Abstract
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.
Highlights
Because of the well-known correspondence between asymptotically anti–de Sitter (AdS) spacetimes and conformal field theories (CFTs) [1,2,3,4], along with the observation that the isometries of de Sitter space act as the conformal group on the dS boundary, it has long been expected that a similar duality should exist between asymptotically dS cosmologies and a different class of conformal field theory (CFT) [5,6,7]
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, equal to the Hartle-Hawking (HH) wave function of an asymptotically dS universe
We have put forward a new correspondence between asymptotically dS space and a CFT dual by showing that the partition function of the CFT is equal to the HH wave function of the dS space
Summary
Because of the well-known correspondence between asymptotically anti–de Sitter (AdS) spacetimes and conformal field theories (CFTs) [1,2,3,4], along with the observation that the isometries of de Sitter (dS) space act as the conformal group on the dS boundary, it has long been expected that a similar duality should exist between asymptotically dS cosmologies and a different class of CFTs [5,6,7]. We have recently proposed that this state should describe the initial state of the Universe [42]; the motivation being that a state of maximal entropy is just what is needed to resolve spacelike singularities such as the interior of an event horizon or the preinflationary Universe The latter case leads to a duality connecting the string state to dS space and, as shown in our current discussion, implies a duality between dS space and a thermal-scalar condensate. Previous studies by Silverstein and collaborators have discussed, in a very different context, how a tachyon condensate can be used to tame spacelike singularities [44,45,46,47] Note though that this dS spacetime is the invented artifact of a late-time observer, who wishes to explain the state’s origins and properties by imposing some form of semiclassical evolution.
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