ON THE WELL-FORMULATION OF THE INITIAL VALUE PROBLEM OF METRIC-AFFINE f(R)-GRAVITY

We study the well-formulation of the initial value problem of f(R)-gravity in the metric-affine formalism. The problem is discussed in vacuo and in presence of perfect-fluid matter, Klein–Gordon and Yang–Mills fields. Adopting Gaussian normal coordinates, it can be shown that the problem is always well-formulated. Our results refute some criticisms to the viability of f(R)-gravity recently appeared in literature.