Intrinsic time in Wheeler-DeWitt conformal superspace

TL;DR

This paper introduces an intrinsic time variable in Geometrodynamics using a scaled Dirac mapping and conformal variables, linking it to cosmological observations like redshift.

Contribution

It proposes a new intrinsic time based on the logarithm of the spatial metric determinant, applicable in cosmology and solved within conformal variables.

Findings

Intrinsic time as logarithm of spatial metric determinant

Existence of global time under constant mean curvature slicing

Redshift evidence supporting intrinsic time

Abstract

An intrinsic time in Geometrodynamics is obtained with using a scaled Dirac's mapping. By addition of a background metric, one can construct a scalar field. It is suitable to play a role of intrinsic time. Cauchy problem was successfully solved in conformal variables because they are physical ones. First, the intrinsic time as a logarithm of determinant of spatial metric, was applied to a cosmological problem by Misner. A global time is exist under condition of constant mean curvature slicing of spacetime. The volume of hypersurface and so-called mean York's time are canonical conjugated pair. So, the volume is the intrinsic global time by its sense. The experimentally observed redshift in cosmology is the evidence of its existence.