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Structure formation provides a strong test of any cosmic acceleration modelbecause a successful dark energy model must not inhibit {\black or overpredict}the development of observed large-scale structures. Traditional approaches tostudies of structure formation in the presence of dark energy or a modifiedgravity implement a modified Press-Schechter formalism, which relates thelinear overdensities to the abundance of dark matter haloes it at the sametime. We critically examine the universality of the Press-Schechter formalismfor different cosmologies, and show that the halo abundance is best correlatedwith spherical linear overdensity at 94% of collapse (or observation) time. Wethen extend this argument to ellipsoidal collapse (which decreases thefractional time of best correlation for small haloes, and show that our resultsagree with deviations from modified Press-Schechter formalism seen in simulatedmass functions. This provides a novel universal prescription to measure lineardensity evolution, based on current and future observations of cluster (or darkmatter) halo mass function. In particular, even observations of clusterabundance in a single epoch will constrain the entire history of linear growthof cosmological of perturbations.

Using Dark Matter Haloes to Learn about Cosmic Acceleration: A New Proposal for a Universal Mass Function