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Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics

The goal of this review is to present an introduction to loop quantum gravity—a background-independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of geometry. Our presentation is pedagogical. Thus, in addition to providing a bird's eye view of the present status of the subject, the review should also serve as a vehicle to enter the field and explore it in detail. To aid non-experts, very little is assumed beyond elements of general relativity, gauge theories and quantum field theory. While the review is essentially self-contained, the emphasis is on communicating the underlying ideas and the significance of results rather than on presenting systematic derivations and detailed proofs. (These can be found in the listed references.) The subject can be approached in different ways. We have chosen one which is deeply rooted in well-established physics and also has sufficient mathematical precision to ensure that there are no hidden infinities. In order to keep the review to a reasonable size, and to avoid overwhelming non-experts, we have had to leave out several interesting topics, results and viewpoints; this is meant to be an introduction to the subject rather than an exhaustive review of it.

Background independent quantum gravity: A Status report

An improved Hamiltonian constraint operator is introduced in loop quantum cosmology. Quantum dynamics of the spatially flat, isotropic model with a massless scalar field is then studied in detail using analytical and numerical methods. The scalar field continues to serve as ''emergent time'', the big bang is again replaced by a quantum bounce, and quantum evolution remains deterministic across the deep Planck regime. However, while with the Hamiltonian constraint used so far in loop quantum cosmology the quantum bounce can occur even at low matter densities, with the new Hamiltonian constraint it occurs only at a Planck-scale density. Thus, the new quantum dynamics retains the attractive features of current evolutions in loop quantum cosmology but, at the same time, cures their main weakness.

Quantum Nature of the Big Bang: Improved dynamics

Loop quantum cosmology (LQC) is the result of applying principles of loop quantum gravity (LQG) to cosmological settings. The distinguishing feature of LQC is the prominent role played by the quantum geometry effects of LQG. In particular, quantum geometry creates a brand new repulsive force which is totally negligible at low spacetime curvature but rises very rapidly in the Planck regime, overwhelming the classical gravitational attraction. In cosmological models, while Einstein's equations hold to an excellent degree of approximation at low curvature, they undergo major modifications in the Planck regime: for matter satisfying the usual energy conditions, any time a curvature invariant grows to the Planck scale, quantum geometry effects dilute it, thereby resolving singularities of general relativity. Quantum geometry corrections become more sophisticated as the models become richer. In particular, in anisotropic models, there are significant changes in the dynamics of shear potentials which tame their singular behavior in striking contrast to older results on anisotropies in bouncing models. Once singularities are resolved, the conceptual paradigm of cosmology changes and one has to revisit many of the standard issues—e.g. the 'horizon problem'—from a new perspective. Such conceptual issues as well as potential observational consequences of the new Planck scale physics are being explored, especially within the inflationary paradigm. These considerations have given rise to a burst of activity in LQC in recent years, with contributions from quantum gravity experts, mathematical physicists and cosmologists. The goal of this review is to provide an overview of the current state of the art in LQC for three sets of audiences: young researchers interested in entering this area; the quantum gravity community in general and cosmologists who wish to apply LQC to probe modifications in the standard paradigm of the early universe. In this review, effort has been made to streamline the material so that each of these communities can read only the sections they are most interested in, without loss of continuity.

/pdf/loop-quantum-cosmology-a-status-report-1zx4841jrd.pdf

Loop Quantum Cosmology: A Status Report

We prove that every solution to Einstein's equations with possibly non-zero cosmological constant that is foliated by non-expanding null surfaces transversal to a single non-expanding null surface belongs to family of the near (extremal) horizon geometries. Our results are local, hold in a neighborhood of the single non-expanding null surface.

Spacetimes foliated by nonexpanding null surfaces in the presence of a cosmological constant

A distinguished (invariant) Bondi-like coordinate system is defined in the spacetime neighborhood of a non-expanding horizon of arbitrary dimension via geometry invariants of the horizon. With its use, the radial expansion of a spacetime metric about the horizon is provided and the free data needed to specify it up to a given order are determined in spacetime dimension 4. For the case of an electro-vacuum horizon in four-dimensional spacetime, the necessary and sufficient conditions for the existence of a Killing field at its neighborhood are identified as differential conditions for the horizon data and data for the null surface transversal to the horizon.

http://iopscience.iop.org/article/10.1088/0264-9381/31/17/175012/pdf

Neighborhoods of isolated horizons and their stationarity

We find all the spin-foams contributing in the first order of the vertex expansion to the transition amplitude of the Bianchi–Rovelli–Vidotto dipole cosmology model. Our algorithm is general and provides spin-foams of arbitrarily given, fixed boundary and a number of internal vertices. We use the recently introduced operator spin-network diagram framework.

http://iopscience.iop.org/article/10.1088/0264-9381/30/2/025007/pdf

One vertex spin-foams with the dipole cosmology boundary

A Two surface quantization of the Lorentzian gravity

It was recently shown that the volume operator of loop quantum cosmology (LQC) and all its positive powers are ill-defined on physical states. In this paper, we investigate how it effects predictions of cosmic microwave background (CMB) power spectra obtained within dressed metric approach for which expectations values of $\hat{a}$ are the key element. We find that almost every step in the procedure is ill-defined and relies heavily upon a (seemingly premature) numerical truncation. Thus, it suggests that more care is needed in making predictions regarding pre-inflationary physics. We propose a new scheme which contains only well-defined quantities. The surprising agreement of the hitherto models with observational data, especially at low angular momenta $l$ is explained.

Jerzy Lewandowski

Papers

Spacetimes foliated by nonexpanding null surfaces in the presence of a cosmological constant

Neighborhoods of isolated horizons and their stationarity

One vertex spin-foams with the dipole cosmology boundary

A Two surface quantization of the Lorentzian gravity

Dressed metric predictions revisited