The physical mechanism behind the acceleration of the universe remains one of the great mysteries of modern cosmology. Given the proliferation of dark energy models on the market, an obvious question is: How can we rule out whole classes of dark energy models? And what quantities, at what redshift, and with what accuracy, should be measured in order to rule out these classes of models? I present answers to these questions by presenting results from several interrelated analyses whose motivation is to compare the geometrical quantities with the growth of structure using current or future cosmological observations. Note: Video recording will be available at https://video.ias.edu/sns.