Bouncing Eddington-inspired Born-Infeld cosmologies: an alternative to Inflation?

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We study the dynamics of a homogeneous and isotropic Friedmann-Robertson-Walker universe in the context of the Eddington-inspired Born-Infeld theory of gravity. We generalize earlier results, obtained in the context of a radiation dominated universe, to account for the evolution of a universe permeated by a perfect fluid with an arbitrary equation of state parameter w. We show that a bounce may occur for κ>0, if w is time-dependent, and we demonstrate that it is free from tensor singularities. We argue that Eddington-inspired Born-Infeld cosmologies may be a viable alternative to the inflationary paradigm as a solution to fundamental problems of the standard cosmological model.