Semiclassical momentum representation in quantum cosmology

TL;DR

This paper explores a novel semiclassical approach in quantum cosmology using momentum representation, addressing limitations of WKB near turning points and enabling the use of curvature as a time variable.

Contribution

It introduces a new class of semiclassical solutions in quantum cosmology based on momentum representation, improving the treatment of turning points and the problem of time.

Findings

Momentum representation offers advantages over traditional methods.

It enables using curvature as a good clock in quantum cosmology.

Semiclassical solutions parametrized by York time are obtained.

Abstract

It is well-known that the standard WKB approximation fails to provide semiclassical solutions in the vicinity of turning points. However, turning points arise in many cosmological scenarios. In a previous work, we obtained a new class of semiclassical solutions of the Wheeler-deWitt equation using the conjugate momentum to the geometric variable. We present here a detailed study of their main properties. We carefully compare them to usual WKB solutions and turning point resolutions using Airy functions. We show that the momentum representation possesses many advantages that are absent in other apporaches. In particular, this framework has a key application in tackling the problem of time. It allows us to use curvature as a time variable, and control the corresponding domain of validity, i.e. under which conditions it provides a good clock. We consider several applications, and in particular show how this allows us to obtain semiclassical solutions of the Wheeler-DeWitt equation parametrized by York time.