A statefinder luminosity distance formula in varying speed of light cosmology

TL;DR

This paper derives a luminosity distance formula in VSL cosmology incorporating higher order expansion parameters, enabling tests of varying speed of light effects on universe evolution through observational data.

Contribution

It introduces a new luminosity distance formula in VSL cosmology that includes jerk, snap, and lerk parameters, allowing for observational testing of varying $c$ effects.

Findings

Varying $c$ effects can be isolated using second-order redshift measurements.

Relations between observational parameters help distinguish $c$ variation from curvature or exotic fluids.

The formula provides a new tool for cosmological tests of VSL theories.

Abstract

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.