  The vierbein (tetrad) fields for closed and open Friedmann-Robertson-Walker
cosmologies are hard to work out in most of the theories featuring absolute
parallelism. The difficulty is traced in the fact that these theories are not
invariant under local Lorentz transformations of the vierbein. We illustrate
this issue in the framework of f(T) theories and Born-Infeld determinantal
gravity. In particular, we show that the early Universe as described by the
Born-Infeld scheme is singularity free and naturally inflationary as a
consequence of the very nature of Born-Infeld gravitational action.
