Principle in Cosmology

We study a d−dimensional FRW universe, containing a perfect fluid with p = wρ and 1 d−1 ≤ w ≤ 1, and find a correspondence principle similar to that of Horowitz and Polchinski in the black hole case. This principle follows quite generally from thermodynamics and the conservation of energy momentum tensor, and can be stated along similar lines as in the black hole case: “When the temperature T of the universe becomes of order string scale the universe makes a transition to a stringy phase containing highly excited strings. At the transition, the entropies and energies of these two phases differ by factors of O(1).” Such a matching is absent for w 6= 1 if the transition is assumed to be when the curvature or the horizon length is of order string scale.