Acceleration of the Universe in Type-0 Noncritical Strings

Abstract

Presently there is preliminary observational evidence that the cosmological constant might be non zero, and hence that our Universe is eternally accelerating (de Sitter). This poses fundamental problems for string theory, since a scattering matrix is not well defined in such Universes. In a previous paper we have presented a model, based on (non-equilibrium) non-critical strings, which is characterized by eventual "graceful" exit from a de Sitter phase. The model is based on a type-0 string theory, involving D3 brane worlds, whose initial quantum fluctuations induce the non criticality. We argue in this article that this model is compatible with the current observations. A crucial rôle for the correct "phenomenology" of the model is played by the relative magnitude of the flux of the five form of the type 0 string to the size of five of the extra dimensions, transverse to the direction of the flux-field. We do not claim, at this stage at least, that this model is a realistic physical model for the Universe, but we find it interesting that the model cannot be ruled out immediately, at least on phenomenological grounds.

The string coupling accelerates the expansion of the universed

“…We see from (2.4) that a(t E ) scales linearly with t E at very large values of this Einsteinframe cosmological time [18]. Hence the cosmic horizon expands logarithmically, allowing for the proper definition of asymptotic states and thus a scattering matrix.…”

“…Thus, the dark energy density relaxes to zero for t E → ∞ in such non-critical string cosmologies [18,15]. Finally, during this epoch the deceleration parameter becomes [15]:…”

“…One example was a ten-dimensional Type-0 string theory [17] compactified on a space with five flat dimensions and a non-trivial flux parallel to the remaining dimension [18]. In this example, the sizes of the extra dimensions rapidly froze to fixed values, while the positive central-charge deficit Q 2 > 0 relaxes to a constant value Q 2 0 at large times.…”

“…Hence the cosmic horizon expands logarithmically, allowing for the proper definition of asymptotic states and thus a scattering matrix. At large t E , the Hubble parameter becomes 5) and the effective four-dimensional vacuum energy density is [18]:…”

“…where we use the fact that [18] the central-charge deficit approaches its equilibrium value Q 0 for large t E . Thus, the dark energy density relaxes to zero for t E → ∞ in such non-critical string cosmologies [18,15].…”