Metric-Palatini gravity unifying local constraints and late-time cosmic acceleration

We present a novel approach to modified theories of gravity which consists of adding to the Einstein-Hilbert Lagrangian an f (R) term constructed \`a la Palatini. Using the respective dynamically equivalent scalar-tensor representation, we show that the theory can pass the Solar System observational constraints even if the scalar field is very light. This implies the existence of a long-range scalar field, which is able to modify the cosmological and galactic dynamics but leaves the Solar System unaffected. We also verify the absence of instabilities in perturbations and provide explicit models which are consistent with local tests and lead to the late-time cosmic acceleration.