The Cauchy problem for metric-affine f(R)-gravity in presence of perfect-fluid matter

The Cauchy problem for metric-affine f(R)-gravity à la Palatini and with torsion, in presence of perfect fluid matter acting as source, is discussed following the well-known Bruhat prescriptions for General Relativity. The problem results well-formulated and well-posed when the perfect-fluid form of the stress-energy tensor is preserved under conformal transformations and the set of viable f(R) models is not empty. The key role of conservation laws in Jordan and in Einstein frame is also discussed.