arXiv subjects
Publications and source records attributed to Claus Kiefer.
Modern cosmological theories invoke the idea that all structure in the Universe originates from quantum fluctuations. Understanding the quantum-to-classical transition for these fluctuations is of central importance not only for the foundations of quantum theory, but also for observational astronomy. In my contribution, I review the essential features of this transition, emphasizing in particular the role of Alexei Starobinsky.
We discuss how the classical notions of time and causal structure may emerge together with quantum-mechanical probabilities from a universal quantum state. For this, the process of decoherence between semiclassical branches is important. Our discussion is based on quantum geometrodynamics, a canonical approach to quantum gravity. In this framework, a particular boundary condition may illuminate the issue of the arrow of (classical) time in connection to the growth of entanglement entropy.
We investigate the quantum fate of the classical singularities that occur by gravitational collapse of a dust cloud. For this purpose, we address the quantization of a model first proposed by Georges Lemaitre in 1933. We find that the singularities can generically be avoided. This is a consequence of unitary evolution in the quantum theory, whereby the quantum dust cloud collapses, bounces at a minimal radius and re-expands.
We discuss how quantum geometrodynamics, a conservative approach to quantum gravity, might explain the emergence of classical spacetime and, with it, the emergence of classical time and its arrow from the universal quantum state. This follows from a particular but reasonable choice of boundary condition motivated by the structure of the Hamiltonian of the theory. This condition can also be seen as defining a quantum version of Penrose's Weyl curvature hypothesis. We comment on the relation of this picture to the `past hypothesis' and the different observed arrows of time, and we consider how quantum geometrodynamics could serve as a unifying and more fundamental framework to explain these observations.
I investigate the question whether Gödel's undecidability theorems play a crucial role in the search for a unified theory of physics. I conclude that unless the structure of space-time is fundamentally discrete we can never decide whether a given theory is the final one or not. This is relevant for both canonical quantum gravity and string theory.
In this review, we focus on whether a canonical quantization of general relativity can produce testable predictions for cosmology. In particular, we examine how this approach can be used to model the evolution of primordial perturbations. This program of quantum geometrodynamics, first advocated by John Wheeler and Bryce DeWitt, has a straightforward classical limit, and it describes the quantum dynamics of all fields, gravitational and matter. In this context, in which a classical background metric is absent, it is necessary to discuss what constitutes an observation. We first address this issue in the classical theory and then turn to the quantum theory. We argue that predictions are relational, that is, relative to physical clocks and rods, and that they can be straightforwardly obtained in a perturbative approach with respect to Newton's constant, which serves as a coupling parameter. This weak-coupling expansion leads to a perturbative Hilbert space for quantum cosmology, and to corrections to the dynamics of quantum fields on a classical, fixed background metric. These corrections imply modifications of primordial power spectra, which may lead to signatures in the anisotropy spectrum of the Cosmic Microwave Background (CMB) radiation, for which we discuss concrete results. We conclude that the subject of quantum geometrodynamics, the oldest and most conservative approach to canonical quantum gravity, not only illuminates conceptual issues in quantum gravitation, but may also lead to observational prospects in cosmology and elsewhere.
We first present a consistent canonical formulation of the general (non-marginal) Oppenheimer-Snyder model. The switching between comoving and stationary observer is achieved by promoting coordinate transformations between dust proper time and Schwarzschild-Killing time to canonical ones. This leads to a multivalued Hamiltonian which is deparameterizable. We then discuss the quantization of comoving and stationary observers by employing the method of Affine Coherent State Quantization (ACSQ). We thereby demonstrate that under certain conditions the quantum corrected trajectories can replace the classical singularity by a bounce. We then show that both comoving and stationary observers see this bouncing collapse behavior. We finally discuss a switching between these classes of observers at the quantum level.
It is generally assumed that the search for a consistent and testable theory of quantum gravity is among the most important open problems of fundamental physics. I review the motivations for this search, the main problems on the way, and the status of present approaches and their physical relevance. I speculate on what the situation could be in 2050.
We study the quantum-gravitational corrections to the power spectrum of a gauge-invariant inflationary scalar perturbations in a closed model of a universe. We consider canonical quantum gravity as an approach to quantizing gravity. This leads to the Wheeler-DeWitt equation, which has been studied by applying a semiclassical Born-Oppenheimer type of approximation. At the corresponding orders of approximation, we recover both the uncorrected and quantum-gravitationally corrected Schroedinger equations for the perturbation modes from which we calculate the quantum-gravitational corrections to the power spectrum in the slow-roll regime. The results are compared to the power spectra for the flat model of the universe.
Extracting quantitative information of neuronal signals by non-invasive imaging is an outstanding challenge for understanding brain function and pathology. However, state-of-the-art techniques offer low sensitivity to deep electrical sources. Stimulus induced rotary saturation (SIRS) is a recently proposed magnetic resonance imaging (MRI) sequence that detects oscillatory magnetic fields using a spin-lock preparation. Phantom experiments and simulations proved its efficiency and sensitivity, but the susceptibility of the method to field inhomogeneities is still not well understood. In this study, we simulated and analyzed the dynamic of three spin-lock preparations and their response to field inhomogeneities in the presence of a resonant oscillating field. We show that the composite spin-lock preparation is more robust against field variations within the double resonance effect. In addition, we tested the capability of the chosen composite spin-lock preparation to recover information about the spectral components of a composite signal. This study sets the bases to move one step further towards the clinical application of MR-based neuronal current imaging.
We give an introduction into quantum cosmology with emphasis on its conceptual parts. After a general motivation we review the formalism of canonical quantum gravity on which discussions of quantum cosmology are usually based. We then present the minisuperspace Wheeler--DeWitt equation and elaborate on the problem of time, the imposition of boundary conditions, the semiclassical approximation, the origin of irreversibility, and singularity avoidance. Restriction is made to the framework of quantum geometrodynamics.
We construct wormholes in Einstein-vector-Gauss-Bonnet theory where a real massless vector field is coupled to the higher curvature Gauss-Bonnet invariant. We consider three coupling functions which depend on the square of the vector field. The respective domains of existence of wormholes possess as their boundaries i) black holes, ii) solutions with a singular throat, iii) solutions with a degenerate throat and iv) solutions with cusp singularities. Depending on the coupling function wormhole solutions can feature a single throat or an equator surrounded by a double throat. The wormhole solutions need a thin shell of matter at the throat, in order to be symmetrically continued into the second asymptotically flat region. These wormhole spacetimes allow for bound and unbound particle motion as well as light rings.
We derive the power spectrum of primordial quantum fluctuations in an inflationary universe for curvature parameter ${\mathcal K}=1$. This is achieved through a Born--Oppenheimer type of approximation scheme from the Wheeler--DeWitt equation of canonical quantum gravity using gauge-invariant variables. Compared to the flat model, the closed model exhibits a deficit of power at large scales.
Roger Penrose's Weyl curvature hypothesis states that the Weyl curvature is small at past singularities, but not at future singularities. We review the motivations for this conjecture and present estimates for the entropy of our Universe. We then extend this hypothesis to the quantum regime by demanding that the initial state of primordial quantum fluctuations be the adiabatic vacuum in a (quasi-) de~Sitter space. We finally attempt a justification of this quantum version from a fundamental theory of quantum gravity and speculate on its consequences in the case of a classically recollapsing universe.
Time in quantum gravity is not a well-defined notion, despite its central role in the very definition of dynamics. Using the formalism of quantum geometrodynamics, we shortly review the problem and illustrate it with two proposed solutions. Our main application is quantum cosmology -- the application of quantum gravity to the Universe as a whole.
We present a brief review of Friedmann's impact on cosmology from a historical and a physical perspective.
In 1955, an international conference took place in Berne at which the state of relativity theory and its possible generalizations were presented and critically discussed. I review the most important contributions to that conference and put them into the perspective of today's knowledge about the nature of space and time.
The concepts of space, time, and matter are of central importance in any theory of the gravitational field. Here I discuss the role that these concepts might play in quantum theories of gravity. To be concrete, I will focus on the most conservative approach, which is quantum geometrodynamics. It turns out that spacetime is absent at the most fundamental level and emerges only in an appropriate limit. It is expected that the dynamics of matter can only be understood from a fundamental quantum theory of all interactions.