  We study a d-dimensional FRW universe, containing a perfect fluid with p = w
\rho and \frac{1} {d - 1} \le w \le 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 {\cal O}(1).'' Such a matching is absent for w \ne 1 if the
transition is assumed to be when the curvature or the horizon length is of
order string scale.
