The Cauchy problem in hybrid metric-Palatini f(X)-gravity
  The well-formulation and the well-posedness of the Cauchy problem is
discussed for {\it hybrid metric-Palatini gravity}, a recently proposed
modified gravitational theory consisting of adding to the Einstein-Hilbert
Lagrangian an $f(R)$ term constructed {\it \`{a} la} Palatini. The theory can
be recast 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 {\it well-formulated} and,
furthermore, can be {\it well-posed} depending on the adopted matter sources.
