A Stringy Correspondence Principle in Cosmology

TL;DR

This paper proposes a correspondence principle in cosmology linking high-temperature universe states to highly excited string states, generalizing black hole string correspondence to cosmological models with perfect fluids.

Contribution

It introduces a new cosmological correspondence principle based on thermodynamics and energy conservation, extending string-black hole ideas to expanding universe scenarios.

Findings

The universe's transition to a string state occurs when T is of order string scale.

Entropy and energy of universe and strings are comparable at transition.

The principle applies generally for w between 1/(d-1) and 1.

Abstract

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.