  We develop a novel statistical strong lensing approach to probe the
cosmological parameters by exploiting multiple redshift image systems behind
galaxies or galaxy clusters. The method relies on free-form mass inversion of
strong lenses and does not need any additional information other than
gravitational lensing. Since in free-form lensing the solution space is a
high-dimensional convex polytope, we consider Bayesian model comparison
analysis to infer the cosmological parameters. The volume of the solution space
is taken as a tracer of the probability of the underlying cosmological
assumption. In contrast to parametric mass inversions, our method accounts for
the mass-sheet degeneracy, which implies a degeneracy between the steepness of
the profile and the cosmological parameters. Parametric models typically break
this degeneracy, introducing hidden priors to the analysis that contaminate the
inference of the parameters. We test our method with synthetic lenses, showing
that it is able to infer the assumed cosmological parameters. Applied to the
CLASH clusters, the method might be competitive with other probes.
