Modification to the Luminosity Distance Redshift Relation in Modified Gravity Theories

Éanna É. Flanagan, Eran Rosenthal, Ira M. Wasserman

Published 2008-10-02, updated 2009-02-11Version 2

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.