  Quantum gravitational effects may affect the large scale dynamics of the
universe. Phenomenologically, quantum gravitational effect at large distances
can be encoded in an extended uncertainty principle that admits a minimal
measurable momentum/energy or a maximal length. This maximal length can be
considered as the size of the cosmological horizon today. In this paper we
study thermostatistics of an expanding universe as a gaseous system and in the
presence of an invariant infrared cutoff. We also compare the thermostatistics
of different eras of the evolution of the universe in two classes, Fermions and
Bosons.
