Modification to the Luminosity Distance Redshift Relation in Modified Gravity Theories

TL;DR

This paper derives a modified luminosity distance-redshift relation in flat Robertson-Walker spacetimes with scalar perturbations, aiming to help distinguish between alternative gravity theories through observational data.

Contribution

It provides a new expression for luminosity distance in modified gravity theories with scalar perturbations, enhancing the tools for testing gravity models against cosmological observations.

Findings

Derived a generalized luminosity distance-redshift relation

Shows how measurements constrain scalar potentials in modified gravity

Offers a method to distinguish gravity theories using luminosity distance data

Abstract

We derive an expression for the luminosity distance as a function of redshift for a flat Robertson-Walker spacetime perturbed by arbitrary scalar perturbations possibly produced by a modified gravity theory with two different scalar perturbation potentials. Measurements of the luminosity distance as function of redshift provide a constraint on a combination of the scalar potentials and so they can complement weak lensing and other measurements in trying to distinguish among the various alternative theories of gravity.