Inflation and oscillations of the Universe in 4D dilatonic gravity

Abstract

We investigate the inflation of the Universe in a model of four-dimensional dilatonic gravity with a massive dilaton field $\ensuremath{\Phi}.$ The dilaton simultaneously plays the role of an inflation field and a quintessence field. It yields a sequential hyperinflation with a graceful exit to asymptotic de Sitter space-time, which is an attractor, and is approached as $\mathrm{exp}(\ensuremath{-}\sqrt{3{\ensuremath{\Lambda}}^{\mathrm{obs}}}ct/2).$ The time duration of the inflation is reciprocal to the mass of the dilaton: $\ensuremath{\Delta}{t}_{\mathrm{infl}}\ensuremath{\sim}{m}_{{}_{\ensuremath{\Phi}}}^{\ensuremath{-}1}.$ The typical number of e-folds in the simplest model of this type is shown to be realistic without fine-tuning.