An extension of cosmological dynamics with York time

  • Philipp Roser
Research Article


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.


York time CMC slicing Cosmological extension  Scalar-field cosmology 



The author would like to thank Antony Valentini for helpful discussions and comments. This work was in part supported by the Foundational Questions Institute (


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Kinard Laboratory, Department of Physics and AstronomyClemson UniversityClemsonUSA

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