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Born-Infeld deformation strategy to smooth theories having divergentsolutions is applied to the teleparallel equivalent of General Relativity. Theequivalence between teleparallelism and General Relativity is exploited toobtain a deformed theory of gravity based on second order differentialequations, since teleparallel Lagrangian is built just from first derivativesof the vierbein. We show that Born-Infeld teleparallelism cures the initialsingularity in a spatially flat FRW universe; moreover, it provides a naturalinflationary stage without resorting to an inflaton field. The Born-Infeldparameter bounds the dynamics of Hubble parameter H(t) and establishes amaximum attainable spacetime curvature.

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