Palatini–Born–Infeld gravity, bouncing universe, and black hole formation

We consider the Palatini formalism of the Born–Infeld gravity. In the Palatini formalism, the propagating mode is only graviton, whose situation is different from that in the metric formalism. We discuss the FRW cosmology by using an effective potential. Especially we consider the condition that the bouncing could occur. We also give some speculations about the black hole formation