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We consider the Palatini formalism of the Born-Infeld gravity. In thePalatini formalism, the propagating mode is only graviton, whose situation isdifferent from that in the metric formalism. We discuss about the FRW cosmologyby using an effective potential. Especially we consider the condition that thebouncing could occur. We also give some speculations about the black holeformation

Palatini-Born-Infeld Gravity, Bouncing Universe, and Black Hole Formation