Constraining primordial non-Gaussianity with cosmological weak lensing: shear and flexion

We examine the cosmological constraining power of future large-scale weak lensing surveys on the model of the ESA planned mission Euclid, with particular reference to primordial non-Gaussianity. Our analysis considers several different estimators of the projected matter power spectrum, based on both shear and flexion. We review the covariance and Fisher matrix for cosmic shear and evaluate those for cosmic flexion and for the cross-correlation between the two. The bounds provided by cosmic shear alone are looser than previously estimated, mainly due to the reduced sky coverage and background number density of sources for the latest Euclid specifications. New constraints for the local bispectrum shape, marginalized over σ8, are at the level of ΔfNL ~ 100, with the precise value depending on the exact multipole range that is considered in the analysis. We consider three additional bispectrum shapes, for which the cosmic shear constraints range from ΔfNL ~ 340 (equilateral shape) up to ΔfNL ~ 500 (orthogonal shape). Also, constraints on the level of non-Gaussianity and on the amplitude of the matter power spectrum σ8 are almost perfectly anti-correlated, except for the orthogonal bispectrum shape for which they are correlated. The competitiveness of cosmic flexion constraints against cosmic shear ones depends by and large on the galaxy intrinsic flexion noise, that is still virtually unconstrained. Adopting the very high value that has been occasionally used in the literature results in the flexion contribution being basically negligible with respect to the shear one, and for realistic configurations the former does not improve significantly the constraining power of the latter. Since the shear shot noise is white, while the flexion one decreases with decreasing scale, by considering high enough multipoles the two contributions have to become comparable. Extending the analysis up to lmax = 20,000 cosmic flexion, while being still subdominant, improves the shear constraints by ~ 10% when added. However on such small scales the highly non-linear clustering of matter, the impact of baryonic physics, and the non-Gaussian part of the covariance matrix make any error estimation uncertain. By considering lower, and possibly more realistic, values of the flexion intrinsic shape noise results in flexion constraining power being a factor of ~ 2 better than that of shear, and the bounds on σ8 and fNL being improved by a factor of ~ 3 upon their combination.