arXiv subjects

Martin Bojowald

Publications and source records attributed to Martin Bojowald.

At least 127 records · Page 7Linked to original sources

arXiv2012

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.

gr-qc↗

arXiv2011

Deformed General Relativity and Effective Actions from Loop Quantum Gravity

Canonical methods can be used to construct effective actions from deformed covariance algebras, as implied by quantum-geometry corrections of loop quantum gravity. To this end, classical constructions are extended systematically to effective constraints of canonical quantum gravity and applied to model systems as well as general metrics, with the following conclusions: (i) Dispersion relations of matter and gravitational waves are deformed in related ways, ensuring a consistent realization of causality. (ii) Inverse-triad corrections modify the classical action in a way clearly distinguishable from curvature effects. In particular, these corrections can be significantly larger than often expected for standard quantum-gravity phenomena. (iii) Finally, holonomy corrections in high-curvature regimes do not signal the evolution from collapse to expansion in a "bounce," but rather the emergence of the universe from Euclidean space at high density. This new version of signature-change cosmology suggests a natural way of posing initial conditions, and a solution to the entropy problem.

gr-qc↗

arXiv2011

Generalized uncertainty principles and localization in discrete space

Generalized uncertainty principles are able to serve as useful descriptions of some of the phenomenology of quantum gravity effects, providing an intuitive grasp on non-trivial space-time structures such as a fundamental discreteness of space, a universal bandlimit or an irreducible extendedness of elementary particles. In this article, uncertainty relations are derived by a moment expansion of states for quantum systems with a discrete coordinate, and correspondingly a periodic momentum. Corrections to standard uncertainty relations are found, with some similarities but also key differences to what is often assumed in this context. The relations provided can be applied to discrete models of matter or space-time, including loop quantum cosmology.

hep-th↗

arXiv2011

Observational test of inflation in loop quantum cosmology

We study in detail the power spectra of scalar and tensor perturbations generated during inflation in loop quantum cosmology (LQC). After clarifying in a novel quantitative way how inverse-volume corrections arise in inhomogeneous settings, we show that they can generate large running spectral indices, which generally lead to an enhancement of power at large scales. We provide explicit formulae for the scalar/tensor power spectra under the slow-roll approximation, by taking into account corrections of order higher than the runnings. Via a standard analysis, we place observational bounds on the inverse-volume quantum correction δ~ a^{- σ} (σ>0, $a$ is the scale factor) and the slow-roll parameter ε_V for power-law potentials as well as exponential potentials by using the data of WMAP 7yr combined with other observations. We derive the constraints on δfor two pivot wavenumbers k_0 for several values of δ. The quadratic potential can be compatible with the data even in the presence of the LQC corrections, but the quartic potential is in tension with observations. We also find that the upper bounds on δ(k_0) for given σand k_0 are insensitive to the choice of the inflaton potentials.

gr-qc↗

arXiv2011

Observational constraints on loop quantum cosmology

In the inflationary scenario of loop quantum cosmology in the presence of inverse-volume corrections, we give analytic formulas for the power spectra of scalar and tensor perturbations convenient to compare with observations. Since inverse-volume corrections can provide strong contributions to the running spectral indices, inclusion of terms higher than the second-order runnings in the power spectra is crucially important. Using the recent data of cosmic microwave background and other cosmological experiments, we place bounds on the quantum corrections.

astro-ph.CO↗

arXiv2011

High-order quantum back-reaction and quantum cosmology with a positive cosmological constant

When quantum back-reaction by fluctuations, correlations and higher moments of a state becomes strong, semiclassical quantum mechanics resembles a dynamical system with a high-dimensional phase space. Here, systematic computational methods to derive the dynamical equations including all quantum corrections to high order in the moments are introduced, together with a (deparameterized) quantum cosmological example to illustrate some implications. The results show, for instance, that the Gaussian form of an initial state is maintained only briefly, but that the evolving state settles down to a new characteristic shape afterwards. Remarkably, even in the regime of large high-order moments, we observe a strong convergence within all considered orders that supports the use of this effective approach.

gr-qc↗

arXiv2011

Quantum gravity in the very early universe

General relativity describes the gravitational field geometrically and in a self-interacting way because it couples to all forms of energy, including its own. Both features make finding a quantum theory difficult, yet it is important in the high-energy regime of the very early universe. This review article introduces some of the results for the quantum nature of space-time which indicate that there is a discrete, atomic picture not just for matter but also for space and time. At high energy scales, such deviations from the continuum affect the propagation of matter, the expansion of the universe, and perhaps even the form of symmetries such as Lorentz or CP transformations. All these effects may leave traces detectable by sensitive measurements, as pointed out here by examples.

gr-qc↗

arXiv2011

An effective approach to the problem of time

A practical way to deal with the problem of time in quantum cosmology and quantum gravity is proposed. The main tool is effective equations, which mainly restrict explicit considerations to semiclassical regimes but have the crucial advantage of allowing the consistent use of local internal times in non-deparameterizable systems. Different local internal times are related merely by gauge transformations, thereby enabling relational evolution through turning points of non-global internal times. The main consequence of the local nature of internal time is the necessity of its complex-valuedness, reminiscent of but more general than non-unitarity of evolution defined for finite ranges of time. By several general arguments, the consistency of this setting is demonstrated. Finally, we attempt an outlook on the nature of time in highly quantum regimes. The focus of this note is on conceptual issues.

gr-qc↗

arXiv2011

Effective approach to the problem of time: general features and examples

The effective approach to quantum dynamics allows a reformulation of the Dirac quantization procedure for constrained systems in terms of an infinite-dimensional constrained system of classical type. For semiclassical approximations, the quantum constrained system can be truncated to finite size and solved by the reduced phase space or gauge-fixing methods. In particular, the classical feasibility of local internal times is directly generalized to quantum systems, overcoming the main difficulties associated with the general problem of time in the semiclassical realm. The key features of local internal times and the procedure of patching global solutions using overlapping intervals of local internal times are described and illustrated by two quantum mechanical examples. Relational evolution in a given choice of internal time is most conveniently described and interpreted in a corresponding choice of gauge at the effective level and changing the internal clock is, therefore, essentially achieved by a gauge transformation. This article complements the conceptual discussion in arXiv:1009.5953.

gr-qc↗

arXiv2011

Black-hole horizons in modified space-time structures arising from canonical quantum gravity

Several properties of canonical quantum gravity modify space-time structures, sometimes to the degree that no effective line elements exist to describe the geometry. An analysis of solutions, for instance in the context of black holes, then requires new insights. In this article, standard definitions of horizons in spherical symmetry are first reformulated canonically, and then evaluated for solutions of equations and constraints modified by inverse-triad corrections of loop quantum gravity. When possible, a space-time analysis is performed which reveals a mass threshold for black holes and small changes to Hawking radiation. For more general conclusions, canonical perturbation theory is developed to second order to include back-reaction from matter. The results shed light on the questions of whether renormalization of Newton's constant or other modifications of horizon conditions should be taken into account in computations of black-hole entropy in loop quantum gravity.

gr-qc↗

arXiv2011

Inflationary observables in loop quantum cosmology

The full set of cosmological observables coming from linear scalar and tensor perturbations of loop quantum cosmology is computed in the presence of inverse-volume corrections. Background inflationary solutions are found at linear order in the quantum corrections; depending on the values of quantization parameters, they obey an exact or perturbed power-law expansion in conformal time. The comoving curvature perturbation is shown to be conserved at large scales, just as in the classical case. Its associated Mukhanov equation is obtained and solved. Combined with the results for tensor modes, this yields the scalar and tensor indices, their running, and the tensor-to-scalar ratio, which are all first order in the quantum correction. The latter could be sizable in phenomenological scenarios. Contrary to a pure minisuperspace parametrization, the lattice refinement parametrization is in agreement with both anomaly cancellation and our results on background solutions and linear perturbations. The issue of the choice of parametrization is also discussed in relation with a possible superluminal propagation of perturbative modes, and conclusions for quantum spacetime structure are drawn.

gr-qc↗

arXiv2011

Loop Quantum Gravity and Cosmology: A dynamical introduction

Loop quantum gravity and cosmology are reviewed with an emphasis on evaluating the dynamics, rather than constructing it. The three crucial parts of such an analysis are (i) deriving effective equations, (ii) controlling the theory's microscopic degrees of freedom that lead to its spatial discreteness and refinement, and (iii) ensuring consistency and anomaly-freedom. All three issues are crucial for making the theory testable by conceptual and observational means, and they remain challenging. Throughout this review, the Hamiltonian nature of the theory will play a large role for properties of space-time structure within the framework discussed.

gr-qc↗

arXiv2010

The high-density regime of kinetic-dominated loop quantum cosmology

We study the dynamics of states perturbatively expanded about a harmonic system of loop quantum cosmology, exhibiting a bounce. In particular, the evolution equations for the first and second order moments of the system are analyzed. These moments back-react on the trajectories of the expectation values of the state and hence alter the energy density at the bounce. This analysis is performed for isotropic loop quantum cosmology coupled to a scalar field with a small but non-zero constant potential, hence in a regime in which the kinetic energy of matter dominates. Analytic restrictions on the existence of dynamical coherent states and the meaning of semi-classicality within these systems are discussed. A numerical investigation of the trajectories of states that remain semi-classical across the bounce demonstrates that, at least for such states, the bounce persists and that its properties are similar to the standard case, in which the moments of the states are entirely neglected. However the bounce density does change, implying that a quantum bounce may not be guaranteed to happen when the potential is no longer negligible.

gr-qc↗

arXiv2010

Quantum cosmology for the 21st century: A debate

Quantum cosmology from the late sixties into the early twenty-first century is reviewed and appraised in the form of a debate, set up by two presentations on mainly the Wheeler-DeWitt quantization and on loop quantum cosmology, respectively. (Open) questions, encouragement and guiding lines shared with the audience are provided here.

gr-qc↗

arXiv2010

Quantum gravity effects on space-time

General relativity promotes space-time to a physical, dynamical object subject to equations of motion. Quantum gravity, accordingly, must provide a quantum framework for space-time, applicable on the smallest distance scales. Just like generic states in quantum mechanics, quantum space-time structures may be highly counter-intuitive. But if low-energy effects can be extracted, they shed considerable light on the implications to be expected for a dynamical quantum space-time. Loop quantum gravity has provided several such effects, but even in the symmetry-reduced setting of loop quantum cosmology no complete picture of effective space-time geometries describing especially the regime near the big bang has been obtained. The overall situation regarding space-time structures and cosmology is reviewed here, with an emphasis on the role of dynamical states, effective equations, and general covariance.

gr-qc↗

arXiv2009

Effective Constraints for Relativistic Quantum Systems

Determining the physical Hilbert space is often considered the most difficult but crucial part of completing the quantization of a constrained system. In such a situation it can be more economical to use effective constraint methods, which are extended here to relativistic systems as they arise for instance in quantum cosmology. By side-stepping explicit constructions of states, such tools allow one to arrive much more feasibly at results for physical observables at least in semiclassical regimes. Several questions discussed recently regarding effective equations and state properties in quantum cosmology, including the spreading of states and quantum back-reaction, are addressed by the examples studied here.

math-ph↗

arXiv2009

Effective Constraints and Physical Coherent States in Quantum Cosmology: A Numerical Comparison

A cosmological model with a cyclic interpretation is introduced, which is subject to quantum back-reaction and yet can be treated rather completely by physical coherent state as well as effective constraint techniques. By this comparison, the role of quantum back-reaction in quantum cosmology is unambiguously demonstrated. Also the complementary nature of strengths and weaknesses of the two procedures is illustrated. Finally, effective constraint techniques are applied to a more realistic model filled with radiation, where physical coherent states are not available.

gr-qc↗

arXiv2009

A Momentous Arrow of Time

Quantum cosmology offers a unique stage to address questions of time related to its underlying (and perhaps truly quantum dynamical) meaning as well as its origin. Some of these issues can be analyzed with a general scheme of quantum cosmology, others are best seen in loop quantum cosmology. The latter's status is still incomplete, and so no full scenario has yet emerged. Nevertheless, using properties that have a potential of pervading more complicated and realistic models, a vague picture shall be sketched here. It suggests the possibility of deriving a beginning within a beginningless theory, by applying cosmic forgetfulness to an early history of the universe.

gr-qc↗