The Cauchy problem in hybrid metric-Palatini f(X)-gravity

The well-formulation and the well-posedness of the Cauchy problem is discussed for hybrid metric-Palatini gravity, a recently proposed modified gravitational theory consisting of adding to the Einstein-Hilbert Lagrangian an f(R) term constructed à la Palatini. The theory can be recasted as a scalar-tensor one predicting the existence of a light long-range scalar field that evades the local Solar System tests and is able to modify galactic and cosmological dynamics, leading to the late-time cosmic acceleration. In this work, adopting generalized harmonic coordinates, we show that the initial value problem can always be well-formulated and, furthermore, can be well-posed depending on the adopted matter sources.