General Canonical Quantum Gravity Theory and that of the Universe and General Black Hole

This paper gives both a general canonical quantum gravity theory and the general canonical quantum gravity theories of the Universe and general black hole, and discovers the relations reflecting symmetric properties of the standard nonlinear gravitational Lagrangian, which are not relevant to any concrete metric models. This paper concretely shows the general commutation relations of the general gravitational field operators and their zeroth, first, second and third style, respectively, of high order canonical momentum operators for the general nonlinear system of the standard gravitational Lagrangian, and then has finished all the four styles of the canonical quantization of the standard gravity.

Hamiltonian Renormalization V: Free Vector Bosons

In a recent proposal we applied methods from constructive QFT to derive a Hamiltonian Renormalization Group in order to employ it ultimately for canonical quantum gravity. The proposal was successfully tested for free scalar fields and thus a natural next step is to test it for free gauge theories. This can be done in the framework of reduced phase space quantization which allows using techniques developed earlier for scalar field theories. In addition, in canonical quantum gravity one works in representations that support holonomy operators which are ill defined in the Fock representation of say Maxwell or Proca theory. Thus, we consider toy models that have both features, i.e. which employ Fock representations in which holonomy operators are well-defined. We adapt the coarse graining maps considered for scalar fields to those theories for free vector bosons. It turns out that the corresponding fixed pointed theories can be found analytically.

Canonical Quantum Gravity, Constructive QFT, and Renormalisation

The canonical approach to quantum gravity has been put on a firm mathematical foundation in the recent decades. Even the quantum dynamics can be rigorously defined, however, due to the tremendously non-polynomial character of the gravitational interaction, the corresponding Wheeler–DeWitt operator-valued distribution suffers from quantisation ambiguities that need to be fixed. In a very recent series of works, we have employed methods from the constructive quantum field theory in order to address those ambiguities. Constructive QFT trades quantum fields for random variables and measures, thereby phrasing the theory in the language of quantum statistical physics. The connection to the canonical formulation is made via Osterwalder–Schrader reconstruction. It is well known in quantum statistics that the corresponding ambiguities in measures can be fixed using renormalisation. The associated renormalisation flow can thus be used to define a canonical renormalisation programme. The purpose of this article was to review and further develop these ideas and to put them into context with closely related earlier and parallel programmes.

Quantum fluctuations and cosmological particle creation from oscillating massive scalar field in two-mode quantum optical states

In this paper, by the use of entangled and nonentangled coherent and squeezed state formalism of two-mode nonclassical states, we studied the chaotic inflationary model of a massive scalar field with quadratic potential in the semiclassical gravity, derived from canonical quantum gravity. It was found that the semiclassical quantum gravity leads to the same power-law expansion of the universe as that of the matter-dominated era [Formula: see text] in an oscillatory phase of the scalar field in all the nonclassical quantum states considered. The coherently oscillating scalar field in the expanding universe suffers from the phenomenon of particle creation which restricts the duration of stable coherent oscillations of the scalar field dependent on the parameters of the states considered and affect in a certain way the abundant particle production owing to the parametric resonance of bosonic fields coupled to this coherently oscillating scalar field.

Modifications to gravitational wave equation from canonical quantum gravity

It is expected that the quantum nature of spacetime leaves its imprint in all semiclassical gravitational systems, at least in certain regimes, including gravitational waves. In this paper we investigate such imprints on gravitational waves within a specific framework: space is assumed to be discrete (in the form of a regular cubic lattice), and this discrete geometry is quantised following Dirac’s canonical quantisation scheme. The semiclassical behavior is then extracted by promoting the expectation value of the Hamiltonian operator on a semiclassical state to an effective Hamiltonian. Considering a family of semiclassical states representing small tensor perturbations to Minkowski background, we derive a quantum-corrected effective wave equation. The deviations from the classical gravitational wave equation are found to be encoded in a modified dispersion relation and controlled by the discreteness parameter of the underlying lattice. For finite discretisations, several interesting effects appear: we investigate the thermodynamical properties of these modified gravitons and, under certain assumptions, derive the tensor power spectrum of the cosmic microwave background. The latter is found to deviate from the classical prediction, in that an amplification of UV modes takes place. We discuss under what circumstances such effect can be in agreement with observations.

Forming the Canon

This chapter charts the early development of the canonical quantum gravity (that is, the quantization of the gravitational field in Hamiltonian form). What we find in this period include: the establishment of a procedure for quantizing in curved spaces; the first expressions for the Hamiltonian of general relativity; recognition of the existence and importance of constraints (i.e. the generators of infinitesimal coordinate transformations); a focus on the problem of observables (and the realisation of conceptual implications in defining these for generally relativistic theories), and a (template of a) method for quantizing the theory. Although it commenced relatively early, the canonical approach was slow in its subsequent development. This had two sources: (1) it required the introduction of tools and concepts from outside of quantum gravity proper (namely, the constraint machinery and the parameter formalism); (2) by its very nature, it is highly rigorous in a conceptual sense, demanding lots of groundwork to be established, in terms of the structure of physical observables, before the actual issue of quantization can even be considered. Work was further complicated by the fact that these two sources of difficulty happened to be entangled. Particular emphasis is placed on the parameter formalism of Paul Weiss.

Conformal cyclic evolution of phantom energy dominated universe

From the Wheeler Dewitt solutions, the scale factor of the initial universe is discussed. In this study scale factors from Wheeler Dewitt solutions, loop quantum gravity, and phantom energy dominated stages are compared. Certain modifications have been attempted in scale factor and quantum potentials driven by canonical quantum gravity approaches. Their results are discussed in this work. Despite increment of phantom energy density avoidance of big rip is reported. Scale factors predicted from various models is discussed in this work. Relationship between scale factors and smooth continuation of aeon is discussed by the application of conformal cyclic cosmology. Quantum potentials for various models are correlated and a correction parameter is included on the cosmological constant. Phantom energy dominated, final stage non-singular evolution of the universe is reported. Eternal increment of phantom energy density without interacting with dark matter is reported for the consequence of evolution of the future universe. Also, the non-interacting solutions of phantom energy and dark matter are explained. As the evolution continues even after the final singularity is approached, the validity of conformal cyclic cosmology is predicted. Non zero values for the scale factor for the set of eigenvalues are reported with a graph

Applications of Canonical Quantum Gravity to Cosmology

We applied quantum gravitational results to spatially unbounded Friedmann universes and tried to answer some questions related to dark energy, dark matter, inflation, and the missing antimatter.

Quantum imploding scalar fields

The d’Alembertian □ ϕ = 0 has the solution ϕ = f ( v )/ r , where f is a function of a null coordinate v , and this allows creation of a divergent singularity out of nothing. In scalar-Einstein theory a similar situation arises both for the scalar field and also for curvature invariants such as the Ricci scalar. Here what happens in canonical quantum gravity is investigated. Two minispace Hamiltonian systems are set up: extrapolation and approximation of these indicates that the quantum mechanical wave function can be finite at the origin.