An extension of cosmological dynamics with York time

TL;DR

This paper explores extending cosmological models using York time beyond the traditional negative domain, analyzing its implications for quantum cosmology and inflationary potentials.

Contribution

It introduces a temporal extension of flat cosmological models with York time to include positive values, crucial for consistent quantization and understanding universe evolution.

Findings

Extended the model to include T>0, covering the 'other side' of cosmological evolution.

Identified potentials that allow smooth transitions across T=0.

Discussed implications for quantum cosmology and inflation theories.

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.