Thermal duality and non-singular cosmology in d-dimensional superstrings

Abstract

We are presenting the basic ingredients of a stringy mechanism able to resolve both the Hagedorn instabilities of finite temperature superstrings as well as the initial singularity of the induced cosmology in arbitrary dimensions. These are shown to be generic in a large class of (4, 0) type II superstring vacua, where non-trivial "gravito-magnetic" fluxes lift the Hagedorn instabilities of the thermal ensemble and the temperature duality symmetry is restored. This symmetry implies a universal maximal critical temperature. In all such models there are three characteristic regimes, each with a distinct effective field theory description: Two dual asymptotically cold regimes associated with the light thermal momentum and light thermal winding states, and the intermediate regime where additional massless thermal states appear. The partition function exhibits a conical structure as a function of the thermal modulus, irrespectively of the spacetime dimension. Thanks to asymptotic right-moving supersymmetry, the genus-1 partition function is well-approximated by that of massless thermal radiation in all of the three effective field theory regimes. The resulting timeevolution describes a bouncing cosmology connecting, via spacelike branes, a contracting thermal "winding" Universe to an expanding thermal "momentum" Universe, free of any essential curvature singularities. The string coupling remains perturbative throughout the cosmological evolution. Bouncing cosmologies are presented for both zero and negative spatial curvature.

Aspects of String Cosmology

“…Under the Z 2 symmetry (−1) F R the right-moving R sector changes sign. This pattern of asymmetric susy breaking leads to extended symmetry points, when the internal radii are at the fermionic point [31][32][33][34][35][36]. At finite temperature, such points in moduli space are preferred, with the moduli participating in the breaking of the right-moving supersymmetries being stabilized at the extended symmetry point values [51].…”

“…We shall focus on another class of bouncing thermal string cosmologies, exploiting stringy phase transitions and phenomena that can occur at temperatures close to the Hagedorn temperature. The non-singular cosmological solutions are based on a mechanism that resolves the Hagedorn instabilities of finite temperature strings, realizable in a large class of initially N = (4, 0) type II superstring models [31][32][33]. We also review some aspects of strings at finite temperature and (partial) spontaneous supersymmetry breaking via geometrical fluxes.…”

“…We have focused on the highly symmetric Hybrid vacua, where the presence of exact rightmoving MSDS symmetry leads to exact computations, as we will see below, but a large class of (4, 0) models can be constructed in various dimensions [32][33][34].…”

“…The Hagedorn free models can be described in terms of freely acting asymmetric orbifolds of the form (−1) F L δ 0 , where δ 0 is a Z 2 -shift along the Euclidean time circle [31,32,34,36]. In the Hybrid example, the partition function is given explicitly by 25) and it is finite for all values of the thermal modulus R 0 .…”

“…Two classes of string cosmological solutions will be discussed to illustrate this pattern. The first class consists of string gas cosmologies associated to certain special, thermal configurations of type II N = (4, 0) models [31][32][33]. Finite temperature is introduced along with non-trivial "gravito-magnetic" fluxes that lift the Hagedorn instabilities of the canonical ensemble and restore thermal T-duality symmetry [34][35][36] 1 .…”