3D cosmic shear: Numerical challenges, 3D lensing random fields generation, and Minkowski functionals for cosmological inference

Cosmic shear-the weak gravitational lensing effect generated by fluctuations of the gravitational tidal fields of the large-scale structure-is one of the most promising tools for current and future cosmological analyses. The spherical-Bessel decomposition of the cosmic shear field (3D cosmic shear) is one way to maximize the amount of redshift information in a lensing analysis and therefore provides a powerful tool to investigate in particular the growth of cosmic structure that is crucial for dark energy studies. However, the computation of simulated 3D cosmic shear covariance matrices presents numerical difficulties, due to the required integrations over highly oscillatory functions. We present and compare two numerical methods and relative implementations to perform these integrations. We then show how to generate 3D Gaussian random fields on the sky in spherical coordinates, starting from the 3D cosmic shear covariances. To validate our field-generation procedure, we calculate the Minkowski functionals associated with our random fields, compare them with the known expectation values for the Gaussian case and demonstrate parameter inference from Minkowski functionals from a cosmic shear survey. This is a first step towards producing fully 3D Minkowski functionals for a lognormal field in 3D to extract Gaussian and non-Gaussian information from the cosmic shear field, as well as towards the use of Minkowski functionals as a probe of cosmology beyond the commonly used two-point statistics.