Born-Infeld-f(R) gravity with de Sitter solutions

In this study, we consider Born-Infeld-f(R) gravity in which the f(R) term enters directly into the square root in the Palatini formulation. We briefly analyzed this model for an explicit f(R) function which includes positive and negative powers of the curvature scalar. We also show that both the ordinary Born-Infeld-f(R) and this modification reduce to the same gravitational action form under the conformal approach. Then, we consider the existence of a maximally symmetric vacuum solution for the gravitational field equations and find the de Sitter solution for this modified model.