Tachyon-Dilaton-induced inflation as an α′-resummed string background

Abstract

Within the framework of a novel functional method on the world-sheet of the string, we discuss simple but re-summed (in the Regge slope) inflationary scenarios in the context of closed Bosonic strings, living in four target-space dimensions, in the presence of non-trivial tachyon, dilaton and graviton cosmological backgrounds. The inflationary solutions are argued to guarantee the vanishing of the corresponding Weyl anomaly coefficients in a given world-sheet renormalization scheme, thereby ensuring conformal invariance of the corresponding σ-model to all orders in the Regge slope. The key property is the requirement of ``homogeneity'' of the corresponding Weyl anomaly coefficients. Inflation entails appropriate relations between the dilaton and tachyon field configurations, whose form can lead to either a de Sitter vacuum, incompatible though (due to the cosmic horizons) with the perturbative string scattering amplitudes, or to cosmic space-times involving brief inflationary periods, interpolating smoothly between power-law and/or Minkowski Universes. The latter situation is characterized by well-defined scattering amplitudes, and is thus compatible with a perturbative string framework. It is this scenario that we consider a self-consistent ground state in our framework, which is based on local field redefinitions of background fields.