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For a large class of dark energy (DE) models, for which the effectivegravitational constant is a constant and there is no direct exchange of energybetween DE and dark matter (DM), knowledge of the expansion history suffices toreconstruct the growth factor of linearized density perturbations in thenon-relativistic matter component on scales much smaller than the Hubbledistance. In this paper we develop a non-parametric method for extractinginformation about the perturbative growth factor from data pertaining to theluminosity or angular size distances. A comparison of the reconstructed densitycontrast with observations of large scale structure and gravitational lensingcan help distinguish DE models such as the cosmological constant andquintessence from models based on modified gravity theories as well as modelsin which DE and DM are either unified, or interact directly. We show that forcurrent SNe data, the linear growth factor at z = 0.3 can be constrained to 5%,and the linear growth rate to 6%. With future SNe data, such as expected fromthe JDEM mission, we may be able to constrain the growth factor to 2-3% and thegrowth rate to 3-4% at z = 0.3 with this unbiased, model-independentreconstruction method. For future BAO data which would deliver measurements ofboth the angular diameter distance and Hubble parameter, it should be possibleto constrain the growth factor at z = 2.5 to 9%. These constraints grow tighterwith the errors on the datasets. With a large quantity of data expected in thenext few years, this method can emerge as a competitive tool for distinguishingbetween different models of dark energy.

Reconstructing Cosmological Matter Perturbations using Standard Candles and Rulers