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We consider two types of modifications of Born-Infeld gravity in the Palatiniformulation and explore their dynamics in the early universe. One of thesefamilies considers $f(R)$ corrections to the Born-Infeld Lagrangian, which canbe seen as modifications of the dynamics produced by the quantum effects ofmatter, while the other consists on different powers of the elementary buildingblock of the Born-Infeld Lagrangian, which we denote by $|\hat\Omega|$. We findthat the two types of nonsingular solutions that arise in the originalBorn-Infeld theory are also present in these extensions, being bouncingsolutions a stable and robust branch. Singular solutions with a period ofapproximate de Sitter inflation are found even in universes dominated byradiation.

Early-time cosmic dynamics in $f(R)$ and $f(|\hat\Omega|)$ extensions of Born-Infeld gravity