The speed of light in extended gravity theories

We shall investigate the possibility of formulation of varying speed of light (VSL) in the framework of Palatini nonlinear Ricci scalar and Ricci squared theories. Different speeds of light including the causal structure constant, electromagnetic and gravitational wave speeds are discussed. We shall see that two local frames are distinguishable and discuss the velocity of light in these two frames. We shall investigate which one of these local frames is inertial.