Modification to the Luminosity Distance Redshift Relation in Modified   Gravity Theories
  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. 
\'Eanna \'E. Flanagan, Eran Rosenthal, and Ira M. Wasserman