  Quantum gravitational effects usually are assumed to be important on small
scale (Planck scale), but actually these effects are also very significant on
large (cosmological) scales. It is recognized that in curved spacetime, the
existence of a minimal measurable momentum is inevitable. In this paper, we
study thermodynamic properties of the late time universe in the presence of a
minimal measurable momentum cutoff that encodes infra-red modification of the
underlying field theory. In this regard, we consider a non-relativistic regime
and show that the existence of a minimal measurable momentum in the very
essence of the theory leads to accelerating expansion of the universe, which
can be interpreted as an alternative to Dark Energy. The universe in this model
has experienced the phantom line crossing in the near past.
