Testing a New Analytic Model for Gravitational Lensing Probabilities

Das, Sudeep; Ostriker, Jeremiah P.

doi:10.1086/504032

Cited by 47 publications

(80 citation statements)

References 75 publications

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“…The one-point probability density function (pdf) of the projected density and lensing convergence are also fitted well by a log-normal pdf (Taruya et al 2002). Even better fits to the convergence pdf, particularly in the tails of the distribution, can be obtained by generalisations of a log-normal pdf (Das & Ostriker 2006;Takahashi et al 2011;.…”

Section: Introductionmentioning

confidence: 87%

Cosmic shear covariance: the log-normal approximation

Hilbert¹,

Hartlap²,

Schneider³

2011

A&A

106

150

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Context. Accurate estimates of the errors on the cosmological parameters inferred from cosmic shear surveys require accurate estimates of the covariance of the cosmic shear correlation functions. Aims. We seek approximations to the cosmic shear covariance that are as easy to use as the common approximations based on normal (Gaussian) statistics, but yield more accurate covariance matrices and parameter errors. Methods. We derive expressions for the cosmic shear covariance under the assumption that the underlying convergence field follows log-normal statistics. We also derive a simplified version of this log-normal approximation by only retaining the most important terms beyond normal statistics. We use numerical simulations of weak lensing to study how well the normal, log-normal, and simplified log-normal approximations as well as empirical corrections to the normal approximation proposed in the literature reproduce shear covariances for cosmic shear surveys. We also investigate the resulting confidence regions for cosmological parameters inferred from such surveys. Results. We find that the normal approximation substantially underestimates the cosmic shear covariances and the inferred parameter confidence regions, in particular for surveys with small fields of view and large galaxy densities, but also for very wide surveys. In contrast, the log-normal approximation yields more realistic covariances and confidence regions, but also requires evaluating slightly more complicated expressions. However, the simplified log-normal approximation, although as simple as the normal approximation, yields confidence regions that are almost as accurate as those obtained from the log-normal approximation. The empirical corrections to the normal approximation do not yield more accurate covariances and confidence regions than the (simplified) log-normal approximation. Moreover, they fail to produce positive-semidefinite data covariance matrices in certain cases, rendering them unusable for parameter estimation. Conclusions. The log-normal or simplified log-normal approximation should be used in favour of the normal approximation for parameter estimation and parameter error forecasts. More generally, any approximation to the cosmic shear covariance should ensure a positive-(semi)definite data covariance matrix.

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Section: Introductionmentioning

confidence: 87%

Cosmic shear covariance: the log-normal approximation

Hilbert¹,

Hartlap²,

Schneider³

2011

A&A

106

150

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show abstract

“…These mocks have also been used to estimate the probability distributions of the convergence or magnification (e.g., Hamana et al 2000;Taruya et al 2002;Das & Ostriker 2006;Hilbert et al 2007;Takahashi et al 2011) and the higher-order moments (skewness and kurtosis) of the convergence (e.g., Petri et al 2016b;Shirasaki 2017).…”

Section: Introductionmentioning

confidence: 99%

Full-sky Gravitational Lensing Simulation for Large-area Galaxy Surveys and Cosmic Microwave Background Experiments

Takahashi

Hamana

Shirasaki

et al. 2017

ApJ

181

248

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We present 108 full-sky gravitational lensing simulation data sets generated by performing multiplelens plane ray-tracing through high-resolution cosmological N -body simulations. The data sets include full-sky convergence and shear maps from redshifts z = 0.05 to 5.3 at intervals of 150 h −1 Mpc comoving radial distance (corresponding to a redshift interval of ∆z ≃ 0.05 at the nearby universe), enabling the construction of a mock shear catalog for an arbitrary source distribution up to z = 5.3. The dark matter halos are identified from the same N -body simulations with enough mass resolution to resolve the host halos of the Sloan Digital Sky Survey (SDSS) CMASS and luminous red galaxies (LRGs). Angular positions and redshifts of the halos are provided by a ray-tracing calculation, enabling the creation of a mock halo catalog to be used for galaxy-galaxy and cluster-galaxy lensing. The simulation also yields maps of gravitational lensing deflections for a source redshift at the last scattering surface, and we provide 108 realizations of lensed cosmic microwave background (CMB) maps in which the post-Born corrections caused by multiple light scattering are included. We present basic statistics of the simulation data, including the angular power spectra of cosmic shear, CMB temperature and polarization anisotropies, galaxy-galaxy lensing signals for halos, and their covariances. The angular power spectra of the cosmic shear and CMB anisotropies agree with theoretical predictions within 5% up to ℓ = 3000 (or at an angular scale θ > 0.5 arcmin). The simulation data sets are generated primarily for the ongoing Subaru Hyper Suprime-Cam survey, but are freely available for download at

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“…Ref. [4][5][6][7]) relates a "universal" form of the lensing PDF to the variance of the convergence, which in turn is fixed by the amplitude of the power spectrum, σ 8 . Moreover the coefficients of the proposed PDF are trained on some specific N-body simulations.…”

Section: Introductionmentioning

confidence: 99%

Accurate modeling of weak lensing with the stochastic gravitational lensing method

Kainulainen

Marra

2011

Phys. Rev. D

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We revise and extend the stochastic approach to cumulative weak lensing (hereafter the sGL method) first introduced in Ref.[1]. Here we include a realistic halo mass function and density profiles to model the distribution of mass between and within galaxies, galaxy groups and galaxy clusters. We also introduce a modeling of the filamentary large-scale structures and a method to embed halos into these structures. We show that the sGL method naturally reproduces the weak lensing results for the Millennium Simulation. The strength of the sGL method is that a numerical code based on it can compute the lensing probability distribution function for a given inhomogeneous model universe in a few seconds. This makes it a useful tool to study how lensing depends on cosmological parameters and its impact on observations. The method can also be used to simulate the effect of a wide array of systematic biases on the observable PDF. As an example we show how simple selection effects may reduce the variance of observed PDF, which could possibly mask opposite effects from very large scale structures. We also show how a JDEM-like survey could constrain the lensing PDF relative to a given cosmological model. The updated turboGL code is available at turboGL.org.

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Testing a New Analytic Model for Gravitational Lensing Probabilities

Cited by 47 publications

References 75 publications

Cosmic shear covariance: the log-normal approximation

Cosmic shear covariance: the log-normal approximation

Full-sky Gravitational Lensing Simulation for Large-area Galaxy Surveys and Cosmic Microwave Background Experiments

Accurate modeling of weak lensing with the stochastic gravitational lensing method

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