New cosmological tracker solution for quintessence

Abstract

In this paper we propose a quintessence model with the potential $V(\ensuremath{\Phi}{)=V}_{0}[\mathrm{sinh}(\ensuremath{\alpha}\sqrt{{\ensuremath{\kappa}}_{0}}\ensuremath{\Delta}\ensuremath{\Phi}){]}^{\ensuremath{\beta}}$ with $\ensuremath{\beta}<0,$ whose asymptotic behavior corresponds to an inverse power-law potential at early times and to an exponential one at late times. We demonstrate that this is a tracker solution and that it could have driven the Universe into its current inflationary stage. The exact solutions and the description for a complete evolution of the Universe are also given. We compare such a model with current cosmological observations.