be expressed in terms of G δ (τ ) (Bernardeau 1992;Bernardeau 1994):…”

Section: The Quasi-linear Regimementioning

confidence: 99%

Tomography and weak lensing statistics

Munshi

Coles

Kilbinger

2014

J. Cosmol. Astropart. Phys.

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Extending previous studies, we derive generic predictions for lower order cumulants and their correlators for individual tomographic bins as well as between two different bins. We derive the corresponding one-and two-point joint probability distribution function for the tomographic convergence maps from different bins as a function of angular smoothing scale. The modelling of weak lensing statistics is obtained by adopting a detailed prescription for the underlying density contrast. In this paper we concentrate on the convergence field κ and use top-hat filter; though the techniques presented can readily be extended to model the PDF of shear components or to include other windows such as the compensated filter. The functional form for the underlying PDF and bias is modelled in terms of the non-linear or the quasilinear form depending on the smoothing angular scale. Results from other semi-analytical models e.g. the lognormal distribution are also presented. Introducing a reduced convergence for individual bins, we are able to show that the tomographic PDFs and bias for each bin sample the same functional form of the underlying PDF of density contrast but with varying variance. The joint probability distribution of the convergence maps that correspond to two different tomographic bins can be constructed from individual tomographic PDF and bias. We study their dependence on cosmological parameters for source distributions corresponding to the realistic surveys such as LSST and DES. We briefly outline how photometric redshift information can be incorporated in our computation of cumulants, cumulant correlators and the PDFs. Various approximate results for cumulants and their correlators are presented. Connection of our results to the full 3D calculations is elucidated. Analytical results for inclusion of realistic noise and finite survey size are presented in detail.

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The nonlinear evolution of rare events

Cited by 241 publications

References 1 publication

Modeling halo mass functions in chameleonf(R)gravity

Modeling halo mass functions in chameleonf(R)gravity

Statistical properties of the linear tidal shear

Tomography and weak lensing statistics

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