Solving the Problem of Time in General Relativity and Cosmology with Phantoms and k -- Essence

TL;DR

This paper demonstrates that a scalar field with derivative-only Lagrangian can fully deparametrize General Relativity, enabling straightforward construction of observables and a positive physical Hamiltonian, with implications for cosmology and universe evolution.

Contribution

It introduces a novel approach to deparametrize General Relativity using a Dirac-Born-Infeld type scalar field, linking quantum gravity considerations with cosmological models.

Findings

Physical observables can be explicitly constructed.

The physical Hamiltonian is positive and closely related to standard cosmological models.

The model predicts a classical recollapse of the universe at late times.

Abstract

We show that if the Lagrangean for a scalar field coupled to General Relativity only contains derivatives, then it is possible to completely deparametrise the theory. This means that 1.Physical observables, i.e. functions which Poisson commute with the spatial diffeomorphism and Hamiltonian constraints of General Relativity, can be easily constructed. 2. The physical time evolution of those observables is generated by a natural physical Hamiltonian which is (constrained to be) positive. The mechanism by which this works is due to Brown and Kucha\v{r}. In order that the physical Hamiltonian is close to the Hamiltonian of the standard model and the one used in cosmology, the required Lagrangean must be that of a Dirac -- Born -- Infeld type. Such matter has been independently introduced previously by cosmologists in the context of k -- essence due to Armendariz-Picon, Mukhanov and Steinhardt in order to solve the cosmological coincidence (dark energy) problem. We arrive at it by totally unrelated physical considerations originating from quantum gravity. Our manifestly gauge invariant approach leads to important modifictaions of the interpretation and the the analytical appearance of the standard FRW equations of classical cosmology in the late universe. In particular, our concrete model implies that the universe should recollapse at late times on purely classical grounds.