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If general relativity is the correct theory of physics on large scales, thenthere is a differential equation that relates the Hubble expansion function,inferred from measurements of angular diameter distance and luminositydistance, to the growth rate of large scale structure. For a dark energy fluidwithout couplings or an unusual sound speed, deviations from this consistencyrelationship could be the signature of modified gravity on cosmological scales.We propose a procedure based on this consistency relation in order todistinguish between some dark energy models and modified gravity models. Theprocedure uses different combinations of cosmological observations and is ableto find inconsistencies when present. As an example, we apply the procedure toa universe described by a recently proposed 5-dimensional modified gravitymodel. We show that this leads to an inconsistency within the dark energyparameter space detectable by future experiments.Comment: 8 pages, 7 figures; expanded paper; matches PRD accepted version;  corrected growth rate formula; main results and conclusion unchange

Probing cosmic acceleration beyond the equation of state: Distinguishing between dark energy and modified gravity models