An extension of cosmological dynamics with York time

Abstract

It has been suggested that the York parameter $T$ (effectively the scalar extrinsic curvature of a spatial hypersurface) may play the role of a fundamental time parameter. In a flat, forever expanding cosmology the York parameter remains always negative, taking values $T=-\infty$ at the big bang and approaching some finite non-positive value as $t\rightarrow\infty$, $t$ being the usual cosmological time coordinate. Based on previous results concerning a simple, spatially flat cosmological model with a scalar field, we provide a temporal extension of this model to include `times' $T>0$, an epoch not covered by the cosmological time coordinate $t$, and discuss the dynamics of this `other side' and its significance. We argue that the extension is necessary if a consistent quantisation scheme is to exist. Furthermore, we investigate which types of potentials lead to smooth transitions, paying particular attention to currently favoured inflaton potentials.