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f(R) Gravity and Cosmology

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A popular alternative to dark energy in explaining the current acceleration of the universe discovered with type Ia supernovae is modifying gravity at cosmological scales. But this is risky: even when everything is well for cosmology, other fundamental and experimental aspects of gravity must be checked in order for the theory to be viable. The successes of modified gravity and its challenges, which have generated a large body of literature in the past ten years, will be reviewed.