  The presence of additional compact dimensions in cosmological models is
studied in the context of modified teleparallel theories of gravity. We focus
the analysis on eleven dimensional spacetimes, where the seven dimensional
extra dimensions are compactified. In particular, and due to the importance
that global vector fields play within the conceptual body of teleparallel
modified gravity models, we consider the additional dimensions to be products
of parallelizable spheres. The global vector fields characterizing the
different topologies are obtained, as well as the equations of motion
associated to them. Using global dynamical system techniques, we discuss some
physical consequences arising because of the existence of the extra dimensions.
In particular, the possibility of having an early inflationary epoch driven by
the presence of extra dimensions without other matter sources is discussed.
