Non-minimal couplings, quantum geometry and black hole entropy

The black hole entropy calculation for type I isolated horizons, based on loop quantum gravity, is extended to include non-minimally coupled scalar fields. Although the non-minimal coupling significantly modifies quantum geometry, the highly non-trivial consistency checks for the emergence of a coherent description of the quantum horizon continue to be met. The resulting expression of black hole entropy now depends also on the scalar field precisely in the fashion predicted by the first law in the classical theory (with the same value of the Barbero-Immirzi parameter as in the case of minimal coupling).Comment: 14 pages, no figures, revtex4. Section III expanded and typos correcte

2+1 Gravity without dynamics

A three dimensional generally covariant theory is described that has a 2+1 canonical decomposition in which the Hamiltonian constraint, which generates the dynamics, is absent. Physical observables for the theory are described and the classical and quantum theories are compared with ordinary 2+1 gravity.Comment: 9 page

Quantum Nature of the Big Bang: An Analytical and Numerical Investigation

Analytical and numerical methods are developed to analyze the quantum nature of the big bang in the setting of loop quantum cosmology. They enable one to explore the effects of quantum geometry both on the gravitational and matter sectors and significantly extend the known results on the resolution of the big bang singularity. Specifically, the following results are established for the homogeneous isotropic model with a massless scalar field: i) the scalar field is shown to serve as an internal clock, thereby providing a detailed realization of the `emergent time' idea; ii) the physical Hilbert space, Dirac observables and semi-classical states are constructed rigorously; iii) the Hamiltonian constraint is solved numerically to show that the big bang is replaced by a big bounce. Thanks to the non-perturbative, background independent methods, unlike in other approaches the quantum evolution is deterministic across the deep Planck regime. Our constructions also provide a conceptual framework and technical tools which can be used in more general models. In this sense, they provide foundations for analyzing physical issues associated with the Planck regime of loop quantum cosmology as a whole.Comment: Revised version to appear in Physical Review D. References added and typos correcte

Phenomenological implications of an alternative Hamiltonian constraint for quantum cosmology

In this paper we review a model based on loop quantum cosmology that arises from a symmetry reduction of the self dual Plebanski action. In this formulation the symmetry reduction leads to a very simple Hamiltonian constraint that can be quantized explicitly in the framework of loop quantum cosmology. We investigate the phenomenological implications of this model in the semi-classical regime and compare those with the known results of the standard Loop Quantum Cosmology.Comment: 10 pages, 7 figure

Inflation from Quantum Geometry

Quantum geometry predicts that a universe evolves through an inflationary phase at small volume before exiting gracefully into a standard Friedmann phase. This does not require the introduction of additional matter fields with ad hoc potentials; rather, it occurs because of a quantum gravity modification of the kinetic part of ordinary matter Hamiltonians. An application of the same mechanism can explain why the present-day cosmological acceleration is so tiny.Comment: 4 pages, 3 figure

Photons from quantized electric flux representations

The quantum theory of U(1) connections admits a diffeomorphism invariant representation in which the electric flux through any surface is quantized. This representation is the analog of the representation of quantum SU(2) theory used in loop quantum gravity. We investigate the relation between this representation, in which the basic excitations are `polymer-like', and the Fock representation, in which the basic excitations are wave-like photons. We show that normalizable states in the Fock space are associated with `distributional' states in the quantized electric flux representation. This work is motivated by the question of how wave-like gravitons in linearised gravity arise from polymer-like states in non-perturbative loop quantum gravity.Comment: 22 pages, no figure

Constructing Hamiltonian quantum theories from path integrals in a diffeomorphism invariant context

Osterwalder and Schrader introduced a procedure to obtain a (Lorentzian) Hamiltonian quantum theory starting from a measure on the space of (Euclidean) histories of a scalar quantum field. In this paper, we extend that construction to more general theories which do not refer to any background, space-time metric (and in which the space of histories does not admit a natural linear structure). Examples include certain gauge theories, topological field theories and relativistic gravitational theories. The treatment is self-contained in the sense that an a priori knowledge of the Osterwalder-Schrader theorem is not assumed.Comment: Plain Latex, 25 p., references added, abstract and title changed (originally :``Osterwalder Schrader Reconstruction and Diffeomorphism Invariance''), introduction extended, one appendix with illustrative model added, accepted by Class. Quantum Gra

Photon inner product and the Gauss linking number

It is shown that there is an interesting interplay between self-duality, loop representation and knots invariants in the quantum theory of Maxwell fields in Minkowski space-time. Specifically, in the loop representation based on self-dual connections, the measure that dictates the inner product can be expressed as the Gauss linking number of thickened loops.Comment: 18 pages, Revtex. No figures. To appear in Class. Quantum Gra

On the Physical Hilbert Space of Loop Quantum Cosmology

In this paper we present a model of Riemannian loop quantum cosmology with a self-adjoint quantum scalar constraint. The physical Hilbert space is constructed using refined algebraic quantization. When matter is included in the form of a cosmological constant, the model is exactly solvable and we show explicitly that the physical Hilbert space is separable consisting of a single physical state. We extend the model to the Lorentzian sector and discuss important implications for standard loop quantum cosmology

Fock representations from U(1) holonomy algebras

We revisit the quantization of U(1) holonomy algebras using the abelian C* algebra based techniques which form the mathematical underpinnings of current efforts to construct loop quantum gravity. In particular, we clarify the role of ``smeared loops'' and of Poincare invariance in the construction of Fock representations of these algebras. This enables us to critically re-examine early pioneering efforts to construct Fock space representations of linearised gravity and free Maxwell theory from holonomy algebras through an application of the (then current) techniques of loop quantum gravity.Comment: Latex file, 30 pages, to appear in Phys Rev