A stringy correspondence principle in cosmology

We study a d-dimensional FRW universe, containing a perfect fluid with p=wρ and 1d−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 state becomes a highly excited string state. At the transition, the entropies and energies of the universe and strings differ by factors of O(1)”. Such a matching is absent for w≠1 if the transition is assumed to be when the curvature or the horizon length is of order string scale.