A statefinder luminosity distance formula in varying speed of light cosmology

We derive a luminosity distance formula for the varying speed of light (VSL) theory which involves higher order characteristics of expansion such as jerk, snap and lerk which can test the impact of varying $c$ onto the evolution of the universe. We show that the effect of varying $c$ is possible to be isolated due to the relations connecting observational parameters already by measuring the second-order term in redshift $z$ unless there is a redundancy between the curvature and an exotic fluid of cosmic strings scaling the same way as the curvature.