NonGaussianity in the Weak Lensing Correlation Function Likelihood  Implications for Cosmological Parameter Biases
Abstract
We study the significance of nonGaussianity in the likelihood of weak lensing shear twopoint correlation functions, detecting significantly nonzero skewness and kurtosis in onedimensional marginal distributions of shear twopoint correlation functions in simulated weak lensing data though the full multivariate distributions are relatively more Gaussian. We examine the implications in the context of future surveys, in particular LSST, with derivations of how the nonGaussianity scales with survey area. We show that there is no significant bias in onedimensional posteriors of $\Omega_{\rm m}$ and $\sigma_{\rm 8}$ due to the nonGaussian likelihood distributions of shear correlations functions using the mock data ($100$ deg$^{2}$). We also present a systematic approach to constructing an approximate multivariate likelihood function by decorrelating the data points using principal component analysis (PCA). When using a subset of the PCA components that account for the majority of the cosmological signal as a data vector, the onedimensional marginal likelihood distributions of those components exhibit less skewness and kurtosis than the original shear correlation functions. We further demonstrate that the difference in cosmological parameter constraints between the multivariate Gaussian likelihood model and more complex nonGaussian likelihood models would be even smaller for an LSSTlike survey due to the area effect. In addition, the PCA approach automatically serves as a data compression method, enabling the retention of the majority of the cosmological information while reducing the dimensionality of the data vector by a factor of $\sim$5.
 Publication:

arXiv eprints
 Pub Date:
 May 2019
 arXiv:
 arXiv:1905.03779
 Bibcode:
 2019arXiv190503779L
 Keywords:

 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 16 pages, 10 figures, submitted to MNRAS