arXiv subjects

Martin Bojowald

Publications and source records attributed to Martin Bojowald.

At least 163 records · Page 9Linked to original sources

arXiv2008

Quantum nature of cosmological bounces

Several examples are known where quantum gravity effects resolve the classical big bang singularity by a bounce. The most detailed analysis has probably occurred for loop quantum cosmology of isotropic models sourced by a free, massless scalar. Once a bounce has been realized under fairly general conditions, the central questions are how strongly quantum it behaves, what influence quantum effects can have on its appearance, and what quantum space-time beyond the bounce may look like. This, then, has to be taken into account for effective equations which describe the evolution properly and can be used for further phenomenological investigations. Here, we provide the first analysis with interacting matter with new effective equations valid for weak self-interactions or small masses. They differ from the free scalar equations by crucial terms and have an important influence on the bounce and the space-time around it. Especially the role of squeezed states, which have often been overlooked in this context, is highlighted. The presence of a bounce is proven for uncorrelated states, but as squeezing is a dynamical property and may change in time, further work is required for a general conclusion.

gr-qc↗

arXiv2007

The radiation equation of state and loop quantum gravity corrections

The equation of state for radiation is derived in a canonical formulation of the electromagnetic field. This allows one to include correction terms expected from canonical quantum gravity and to infer implications to the universe evolution in radiation dominated epochs. Corrections implied by quantum geometry can be interpreted in physically appealing ways, relating to the conformal invariance of the classical equations.

gr-qc↗

arXiv2007

Harmonic cosmology: How much can we know about a universe before the big bang?

Quantum gravity may remove classical space-time singularities and thus reveal what a universe at and before the big bang could be like. In loop quantum cosmology, an exactly solvable model is available which allows one to address precise dynamical coherent states and their evolution in such a setting. It is shown here that quantum fluctuations before the big bang are generically unrelated to those after the big bang. A reliable determination of pre-big bang quantum fluctuations would require exceedingly precise observations.

gr-qc↗

arXiv2007

Loop quantum gravity corrections to gravitational wave dispersion

Cosmological tensor perturbations equations are derived for Hamiltonian cosmology based on Ashtekar's formulation of general relativity, including typical quantum gravity effects in the Hamiltonian constraint as they are expected from loop quantum gravity. This translates to corrections of the dispersion relation for gravitational waves. The main application here is the preservation of causality which is shown to be realized due to the absence of anomalies in the effective constraint algebra used.

gr-qc↗

arXiv2007

Cosmological vector modes and quantum gravity effects

In contrast to scalar and tensor modes, vector modes of linear perturbations around an expanding Friedmann--Robertson--Walker universe decay. This makes them largely irrelevant for late time cosmology, assuming that all modes started out at a similar magnitude at some early stage. By now, however, bouncing models are frequently considered which exhibit a collapsing phase. Before this phase reaches a minimum size and re-expands, vector modes grow. Such modes are thus relevant for the bounce and may even signal the breakdown of perturbation theory if the growth is too strong. Here, a gauge invariant formulation of vector mode perturbations in Hamiltonian cosmology is presented. This lays out a framework for studying possible canonical quantum gravity effects, such as those of loop quantum gravity, at an effective level. As an explicit example, typical quantum corrections, namely those coming from inverse densitized triad components and holonomies, are shown to increase the growth rate of vector perturbations in the contracting phase, but only slightly. Effects at the bounce of the background geometry can, however, be much stronger.

gr-qc↗

arXiv2007

Effective equations for isotropic quantum cosmology including matter

Effective equations often provide powerful tools to develop a systematic understanding of detailed properties of a quantum system. This is especially helpful in quantum cosmology where several conceptual and technical difficulties associated with the full quantum equations can be avoided in this way. Here, effective equations for Wheeler-DeWitt and loop quantizations of spatially flat, isotropic cosmological models sourced by a massive or interacting scalar are derived and studied. The resulting systems are remarkably different from that given for a free, massless scalar. This has implications for the coherence of evolving states and the realization of a bounce in loop quantum cosmology.

gr-qc↗

arXiv2007

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.

gr-qc↗

arXiv2007

Lattice refining loop quantum cosmology, anisotropic models and stability

A general class of loop quantizations for anisotropic models is introduced and discussed, which enhances loop quantum cosmology by relevant features seen in inhomogeneous situations. The main new effect is an underlying lattice which is being refined during dynamical changes of the volume. In general, this leads to a new feature of dynamical difference equations which may not have constant step-size, posing new mathematical problems. It is discussed how such models can be evaluated and what lattice refinements imply for semiclassical behavior. Two detailed examples illustrate that stability conditions can put strong constraints on suitable refinement models, even in the absence of a fundamental Hamiltonian which defines changes of the underlying lattice. Thus, a large class of consistency tests of loop quantum gravity becomes available. In this context, it will also be seen that quantum corrections due to inverse powers of metric components in a constraint are much larger than they appeared recently in more special treatments of isotropic, free scalar models where they were artificially suppressed.

gr-qc↗

arXiv2007

Dynamical coherent states and physical solutions of quantum cosmological bounces

A new model is studied which describes the quantum behavior of transitions through an isotropic quantum cosmological bounce in loop quantum cosmology sourced by a free and massless scalar field. As an exactly solvable model even at the quantum level, it illustrates properties of dynamical coherent states and provides the basis for a systematic perturbation theory of loop quantum gravity. The detailed analysis is remarkably different from what is known for harmonic oscillator coherent states. Results are evaluated with regard to their implications in cosmology, including a demonstration that in general quantum fluctuations before and after the bounce are unrelated. Thus, even within this solvable model the condition of classicality at late times does not imply classicality at early times before the bounce without further assumptions. Nevertheless, the quantum state does evolve deterministically through the bounce.

gr-qc↗

arXiv2007

Large scale effective theory for cosmological bounces

An exactly solvable bounce model in loop quantum cosmology is identified which serves as a perturbative basis for realistic bounce scenarios. Its bouncing solutions are derived analytically, demonstrating why recent numerical simulations robustly led to smooth bounces under the assumption of semiclassicality. Several effects, easily included in a perturbative analysis, can however change this smoothness. The effective theory is not only applicable to such situations where numerical techniques become highly involved but also allows one to discuss conceptual issues. For instance, consequences of the notoriously difficult physical inner product can be implemented at the effective level. This indicates that even physical predictions from full quantum gravity can be obtained from perturbative effective equations.

gr-qc↗

arXiv2007

Singularities and Quantum Gravity

Although there is general agreement that a removal of classical gravitational singularities is not only a crucial conceptual test of any approach to quantum gravity but also a prerequisite for any fundamental theory, the precise criteria for non-singular behavior are often unclear or controversial. Often, only special types of singularities such as the curvature singularities found in isotropic cosmological models are discussed and it is far from clear what this implies for the very general singularities that arise according to the singularity theorems of general relativity. In these lectures we present an overview of the current status of singularities in classical and quantum gravity, starting with a review and interpretation of the classical singularity theorems. This suggests possible routes for quantum gravity to evade the devastating conclusion of the theorems by different means, including modified dynamics or modified geometrical structures underlying quantum gravity. The latter is most clearly present in canonical quantizations which are discussed in more detail. Finally, the results are used to propose a general scheme of singularity removal, quantum hyperbolicity, to show cases where it is realized and to derive intuitive semiclassical pictures of cosmological bounces.

gr-qc↗

arXiv2007

Quantum gravity and cosmological observations

Quantum gravity places entirely new challenges on the formulation of a consistent theory as well as on an extraction of potentially observable effects. Quantum corrections due to the gravitational field are commonly expected to be tiny because of the smallness of the Planck length. However, a consistent formulation now shows that key features of quantum gravity imply magnification effects on correction terms which are especially important in cosmology with its long stretches of evolution. After a review of the salient features of recent canonical quantizations of gravity and their implications for the quantum structure of space-time a new example for potentially observable effects is given.

gr-qc↗

arXiv2006

Formation and Evolution of Structure in Loop Cosmology

Inhomogeneous cosmological perturbation equations are derived in loop quantum gravity, taking into account corrections in particular in gravitational parts. This provides a framework for calculating the evolution of modes in structure formation scenarios related to inflationary or bouncing models. Applications here are corrections to the Newton potential and to the evolution of large scale modes which imply non-conservation of curvature perturbations possibly noticeable in a running spectral index. These effects are sensitive to quantization procedures and test the characteristic behavior of correction terms derived from quantum gravity.

astro-ph↗

arXiv2006

Effective constraints of loop quantum gravity

Within a perturbative cosmological regime of loop quantum gravity corrections to effective constraints are computed. This takes into account all inhomogeneous degrees of freedom relevant for scalar metric modes around flat space and results in explicit expressions for modified coefficients and of higher order terms. It also illustrates the role of different scales determining the relative magnitude of corrections. Our results demonstrate that loop quantum gravity has the correct classical limit, at least in its sector of cosmological perturbations around flat space, in the sense of perturbative effective theory.

gr-qc↗

arXiv2006

Loop quantum cosmology and inhomogeneities

Inhomogeneities are introduced in loop quantum cosmology using regular lattice states, with a kinematical arena similar to that in homogeneous models considered earlier. The framework is intended to encapsulate crucial features of background independent quantizations in a setting accessible to explicit calculations of perturbations on a cosmological background. It is used here only for qualitative insights but can be extended with further more detailed input. One can thus see how several parameters occuring in homogeneous models appear from an inhomogeneous point of view. Their physical roles in several cases then become much clearer, often making previously unnatural choices of values look more natural by providing alternative physical roles. This also illustrates general properties of symmetry reduction at the quantum level and the roles played by inhomogeneities. Moreover, the constructions suggest a picture for gravitons and other metric modes as collective excitations in a discrete theory, and lead to the possibility of quantum gravity corrections in large universes.

gr-qc↗

arXiv2006

Quantum Geometry and its Implications for Black Holes

General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will provide a more complete, non-singular extension which, however, was difficult to verify in the absence of a quantum theory of gravity. By now there are several candidates which show essential hints as to what a quantum theory of gravity may look like. In particular, loop quantum gravity is a non-perturbative formulation which is background independent, two properties which are essential close to a classical singularity with strong fields and a degenerate metric. In cosmological and black hole settings one can indeed see explicitly how classical singularities are removed by quantum geometry: there is a well-defined evolution all the way down to, and across, the smallest scales. As for black holes, their horizon dynamics can be studied showing characteristic modifications to the classical behavior. Conceptual and physical issues can also be addressed in this context, providing lessons for quantum gravity in general. Here, we conclude with some comments on the uniqueness issue often linked to quantum gravity in some form or another.

gr-qc↗

arXiv2006

Effective Equations of Motion for Quantum Systems

In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and geometrical picture is developed and shown to agree with effective action results, commonly derived through path integration, for perturbations around a harmonic oscillator ground state. The same methods are used to describe dynamical coherent states, which in turn provide means to compute quantum corrections to the symplectic structure of an effective system.

math-ph↗

arXiv2006

Quantum Gravity and Higher Curvature Actions

Effective equations are often useful to extract physical information from quantum theories without having to face all technical and conceptual difficulties. One can then describe aspects of the quantum system by equations of classical type, which correct the classical equations by modified coefficients and higher derivative terms. In gravity, for instance, one expects terms with higher powers of curvature. Such higher derivative formulations are discussed here with an emphasis on the role of degrees of freedom and on differences between Lagrangian and Hamiltonian treatments. A general scheme is then provided which allows one to compute effective equations perturbatively in a Hamiltonian formalism. Here, one can expand effective equations around any quantum state and not just a perturbative vacuum. This is particularly useful in situations of quantum gravity or cosmology where perturbations only around vacuum states would be too restrictive. The discussion also demonstrates the number of free parameters expected in effective equations, used to determine the physical situation being approximated, as well as the role of classical symmetries such as Lorentz transformation properties in effective equations. An appendix collects information on effective correction terms expected from loop quantum gravity and string theory.

hep-th↗