The understanding of the physical origin of the acceleration of our universe is a big puzzle for both cosmology and theoretical physics. I will first briefly review the evidence for the acceleration of the expansion of the universe, focusing on the assumptions that lead to this conclusion. I will then describe a general classification of the models that could explain this acceleration and explain why it calls for better tests of general relativity on astrophysical and cosmological scales. I will review some of the possible tests and then discuss what constraints can be set from cosmology on a general class of theories including general relativity, namely scalar-tensor
theories.
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