  We study a de-Sitter model in the framework of a Deformed Special Relativity
(DSR) inspired structure. The effects of this framework appear as the existence
of a fundamental length which influences the behavior of the scale factor. We
show that such a deformation can either be used to control the unbounded growth
of the scale factor in the present accelerating phase or account for the
inflationary era in the early evolution of the universe.
