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 minimalmeasurablemomentum/energy or amaximal 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.
