The Universe emerging from a vacuum in loop-string cosmology

In this paper we study a description of the Universe based on a low energy superstring theory modified by loop quantum gravity effects. This approach was proposed by De Risi et al (2007 Phys. Rev. D 76 103531). We show that in contrast with the case for a string motivated pre-big bang scenario, the cosmological realization of the t-duality transformation is not necessary to avoid an initial singularity. In the model considered, the Universe starts its evolution in the vacuum phase at time t ->-infinity. In this phase the scale factor a -> 0, energy density. rho -> 0 and the coupling of the interactions g(s)(2)-> 0. After this stage the Universe evolves to the non- singular hot big bang phase, rho -> rho(max) < infinity. Then the standard classical Universe emerges. During the whole evolution the scale factor increases monotonically. We solve this model analytically. We also propose and solve numerically the model with an additional dilaton potential in which the Universe starts its evolution from the asymptotically free vacuum phase, g(s)(2)-> 0, and then evolves non- singularly to the emerging dark energy dominated phase with the saturated coupling constant g(s)(2)-> 0 const.