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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 ofthe universe. We show that the effect of varying $c$ is possible to be isolateddue to the relations connecting observational parameters already by measuringthe second-order term in redshift $z$ unless there is a redundancy between thecurvature and an exotic fluid of cosmic strings scaling the same way as thecurvature.

A statefinder luminosity distance formula in varying speed of light cosmology