Quantum gravity, space-time structure, and cosmology

A set of diverse but mutually consistent results obtained in different settings has spawned a new view of loop quantum gravity and its physical implications, based on the interplay of operator calculations and effective theory: Quantum corrections modify, but do not destroy, space-time and the notion of covariance. Potentially observable effects much more promising than those of higher-curvature effective actions result; loop quantum gravity has turned into a falsifiable framework, with interesting ingredients for new cosmic world views. At Planckian densities, space-time disappears and is replaced by 4-dimensional space without evolution.Comment: 8 pages, 7 figures, Plenary talk at CosGrav12, held at Indian Statistical Institute, Kolkat

A no-singularity scenario in loop quantum gravity

Canonical methods allow the derivation of effective gravitational actions from the behavior of space-time deformations reflecting general covariance. With quantum effects, the deformations and correspondingly the effective actions change, revealing dynamical implications of quantum corrections. A new systematic way of expanding these actions is introduced showing as a first result that inverse-triad corrections of loop quantum gravity simplify the asymptotic dynamics near a spacelike collapse singularity. By generic quantum effects, the singularity is removed.Comment: 10 page

Hubble operator in isotropic loop quantum cosmology

We present a construction of the Hubble operator for the spatially flat isotropic loop quantum cosmology. This operator is a Dirac observable on a subspace of the space of physical solutions. This subspace gets selected dynamically, requiring that its action be invariant on the physical solution space. As a simple illustrative application of the expectation value of the operator, we do find a generic phase of (super)inflation, a feature shown by Bojowald from the analysis of effective Friedmann equation of loop quantum cosmology.Comment: 20 pages, 3 eps figures, few comments and clarifications added to match with the published versio

The Dark Side of a Patchwork Universe

While observational cosmology has recently progressed fast, it revealed a serious dilemma called dark energy: an unknown source of exotic energy with negative pressure driving a current accelerating phase of the universe. All attempts so far to find a convincing theoretical explanation have failed, so that one of the last hopes is the yet to be developed quantum theory of gravity. In this article, loop quantum gravity is considered as a candidate, with an emphasis on properties which might play a role for the dark energy problem. Its basic feature is the discrete structure of space, often associated with quantum theories of gravity on general grounds. This gives rise to well-defined matter Hamiltonian operators and thus sheds light on conceptual questions related to the cosmological constant problem. It also implies typical quantum geometry effects which, from a more phenomenological point of view, may result in dark energy. In particular the latter scenario allows several non-trivial tests which can be made more precise by detailed observations in combination with a quantitative study of numerical quantum gravity. If the speculative possibility of a loop quantum gravitational origin of dark energy turns out to be realized, a program as outlined here will help to hammer out our ideas for a quantum theory of gravity, and at the same time allow predictions for the distant future of our universe.Comment: 24 pages, 2 figures, Contribution to the special issue on Dark Energy by Gen. Rel. Gra

Spherically Symmetric Quantum Geometry: Hamiltonian Constraint

Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and Lorentzian Hamiltonian constraints. The construction fits completely into the general scheme available in loop quantum gravity for the quantization of the full theory as well as symmetric models. This then presents a further consistency check of the whole scheme in inhomogeneous situations, lending further credence to the physical results obtained so far mainly in homogeneous models. New applications in particular of the spherically symmetric model in the context of black hole physics are discussed.Comment: 33 page

The picture of the Bianchi I model via gauge fixing in Loop Quantum Gravity

The implications of the SU(2) gauge fixing associated with the choice of invariant triads in Loop Quantum Cosmology are discussed for a Bianchi I model. In particular, via the analysis of Dirac brackets, it is outlined how the holonomy-flux algebra coincides with the one of Loop Quantum Gravity if paths are parallel to fiducial vectors only. This way the quantization procedure for the Bianchi I model is performed by applying the techniques developed in Loop Quantum Gravity but restricting the admissible paths. Furthermore, the local character retained by the reduced variables provides a relic diffeomorphisms constraint, whose imposition implies homogeneity on a quantum level. The resulting picture for the fundamental spatial manifold is that of a cubical knot with attached SU(2) irreducible representations. The discretization of geometric operators is outlined and a new perspective for the super-Hamiltonian regularization in Loop Quantum Cosmology is proposed.Comment: 6 page

Hilbert space structure of covariant loop quantum gravity

We investigate the Hilbert space in the Lorentz covariant approach to loop quantum gravity. We restrict ourselves to the space where all area operators are simultaneously diagonalizable, assuming that it exists. In this sector quantum states are realized by a generalization of spin network states based on Lorentz Wilson lines projected on irreducible representations of an SO(3) subgroup. The problem of infinite dimensionality of the unitary Lorentz representations is absent due to this projection. Nevertheless, the projection preserves the Lorentz covariance of the Wilson lines so that the symmetry is not broken. Under certain conditions the states can be thought as functions on a homogeneous space. We define the inner product as an integral over this space. With respect to this inner product the spin networks form an orthonormal basis in the investigated sector. We argue that it is the only relevant part of a larger state space arising in the approach. The problem of the noncommutativity of the Lorentz connection is solved by restriction to the simple representations. The resulting structure shows similarities with the spin foam approach.Comment: 20 pages, RevTE

Anomaly-free scalar perturbations with holonomy corrections in loop quantum cosmology

Holonomy corrections to scalar perturbations are investigated in the loop quantum cosmology framework. Due to the effective approach, modifications of the algebra of constraints generically lead to anomalies. In order to remove those anomalies, counter-terms are introduced. We find a way to explicitly fulfill the conditions for anomaly freedom and we give explicit expressions for the counter-terms. Surprisingly, the "new quantization scheme" naturally arises in this procedure. The gauge invariant variables are found and equations of motion for the anomaly-free scalar perturbations are derived. Finally, some cosmological consequences are discussed qualitatively.Comment: 19 pages, 1 figure, v2, new comments and references added, minor correction

Classical Setting and Effective Dynamics for Spinfoam Cosmology

We explore how to extract effective dynamics from loop quantum gravity and spinfoams truncated to a finite fixed graph, with the hope of modeling symmetry-reduced gravitational systems. We particularize our study to the 2-vertex graph with N links. We describe the canonical data using the recent formulation of the phase space in terms of spinors, and implement a symmetry-reduction to the homogeneous and isotropic sector. From the canonical point of view, we construct a consistent Hamiltonian for the model and discuss its relation with Friedmann-Robertson-Walker cosmologies. Then, we analyze the dynamics from the spinfoam approach. We compute exactly the transition amplitude between initial and final coherent spin networks states with support on the 2-vertex graph, for the choice of the simplest two-complex (with a single space-time vertex). The transition amplitude verifies an exact differential equation that agrees with the Hamiltonian constructed previously. Thus, in our simple setting we clarify the link between the canonical and the covariant formalisms.Comment: 38 pages, v2: Link with discretized loop quantum gravity made explicit and emphasize

Anomaly-free vector perturbations with holonomy corrections in loop quantum cosmology

We investigate vector perturbations with holonomy corrections in the framework of loop quantum cosmology. Conditions to achieve anomaly freedom for these perturbations are found at all orders. This requires the introduction of counter-terms in the hamiltonian constraint. We also show that anomaly freedom requires the diffeomorphism constraint to hold its classical form when scalar matter is added although the issue of a vector matter source, required for full consistency, remains to be investigated. The gauge-invariant variable and the corresponding equation of motion are derived. The propagation of vector modes through the bounce is finally discussed.Comment: 16 pages, 1 figure. Matches version published in Class. Quantum Gra