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_{\rm 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^{+0.10}_{-0.15} $. Combining the CDFS data with the parameter constraints from WMAP5 yields $\Omega_{\rm m} = 0.26^{+0.03}_{-0.02}$ and $\sigma_8 = 0.79^{+0.04}_{-0.03}$ for a flat universe.

💡 Analysis

(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_{\rm 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^{+0.10}_{-0.15} $. Combining the CDFS data with the parameter constraints from WMAP5 yields $\Omega_{\rm m} = 0.26^{+0.03}_{-0.02}$ and $\sigma_8 = 0.79^{+0.04}_{-0.03}$ for a flat universe.

📄 Content

arXiv:0901.3269v2 [astro-ph.CO] 29 Jul 2009 Astronomy & Astrophysics manuscript no. 11697 c⃝ESO 2021 June 29, 2021 The non-Gaussianity of the cosmic shear likelihood or How odd is the Chandra Deep Field South? J. Hartlap1, T. Schrabback2,1, P. Simon3, and P. Schneider1 1 Argelander-Institut f¨ur Astronomie, Universit¨at Bonn, Auf dem H¨ugel 71, D-53121 Bonn, Germany 2 Leiden Observatory, Universiteit Leiden, Niels Bohrweg 2, NL-2333 CA Leiden, The Netherlands 3 The Scottish Universities Physics Alliance (SUPA), Institute for Astronomy, School of Physics, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK Received 22 January 2009 / Accepted 19 June 2009 ABSTRACT Aims. 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 σ8 really is as derived from the 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. Methods. A brute force approach to estimating the likelihood from simulations must fail because of the high dimensionality of the problem. We therefore use independent component analysis to transform the cosmic shear correlation functions to a new basis, in which the likelihood approximately factorises into a product of one-dimensional distributions. Results. 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 in combination with conservative galaxy selection criteria that minimise calibration uncertainties. Assuming that the CDFS is a random pointing, we find σ8 = 0.68+0.09 −0.16 for fixed Ωm = 0.25. In a WMAP5-like cosmology, a value equal to or lower than this would be expected in ≈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 σ8 = 0.71+0.10 −0.15. Combining the CDFS data with the parameter constraints from WMAP5 yields Ωm = 0.26+0.03 −0.02 and σ8 = 0.79+0.04 −0.03 for a flat universe.

1. Introduction Weak gravitational lensing by the large-scale structure in the Universe, or cosmic shear, is becoming a more and more im- portant tool to constrain cosmological parameters. It is largely complementary to other cosmological probes like the cosmic microwave background or the clustering of galaxies, and partic- ularly sensitive to the matter density Ωm and the normalisation of the matter power spectrum σ8. Important constraints have al- ready been obtained by Benjamin et al. (2007), who compiled a set of five weak lensing surveys, and from the CFHT Legacy Survey (Hoekstra et al. 2006; Semboloni et al. 2006; Fu et al. 2008). In subsequent years, a new generation of surveys like KIDS or Pan-STARRS (Kaiser & Pan-STARRS Collaboration

2005. will allow cosmic shear to be measured with statistical uncertainties that are much smaller than the systematic errors both on the observational and the theoretical sides. Strong ef- forts are now being made to find sources of systematics in the process of shape measurement and shear estimation (e.g. Massey et al. 2007a). In addition, new methods of shape mea- surement are being explored, such as the shapelet formalism (Refregier & Bacon 2003; Kuijken 2006) or the methods pro- posed in Bernstein & Jarvis (2002) and Miller et al. (2007). It is equally important to have accurate theoretical model predictions that can be fit to the expected high-quality mea- surements. Currently, these models are all based on fitting for- mulae for the three-dimensional matter power spectrum de- rived from N-body simulations as given by Peacock & Dodds (1996) and more recently by Smith et al. (2003). However, these are only accurate at best to the percent level on the scales relevant to this and similar works when compared to ray-tracing simulations based on state-of-the-art N-body sim- ulations (Hilbert et al. 2009), such as the Millennium Run (Springel et al. 2005). Therefore, there is a strong need for a 2 Hartlap et al.: The non-Gaussianity of the cosmic shear likelihood large ray-tracing effort to obtain accurate semi-numerical pre- dictions for a range of cosmological parameters. While a tremendous effort is currently being directed to the solution of these problems, the actual process of parameter esti- mation has so far received relatively little attention. Obviously, the statistical data analysis has to achieve the same accuracy as the data acquisition if the aforementioned efforts are not to be w

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