  Cosmologies based on General Relativity encompassing an anti-symmetric
connection (torsion) can display nice desirable features as the absence of the
initial singularity and the possibility of inflation in the early stage of the
universe. After briefly reviewing the standard approach to the cosmology with
torsion, we generalize it to demonstrate that several theories of torsion
gravity are possible using different choices of the diffeomorphic invariants in
the Lagrangians. As a result, distinct cosmologies emerge. In all of them it is
possible that the universe avoids the initial singularity and passes through an
initial accelerated expansion. Differences between these theories are
highlighted.
