Astronomical observations strongly suggest that the universe is mostly dark. Its two dominant components, dark energy and dark matter, remain among the most mysterious concepts in cosmology today. The effects of these two substances are imprinted in the remaining few percent of the universe that consists of normal (baryonic) matter. Dark energy is responsible for the accelerating expansion of the universe and the existence of dark matter is deduced from the orbital properties of stars in galaxies. This thesis probes the observable effects of both these phenomena. The first part is about Baryon Acoustic Oscillations (BAO) by which we can measure the expansion rate of the universe and constrain dark energy. The second part focuses on ways to probe the nature of dark matter by studying the dynamics of galaxies and the orbital properties of their stars. The third and final part of this thesis discusses Optimal Transport (OT) theory, which unites the BAO and the Galactic Dynamics parts. The results of this thesis would develop novel ways to place stronger constraints on cosmology and dark energy; while also revealing the distribution of dark matter in galaxies, thus constraining dark matter's properties.