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Theoretical Aspects of Cosmic Acceleration

Efforts to understand and map the possible explanations for the late time acceleration of the universe have led to a broad range of suggestions, ranging from the cosmological constant and straightforward dark energy, to exotically coupled models, to infrared modifications of General Relativity. If we are to uncover which, if any, of these approaches might provide a serious answer to the problem, it is crucial to understand the constraints that theoretical consistency places on the models, and on the regimes in which they make predictions. In this talk, delivered as an invited plenary lecture at the Dark Side of the Universe conference in Kyoto, Japan, I briefly describe some modern attempts to carry out this program and some of the more interesting ideas that have emerged. As an example, I use the Galileon model, discussing how the Vainshtein mechanism occurs, and how a number of these theoretical problems arise around such backgrounds.