The non-Gaussianity of the cosmic shear likelihood - or: How odd is the Chandra Deep Field South?

Abstract

(abridged) We study the validity of the approximation of a Gaussian cosmic shear likelihood. We estimate the true likelihood for a fiducial cosmological model from a large set of ray-tracing simulations and investigate the impact of non-Gaussianity on cosmological parameter estimation. We investigate how odd the recently reported very low value of ${\sigma }_8$ really is as derived from the \textit{Chandra} Deep Field South (CDFS) using cosmic shear by taking the non-Gaussianity of the likelihood into account as well as the possibility of biases coming from the way the CDFS was selected. We find that the cosmic shear likelihood is significantly non-Gaussian. This leads to both a shift of the maximum of the posterior distribution and a significantly smaller credible region compared to the Gaussian case. We re-analyse the CDFS cosmic shear data using the non-Gaussian likelihood. Assuming that the CDFS is a random pointing, we find ${\sigma }_8=0.68_{-0.16}^{+0.09}$ for fixed ${\Omega }_{\mathrm{m}}=0.25$. In a WMAP5-like cosmology, a value equal to or lower than this would be expected in $\approx 5$ of the times. Taking biases into account arising from the way the CDFS was selected, which we model as being dependent on the number of haloes in the CDFS, we obtain ${\sigma }_8=0.71_{-0.15}^{+0.10}$. Combining the CDFS data with the parameter constraints from WMAP5 yields ${\Omega }_{\mathrm{m}}=0.26_{-0.02}^{+0.03}$ and ${\sigma }_8=0.79_{-0.03}^{+0.04}$ for a flat universe.

18 pages, 16 figures, accepted for publication in A&A; New Bayesian treatment of field selection bias

References in corpus (16)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Likelihoods and Parameters from the WMAP data
• Why your model parameter confidences might be too optimistic -- unbiased estimation of the inverse covariance matrix
• Very weak lensing in the CFHTLS Wide: Cosmology from cosmic shear in the linear regime
• The Shear TEsting Programme 2: Factors affecting high precision weak lensing analyses
• Ray-tracing through the Millennium Simulation: Born corrections and lens-lens coupling in cosmic shear and galaxy-galaxy lensing
• The GOODS-MUSIC sample: a multicolour catalog of near-IR selected galaxies in the GOODS-South field
• COSMOS: 3D weak lensing and the growth of structure
• Bayesian Galaxy Shape Measurement for Weak Lensing Surveys -I. Methodology and a Fast Fitting Algorithm
• Cosmological Constraints From the 100 Square Degree Weak Lensing Survey
• The Impact of Non-Gaussian Errors on Weak Lensing Surveys
• Dependence of cosmic shear covariances on cosmology - Impact on parameter estimation
• Analysis of two-point statistics of cosmic shear: III. Covariances of shear measures made easy
• Cosmic shear analysis of archival HST/ACS data: I. Comparison of early ACS pure parallel data to the HST/GEMS Survey
• Cosmic variance of weak lensing surveys in the non-Gaussian regime
• Sources of contamination to weak lensing tomography: redshift-dependent shear measurement bias

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