Intrinsic time in Geometrodynamics: introduction and application to Friedmann cosmology

Abstract

An intrinsic local 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. A volume of hypersurface and the 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. An intrinsic time of homogeneous models is global. The Friedmann equation by its sense ties time intervals. Exact solutions of the Friedmann equation in Standard cosmology with standard and conformal units are presented. Theoretical curves interpolated the Hubble diagram on latest supernovae are expressed in analytical form. The class of functions in which the concordance model is described is Weierstrass meromorphic functions. The Standard cosmological model is used for fitting the modern Hubble diagram. The physical interpretation of the modern data from concept of conformal magnitudes is simpler, so is preferable. Contents 1 Introduction. Physical observables 2 ADM variational functional of General Relativity. Notations 3 Shape dynamics 4 Cauchy problem in Conformal gravitation 5 Many-fingered intrinsic time in Geometrodynamics 6 Deparametrization 7 Global time 8 Global intrinsic time in FRW universe 9 Global time in perturbed FRW universe 10 Friedmann equation in Classical cosmology 11 Friedmann equation in Classical cosmology with conformal units 12 Comparisons of approaches 13 Conclusions