K-Inflation with a Dark Energy Coupling

It is usually thought that the quintessence as a fundamental scalar field was already present during the inflationary epoch. While there are various models in which the quintessence couples to other species, it is attractive to anticipate a coupling between the quintessence and the inflaton in the very early universe as well. We consider such a coupling in the context of k-inflation. The coupling function and the potential of the quintessence are chosen to be of power law forms. We show such a coupling affects the speed of sound for the inflaton field as well as the power spectra of perturbations.