Game of cones: A nulling strategy for modelling lensing convergence in cones with large deviation theory

The distribution of the cosmic convergence field is modeled using a large-deviation principle where all non-Gaussian contributions are computed from first principles. The geometry of the past light cone is accounted for by constructing the total weak-lensing signal from contributions of the matter density in thin disk slices. The prediction of this model is successfully tested against numerical simulation with ray tracing, and found to be accurate within at least 5 per cent in the tails at redshift 1 and opening angle of 10 arcmin and even more so with increasing source redshift and opening angle. An accurate analytical approximation to the theory is also provided for practical implementation. The lensing kernel that mixes physical scales along the line-of-sight tends to reduce the domain of validity of this theoretical approach compared to the three dimensional case of cosmic densities in spherical cells. This effect is shown to be avoidable if a nulling procedure is implemented in order to localise the lensing line-of-sight integrations in a tomographic analysis. Accuracy in the tails is thus achieved within a percent for source redshifts between 0.5 and 1.5 and an opening angle of 10 arcmin. Applications to future weak-lensing surveys like Euclid and the specific issue of shape noise are discussed.