We consider solutions of the cosmological equations pertaining to a dissipative, dilatondriven off-equilibrium Liouville Cosmological model, which may describe the effective field theoretic limit of a non-critical string model of the Universe. The non-criticality may be the result of an early-era catastrophic cosmic event, such as a big-bang, brane-world collision etc. The evolution of the various cosmological parameters of the model are obtained, and the effects of the dilaton and off-shell Liouville terms, including briefly those on relic densities, which distinguish the model from conventional cosmologies, are emphasised. May 2006The current astrophysical data [1][2][3][4] are capable of placing stringent constraints on the nature of the dark energy, whose equation of state may be determined by means of an appropriate global fit. Most of the analyses so far are based on effective four-dimensional Robertson-Walker Universes, which satisfy on-shell dynamical equations of motion of the Einstein-Friedmann form. Even in modern approaches to brane cosmology, which are described by equations that deviate during early eras of the Universe from the standard Friedmann equation (which is linear in the energy density), the underlying dynamics is assumed to be of classical equilibrium (on-shell) nature, in the sense that it satisfies a set of equations of motion derived from the appropriate minimisation of an effective space-time Lagrangian.However, cosmology may not be an entirely classical equilibrium situation [5,6]. The initial Big Bang or other catastrophic cosmic event, such as the collision of two brane worlds in the modern context of brane theories [7], which led to the initial rapid expansion of the Universe, may have caused a significant departure from classical equilibrium dynamics in the early Universe, whose signatures may still be present at later epochs including the present era. In [6,8] there have been proposed specific models for the cosmological dark energy which are of this type, being associated with a rolling dilaton field that is a remnant of this non-equilibrium phase, described by a generic non-critical string theory [5,9,10]. The basic ingredient of this approach is the identification of target time with a local, dynamical (irreversible) renormalization group scale on the world sheet of the string [7,11], being representing by the so-called Liouville mode [5,10]. The consistency of the approach is guaranteed by the existence of solutions to the pertinent equations ("Liouville conditions") for the various background target-space fields over which the non-critical Liouville-dressed [9] σ-model propagates. The latter express the restoration of conformal invariance conditions after Liouville dressing. We call this scenario 'Q-cosmology' [6].It must be stressed that this Q-cosmology is physically very different from standard dilaton cosmologies in critical strings [12], where on-shell equations of motion for the background fields are satisfied. Our non-equilibrium, non-classical theory is not described...

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.

We study the cosmological evolution of a type-0 string theory by employing noncriticality, which may be induced by fluctuations of the D3 brane worlds. We check the consistency of the approach to O(α ′ ) in the corresponding σ-model. The ten-dimensional theory is reduced to an effective four-dimensional model, with only time dependent fields.We show that the four-dimensional universe has an inflationary phase and graceful exit from it, while the other extra dimensions are stabilized to a constant value, with the fifth dimension much larger than the others. We pay particular attention to demonstrating the rôle of tachyonic matter in inducing these features. The Universe asymptotes, for large times, to a non-accelerating linearly-expanding Universe with a time-dependent dilaton and a relaxing to zero vacuum energy a lá quintessence.