A type of Born-Infeld regular gravity and its cosmological consequences

Born-Infeld deformation strategy to smooth theories having divergent solutions is applied to the teleparallel equivalent of General Relativity. The equivalence between teleparallelism and General Relativity is exploited to obtain a deformed theory of gravity based on second order differential equations, since teleparallel Lagrangian is built just from first derivatives of the vierbein. We show that Born-Infeld teleparallelism cures the initial singularity in a spatially flat FRW universe; moreover, it provides a natural inflationary stage without resorting to an inflaton field. The Born-Infeld parameter bounds the dynamics of Hubble parameter H(t) and establishes a maximum attainable spacetime curvature.