  Key non-Gaussian properties of cosmological fields can be captured by their
one-point statistics, providing a complement to two-point statistical
measurements from power spectra or correlation functions. Large deviation
theory can robustly predict the one-point statistics of cosmological density
fields on mildly non-linear scales from first principles. It provides a direct
prediction for the cumulant generating function (CGF) of such fields, from
which a prediction for the more commonly used probability density function
(PDF) is extracted through an inverse Laplace transform. For joint one-point
statistics of multiple fields, the inverse Laplace transform rapidly becomes
more cumbersome and computationally expensive. In this work, we demonstrate for
the first time that the weak lensing CGF itself can be used as an observable
that captures an equal amount of cosmological information to the PDF. While we
use the weak-lensing convergence field as a simplistic and instructive example,
this work is intended as a first step towards a cosmological analysis based on
large deviation theory in the context of a nulling framework, which excludes
contributions from small scales to facilitate highly accurate theoretical
predictions. In this context, the method should be generally applicable for a
multi-scale tomographic analysis of weak lensing and galaxy clustering.
