A New Approach in Quantum Gravity and its Cosmological Implications

TL;DR

This paper introduces a reformulation of quantum geometrodynamics that resolves slicing ambiguities and leads to a Schrödinger-like evolution, with significant implications for cosmology and dark matter modeling.

Contribution

It presents a novel approach fixing the reference frame in quantum gravity, transforming constraints into evolutive equations, and linking the theory to cosmological dark matter effects.

Findings

Provides a parabolic Hamiltonian constraint formulation.

Introduces a pressureless perfect fluid as a reference frame.

Suggests a dust component as dark matter in cosmology.

Abstract

This work concerns a new reformulation of quantum geometrodynamics, which allows to overcome a fundamental ambiguity contained in the canonical approach to quantum gravity: the possibility of performing a (3+1)-slicing of space-time, when the metric tensor is in a quantum regime. Our formulation provides also a procedure to solve the problems connected to the so called "frozen formalism". In particular we fix the reference frame (i.e. the lapse function and the shift vector) by introducing the so called "kinematical action"; as a consequence, the new hamiltonian constraints become parabolic, so arriving to evolutive (Schroedinger-like) equations for the quantum dynamics. The kinematical action can be interpreted as the action of a pressureless, but, in general, non geodesic perfect fluid, so in the semi classical limit our theory leads to the dynamics of the gravitational field coupled to a dust which represents the material reference frame we have introduced fixing the slicing. We also investigate the cosmological implications of the presence of the dust, which, in the WKB limit of a cosmological problem, makes account for a "dark matter" component and could play, at present time, a dynamical role.