SNUTP 96/043 hep-th/9605176 Back Reaction and Graceful Exit in String Inflationary Cosmology

Classical string cosmology consists of two branches related to each other by scale-factor duality: a super-inflation branch and a Friedmann-RobertsonWalker (FRW) branch. Curvature and string coupling singularity separates the two branches, hence posing ‘graceful exit problem’ to super-inflationary string cosmology. In an exactly soluble two-dimensional compactification model it is shown that quantum back reaction retards curvature and string coupling growth and connects the super-inflation branch to the FRW branch without encountering a singularity. This may offer an attractive solution to the ‘graceful exit problem’ in string inflationary cosmology. 04.60.Kz,11.25.-w,98.80.Cq,98.80.Hw Typeset using REVTEX 1 In the Standard Model of big bang cosmology horizon and flatness problems constitute two notorious naturalness problems. Inflationary cosmology [1] was invented to solve these problems through a long period of accelerated expansion ȧ(t) > 0, ä(t) > 0. Three different types of inflation satisfy these conditions: de Sitter a(t) ∼ e, power-law a(t) ∼ t(p > 1) and super-inflation a(t) ∼ (−t)(p < 0). Among them super-inflation is regarded as the most attractive: super-inflation is driven by kinetic energy, hence, largely model-independent and free from fine-tuning problem typically present in potential energy driven de Sitter or powerlaw inflation models. Veneziano [2] has first pointed out that, in classical string cosmology, thanks to the scalefactory duality the super-inflation arises naturally in addition to decelerating expansion of Friedmann-Robertson-Walker (FRW) type. One might then hope that superstring theory gives rise to a successful big bang cosmology starting from a super-inflationary branch and then smoothly evolve into a FRW-type branch. It has been noted, however, that such evolution cannot be realized since the super-inflation phase ends with divergent curvature and string coupling and cannot be continued to regular FRW phase. Because of this string inflationary cosmology is afflicted by a ‘graceful exit problem’ [3]. The fact that both curvature and string coupling grow arbitrarily strong as the superinflation phase evolves is a universal feature of Veneziano’s string cosmology in all spacetime dimensions [4]. This indicates that classical description of string cosmology breaks down and that quantum effects modify evolution of the two classical branches significantly. One may then wonder if quantum back reaction can wash out curvature and string coupling divergences completely that a transition to FRW phase becomes possible. In this Letter, we show that branch change, hence, graceful exit is indeed possible after quantum back reaction is taken into account. To address quantum back reaction in a controlled approximation we consider an exactly soluble two dimensional string compactification model. The model is described by the same action as the dilaton gravity of Callan, Harvey, Giddings and Strominger (CGHS) [5]