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We determine the cosmic expansion rate from supernovae of type Ia to set up adata-based distance measure that does not make assumptions about theconstituents of the universe, i.e. about a specific parametrisation of aFriedmann cosmological model. The scale, determined by the Hubble constant$H_0$, is the only free cosmological parameter left in the gravitationallensing formalism. We investigate to which accuracy and precision the lensingdistance ratio $D$ is determined from the Pantheon sample. Inserting $D$ andits uncertainty into the lensing equations for given $H_0$, esp. the time-delayequation between a pair of multiple images, allows to determine lensproperties, esp. differences in the lensing potential ($\Delta \phi$), withoutspecifying a cosmological model. We expand the luminosity distances into ananalytic orthonormal basis, determine the maximum-likelihood weights for thebasis functions by a globally optimal $\chi^2$-parameter estimation, and deriveconfidence bounds by Monte-Carlo simulations. For typical strong lensingconfigurations between $z=0.5$ and $z=1.0$, $\Delta \phi$ can be determinedwith a relative imprecision of 1.7%, assuming imprecisions of the time delayand the redshift of the lens on the order of 1%. With only a small, tolerableloss in precision, the model-independent lens characterisation developed inthis paper series can be generalised by dropping the specific Friedmann modelto determine $D$ in favour of a data-based distance ratio. Moreover, for anyastrophysical application, the approach presented here, provides distancemeasures for $z\le2.3$ that are valid in any homogeneous, isotropic universewith general relativity as theory of gravity.

monthly notices of the royal astronomical society

Generalised model-independent characterisation of strong gravitational  lenses V: reconstructing the lensing distance ratio by supernovae for a  general Friedmann universe