  A correspondence between closed strings in their high-temperature Hagedorn
phase and asymptotically de Sitter (dS) space is established. We identify a
thermal, conformal field theory (CFT) whose partition function is, on the one
hand, equal to the partition function of closed, interacting, fundamental
strings in their Hagedorn phase yet is, on the other hand, also equal to the
Hartle-Hawking (HH) wavefunction of an asymptotically dS Universe. The
Lagrangian of the CFT is a functional of a single scalar field, the condensate
of a thermal scalar, which is proportional to the entropy density of the
strings. The correspondence has some aspects in common with the anti-de
Sitter/CFT correspondence, as well as with some of its proposed analytic
continuations to a dS/CFT correspondence, but it also has some important
conceptual and technical differences. The equilibrium state of the CFT is one
of maximal pressure and entropy, and it is at a temperature that is above but
parametrically close to the Hagedorn temperature. The CFT is valid beyond the
regime of semiclassical gravity and thus defines the initial quantum state of
the dS Universe in a way that replaces and supersedes the HH wavefunction.
Two-point correlation functions of the CFT scalar field are used to calculate
the spectra of the corresponding metric perturbations in the asymptotically dS
Universe and, hence, cosmological observables in the post-inflationary epoch.
Similarly, higher-point correlation functions in the CFT should lead to more
complicated cosmological observables.
