Graceful exit problem and stress-energy-momentum tensors revisited in the two-dimensional string cosmology

We study the graceful exit problem and the role of the stress-energymomentum tensors in the two-dimensional string cosmology. The one-loop quantum correction of conformal fields is incorporated in the arbitrary large N limit to ensure exact quantum solvability. The only solution which gives the bounded curvature with the asymptotic flatness is restricted to the first branch under some conditions. However, even in this case, the accelerating expansion is forever. We show that the only nonvanishing quantum stressmomentum tensor is the pressure part(Txx) which is of relevance to the dynamical evolution of the universe in the comoving coordinate. The quantum energy part is zero since the negative contribution of the induced conformal matters always cancels the positive quantity of the induced dilaton part in terms of the constraint equation. electronic address:[email protected] electronic address:[email protected] 1 Recently, there has been much interests in the graceful exit problem [1] of the string inflationary cosmology [2] with the scale factor duality [3]. The essential problem is due to the curvature singularity arising from the classical cosmological solutions of low-energy string theory. On the other hand, in the four-dimensional Einstein gravity with the loop effect which is regarded as Einstein frame of string theory [4], some cosmological singularity problems have been studied in terms of the quantum back reaction of space time [5,6]. Further, the quantum tunneling with the finite probability between the classically distinct phases corresponding to the pre(accelerated) and post(decelerating) big bang can be possible in the low energy string background [7]. This fact may solve the graceful exit problem of the string cosmology. The exactly soluble Callan-Gidding-Harvey-Strominger(CGHS) model [8,9], which has been successful to deal with the two-dimensional black holes, has been recently investigated by Rey [10] to show whether or not the branch-changing phase transition appears in the two-dimensional string cosmology. This model was also extended to the generalized twodimensional dilaton gravity model by Gasperini and Veneziano [11]. The quantum backreacted solution of the first branch (second branch) with the bounded curvature scalar has been defined within the whole comoving time from the past infinity to the future infinity, so that the second branch (first branch) effectively disappear instead of connecting two distinct branches. On the other hand, this model has the negative anomaly coefficient which corresponds to the negative Hawking radiation and the number of conformal matter fields are restricted to less than 24. Thus it is natural to study the CGHS model in the manner to take the arbitrary large positive number of matter fields to take good approximation within the oneloop vacuum polarization of the conformal matter fields [13]. Very recently, Bose and Kar [14] suggest the way how to overcome the limit of N by adding a local covariant counter-term and the exact scale factor is obtained. In this paper, we reconsider the graceful exit problem in the two-dimensional string cosmology with the slightly generalized counter-terms containing the local term of Ref. [14] 2 and mainly study the role of the stress-momentum tensors induced by the quantum corrections. The only solution which gives the bounded curvature with the asymptotic flatness is restricted to the first branch. However, even in this case, the decelerating phase does not appear although the solution has asymptotic flatness. We show that the only nonvanishing quantum stress-energy-momentum tensor is the pressure part(Txx) which is of relevance to the dynamical evolution of the universe in the comoving coordinate. The total quantummechanical energy is zero since the negative contribution of the induced conformal matters always cancels the positive quantity of the induced dilaton part in terms of constraint equation. Let us now consider the two-dimensional low-energy string theory given by SDG = 1 2π ∫