Inspired by quantum gravity proposals, we construct a deformed phase space which supports the UVand IR cutoffs. We show that the Liouville theorem is satisfied in the deformed phase space which allows us to formulate the thermodynamics of the early universe in the semiclassical regime. Applying the proposed method to the Snyder noncommutative space, we find a temperature dependent equation of state which opens a new window for the natural realization of inflation as a phase transition from the quantum gravity regime to the standard radiation dominated era. Also, we obtain finite energy and entropy densities for the Universe when at least the weak energy condition is satisfied.We show that there is a minimum size for the Universe which is proportional to the Planck length and consequently the big bang singularity is removed.
