Andrea Dapor

Rainbow metric from quantum gravity

Abstract In this Letter, we describe a general mechanism for emergence of a rainbow metric from a quantum cosmological model. This idea is based on QFT on a quantum spacetime. Under general assumptions, we discover that the quantum spacetime on which the field propagates can be replaced by a classical spacetime, whose metric depends explicitly on the energy of the field: as shown by an analysis of dispersion relations, quanta of different energy propagate on different metrics, similar to photons in a refractive material (hence the name “rainbow” used in the literature). In deriving this result, we do not consider any specific theory of quantum gravity: the qualitative behaviour of high-energy particles on quantum spacetime relies only on the assumption that the quantum spacetime is described by a wave-function Ψ o in a Hilbert space H G .

QFT on quantum spacetime: a compatible classical framework

(Dated: May 21, 2013)We develop a systematic classical framework to accommodate canonical quantization of geomet-ric and matter perturbations on a quantum homogeneous isotropic flat spacetime. The existingapproach of standard cosmological perturbations is indeed proved to be good only up to first orderin the inhomogeneities, and only if the background is treated classically. To consistently quantizethe perturbations

Semiclassical dynamics of horizons in spherically symmetric collapse

In this paper, we consider a semiclassical description of the spherically symmetric gravitational collapse with a massless scalar field. In particular, we employ an effective scenario provided by holonomy corrections from loop quantum gravity (LQG), to the homogeneous interior spacetime. The singularity that would arise at the final stage of the corresponding classical collapse, is resolved in this context and is replaced by a bounce. Our main purpose is to investigate the evolution of trapped surfaces during this semiclassical collapse. Within this setting, we obtain a threshold radius for the collapsing shells in order to have horizons formation. In addition, we study the final state of the collapse by employing a suitable matching at the boundary shell from which quantum gravity effects are carried to the exterior geometry.

Relational evolution of observables for Hamiltonian-constrained systems

Evolution of systems whose Hamiltonians are generators of gauge transformations is a notion that requires more structure than the canonical theory provides. We identify and study this additional structure in the framework of relational observables (“partial observables”). We formulate necessary and sufficient conditions for the resulting evolution in the physical phase space to be a symplectomorphism. We give examples which satisfy those conditions and examples which do not. We point out that several classic positions in the literature on relational observables contain incomplete approach to the issue of evolution and false statements. Our work provides useful clarification and opens the door to studying correctly formulated definitions.

Cosmological coherent state expectation values in loop quantum gravity I. Isotropic kinematics

This is the first paper of a series dedicated to LQG coherent states and cosmology. The concept is based on the effective dynamics program of Loop Quantum Cosmology, where the classical dynamics generated by the expectation value of the Hamiltonian on semiclassical states is found to be in agreement with the quantum evolution of such states. We ask the question of whether this expectation value agrees with the one obtained in the full theory. The answer is in the negative, [30]. This series of papers is dedicated to detailing the computations that lead to that surprising result. In the current paper, we construct the family of coherent states in LQG which represent flat (k = 0) Robertson-Walker spacetimes, and present the tools needed to compute expectation values of polynomial operators in holonomy and flux on such states. These tools will be applied to the LQG Hamiltonian operator (in Thiemann regularization) in the second paper of the series. The third paper will present an extension to k 6= 0 cosmologies and a comparison with alternative regularizations of the Hamiltonian.

Metric emerging to massive modes in quantum cosmological space-times

(Dated: January 8, 2014)We consider a massive quantum test Klein-Gordon field probing an homogeneous isotropic quan-tum cosmological space-time in the background. In particular, we derive a semi-classical space-timewhich emerges to a mode of the field. The method consists of a comparison between QFT on aquantum background and QFT on a classical curved space-time, giving rise to an emergent metrictensor (its components being computed from the equation of propagation of the quantum K-G fieldin the test field approximation). If the field is massless the emergent metric is of the FRW form,but if a mass term is considered it turns out that the simplest emergent metric that displays thesymmetries of the system is of the Bianchi I type, deformed in the direction of propagation of theparticle. This anisotropy is of a quantum nature: it is proportional to ~and ”dresses” the isotropicclassical space-time obtained in the classical limit.

Rainbow metric from quantum gravity: Anisotropic cosmology

In this paper we present a construction of effective cosmological models which describe the propagation of a massive quantum scalar field on a quantum anisotropic cosmological spacetime. Each obtained effective model is represented by a rainbow metric in which particles of distinct momenta propagate on different classical geometries. Our analysis shows that upon certain assumptions and conditions on the parameters determining such anisotropic models, we surprisingly obtain a unique deformation parameter

Dynamics of Apparent Horizons in Quantum Gravitational Collapse

\beta

Smooth Big Bounce from Affine Quantization

in the modified dispersion relation of the modes. Hence inducing an isotropic deformation despite the general starting considerations. We then ensure the recovery of the dispersion relation realized in the isotropic case, studied in [arXiv:1412.6000], when some proper symmetry constraints are imposed, and we estimate the value of the deformation parameter for this case in loop quantum cosmology context.

Inflation from non-minimally coupled scalar field in loop quantum cosmology

We study the gravitational collapse of a massless scalar field within the effective scenario of loop quantum gravity. Classical singularity is avoided and replaced by a quantum bounce in this model. It is shown that, quantum gravity effects predict a threshold scale bellow which no horizon can form as the collapse evolves towards the bounce.