arXiv subjects

Claus Kiefer

Publications and source records attributed to Claus Kiefer.

At least 37 records · Page 2Linked to original sources

arXiv2019

Phantom singularities and their quantum fate: general relativity and beyond

Cosmological observations allow the possibility that dark energy is caused by phantom fields. These fields typically lead to the occurrence of singularities in the late Universe. We review here the status of phantom singularities and their possible avoidance in a quantum theory of gravity. We first introduce phantom energy and discuss its behavior in cosmology. We then list the various types of singularities that can occur from its presence. We also discuss the possibility that phantom behavior is mimicked by an alternative theory of gravity. We finally address the quantum cosmology of these models and discuss in which sense the phantom singularities can be avoided.

gr-qc↗

arXiv2019

Singularity avoidance in Bianchi I quantum cosmology

We extend recent discussions of singularity avoidance in quantum gravity from isotropic to anisotropic cosmological models. The investigation is done in the framework of quantum geometrodynamics (Wheeler-DeWitt equation). We formulate criteria of singularity avoidance for general Bianchi class A models and give explicit and detailed results for Bianchi I models with and without matter. We find that the classical singularities can generally be avoided in these models.

gr-qc↗

arXiv2019

Does the quantum mechanical wave function exist?

I address the question whether the wave function in quantum theory exists as a real (ontic) quantity or not. For this purpose, I discuss the essentials of the quantum formalism and emphasize the central role of the superposition principle. I then explain the measurement problem and discuss the process of decoherence. Finally, I address the special features that the quantization of gravity brings into the game. From all of this I conclude that the wave function really exists, that is, it is a real (ontic) feature of Nature.

quant-ph↗

arXiv2019

Quantum-gravity effects for excited states of inflationary perturbations

We generalize former findings regarding quantum-gravitational corrections arising from a canonical quantization of a perturbed FLRW universe during inflation by considering an initial state for the scalar and tensor perturbations that generalizes the adiabatic vacuum state and allows us to consider the scenario that the perturbation modes start their evolution in an excited state. Our result shows that the quantum-gravitationally corrected power spectra get modified by pre-factors including the excitation numbers.

gr-qc↗

arXiv2019

Singularity avoidance for collapsing quantum dust in the Lemaitre-Tolman-Bondi model

We investigate the fate of the classical singularity in a collapsing dust cloud. For this purpose, we quantize the marginally bound Lemaitre-Tolman-Bondi model for spherically-symmetric dust collapse by considering each dust shell in the cloud individually, taking the outermost shell as a representative. Because the dust naturally provides a preferred notion of time, we can construct a quantum mechanical model for this shell and demand unitary evolution for wave packets. It turns out that the classical singularity can generically be avoided provided the quantization ambiguities fulfill some weak conditions. We demonstrate that the collapse to a singularity is replaced by a bounce followed by an expansion. We finally construct a quantum corrected spacetime describing bouncing dust collapse and calculate the time from collapse to expansion.

gr-qc↗

arXiv2018

On the dynamics of the general Bianchi IX spacetime near the singularity

We show that the complex dynamics of the general Bianchi IX universe in the vicinity of the spacelike singularity can be approximated by a simplified system of equations. Our analysis is mainly based on numerical simulations. The properties of the solution space can be studied by using this simplified dynamics. Our results will be useful for the quantization of the general Bianchi IX model.

gr-qc↗

arXiv2018

Semiclassical approximation of the Wheeler-DeWitt equation: arbitrary orders and the question of unitarity

We extend the Born-Oppenheimer type of approximation scheme for the Wheeler-DeWitt equation of canonical quantum gravity to arbitrary orders in the inverse Planck mass squared. We discuss in detail the origin of unitarity violation in this scheme and show that unitarity can be restored by an appropriate modification which requires back reaction from matter onto the gravitational sector. In our analysis, we heavily rely on the gauge aspects of the standard Born-Oppenheimer scheme in molecular physics.

gr-qc↗

arXiv2017

Comparison of the DeWitt metric in general relativity with the fourth-rank constitutive tensors in electrodynamics and in elasticity theory

We perform a short comparison between the local and linear constitutive tensor $χ^{λνσκ}$ in four-dimensional electrodynamics (Sec.2), the elasticity tensor $c^{ijkl}$ in three-dimensional elasticity theory (Sec.3), and the DeWitt metric $G^{abcd}$ in general relativity, with ${a,b,\dots=1,2,3}$ (Sec.4). We find that the DeWitt metric has only six independent components.

gr-qc↗

arXiv2017

Cosmic screening of the gravitational interaction

We study a universe filled with cold dark matter in the form of discrete inhomogeneities (e.g., galaxies) and dark energy in the form of a continuous perfect fluid. We develop a first-order scalar perturbation theory in the weak gravity limit around a spatially flat Friedmann universe. Our approach works at all cosmic scales and incorporates linear and nonlinear effects with respect to energy density fluctuations. The gravitational potential can be split into individual contributions from each matter source. Each potential is characterized by a Yukawa interaction with the same range, which is of the order of 3700 Mpc at the present time. The derived equations can form the theoretical basis for numerical simulations for a wide class of modern cosmological models.

gr-qc↗

arXiv2017

The Milky Way's Supermassive Black Hole: How good a case is it? A Challenge for Astrophysics & Philosophy of Science

The compact and, with 4.3+-0.3 million solar masses, very massive object located at the center of the Milky Way is currently the very best candidate for a supermassive black hole (SMBH) in our immediate vicinity. The strongest evidence for this is provided by measurements of stellar orbits, variable X-ray emission, and strongly variable polarized near-infrared emission from the location of the radio source Sagittarius~A* (SgrA*) in the middle of the central stellar cluster. If SgrA* is indeed a SMBH it will, in projection onto the sky, have the largest event horizon and will certainly be the first and most important target of the Event Horizon Telescope (EHT) Very Long Baseline Interferometry (VLBI) observations currently being prepared. These observations in combination with the infrared interferometry experiment GRAVITY at the Very Large Telescope Interferometer (VLTI) and other experiments across the electromagnetic spectrum might yield proof for the presence of a black hole at the center of the Milky Way. It is, however, unclear when the ever mounting evidence for SgrA* being associated with a SMBH will suffice as a convincing proof. Additional compelling evidence may come from future gravitational wave observatories. This manuscript reviews the observational facts, theoretical grounds and conceptual aspects for the case of SgrA* being a black hole. We treat theory and observations in the framework of the philosophical discussions about "(Anti)Realism and Underdetermination", as this line of arguments allows us to describe the situation in observational astrophysics with respect to supermassive black holes. Questions concerning the existence of supermassive black holes and in particular SgrA* are discussed using causation as an indispensable element. We show that the results of our investigation are convincingly mapped out by this combination of concepts.

astro-ph.HE↗

arXiv2017

Thermal and nonthermal scaling of the Casimir-Polder interaction in a black hole spacetime

We study the Casimir-Polder force arising between two identical two-level atoms and mediated by a massless scalar field propagating in a black-hole background. We study the interplay of Hawking radiation and Casimir-Polder forces and find that, when the atoms are placed near the event horizon, the scaling of the Casimir-Polder interaction energy as a function of interatomic distance displays a transition from a thermallike character to a nonthermal behavior. We corroborate our findings for a quantum field prepared in the Boulware, Hartle-Hawking, and Unruh vacua. Our analysis is consistent with the nonthermal character of the Casimir-Polder interaction of two-level atoms in a relativistic accelerated frame [J. Marino et al., Phys. Rev. Lett. 113, 020403 (2014)], where a crossover from thermal scaling, consistent with the Unruh effect, to a nonthermal scaling has been observed. The two crossovers are a consequence of the noninertial character of the background where the field mediating the Casimir interaction propagates. While in the former case the characteristic crossover length scale is proportional to the inverse of the surface gravity of the black hole, in the latter it is determined by the inverse of the proper acceleration of the atoms.

gr-qc↗

arXiv2017

Conformal and Weyl-Einstein gravity: Classical geometrodynamics

We present a new formulation for the canonical approach to conformal (Weyl-squared) gravity and its extension by the Einstein-Hilbert term and a nonminimally coupled scalar field. For this purpose we use a unimodular decomposition of the three-metric and introduce unimodular-conformal canonical variables. The important feature of this choice is that only the scale part of the three-metric and the rescaled trace part of the extrinsic curvature change under a conformal transformation. This significantly simplifies the constraint analysis and manifestly reveals the conformal properties of a theory that contains the conformally invariant Weyl-tensor term. The conformal symmetry breaking which occurs in the presence of the Einstein-Hilbert term and a nonconformally coupled scalar field can then be interpreted directly in terms of this scale and this trace. We also discuss in detail the generator for the conformal transformations. This new Hamiltonian formulation is especially suitable for quantization, which will be the subject of a separate paper.

gr-qc↗

arXiv2016

Quantum-gravitational effects on gauge-invariant scalar and tensor perturbations during inflation: The slow-roll approximation

We continue our study on corrections from canonical quantum gravity to the power spectra of gauge-invariant inflationary scalar and tensor perturbations. A direct canonical quantization of a perturbed inflationary universe model is implemented, which leads to a Wheeler-DeWitt equation. For this equation, a semiclassical approximation is applied in order to obtain a Schroedinger equation with quantum-gravitational correction terms, from which we calculate the corrections to the power spectra. We go beyond the de Sitter case discussed earlier and analyze our model in the first slow-roll approximation, considering terms linear in the slow-roll parameters. We find that the dominant correction term from the de Sitter case, which leads to an enhancement of power on the largest scales, gets modified by terms proportional to the slow-roll parameters. A correction to the tensor-to-scalar ratio is also found at second order in the slow-roll parameters. Making use of the available experimental data, the magnitude of these quantum-gravitational corrections is estimated. Finally, the effects for the temperature anisotropies in the cosmic microwave background are qualitatively obtained.

gr-qc↗

arXiv2016

Notes on semiclassical Weyl gravity

In any quantum theory of gravity, it is of the utmost importance to recover the limit of quantum theory in an external spacetime. In quantum geometrodynamics (quantization of general relativity in the Schrödinger picture), this leads in particular to the recovery of a semiclassical (WKB) time which governs the dynamics of non-gravitational fields in spacetime. Here, we first review this procedure with special emphasis on conceptual issues. We then turn to an alternative theory - Weyl (conformal) gravity, which is defined by a Lagrangian that is proportional to the square of the Weyl tensor. We present the canonical quantization of this theory and develop its semiclassical approximation. We discuss in particular the extent to which a semiclassical time can be recovered and contrast it with the situation in quantum geometrodynamics.

gr-qc↗

arXiv2016

Scalar and vector perturbations in a universe with discrete and continuous matter sources

We study a universe filled with dust-like matter in the form of discrete inhomogeneities (e.g., galaxies and their groups and clusters) and two sets of perfect fluids with linear and nonlinear equations of state, respectively. The background spacetime geometry is defined by the FLRW metric. In the weak gravitational field limit, we develop the first-order scalar and vector cosmological perturbation theory. Our approach works at all cosmological scales (i.e. sub-horizon and super-horizon ones) and incorporates linear and nonlinear effects with respect to energy density fluctuations. We demonstrate that the scalar perturbation (i.e. the gravitational potential) as well as the vector perturbation can be split into individual contributions from each matter source. Each of these contributions satisfies its own equation. The velocity-independent parts of the individual gravitational potentials are characterized by a finite time-dependent Yukawa interaction range being the same for each individual contribution. We also obtain the exact form of the gravitational potential and vector perturbation related to the discrete matter sources. The self-consistency of our approach is thoroughly checked. The derived equations can form the theoretical basis for numerical simulations for a wide class of cosmological models.

gr-qc↗

arXiv2016

Classical and quantum cosmology of the little rip abrupt event

We analyze from a classical and quantum point of view the behavior of the universe close to a little rip, which can be interpreted as a big rip sent towards the infinite future. Like a big rip singularity, a little rip implies the destruction of all bounded structure in the Universe and is thus an event where quantum effects could be important. We present here a new phantom scalar field model for the little rip. The quantum analysis is performed in quantum geometrodynamics, with the Wheeler-DeWitt equation as its central equation. We find that the little rip can be avoided in the sense of the DeWitt criterion, that is, by having a vanishing wave function at the place of the little rip. Therefore our analysis completes the answer to the question: can quantum cosmology smoothen or avoid the divergent behavior genuinely caused by phantom matter? We show that this can indeed happen for the little rip, similar to the avoidance of a big rip and a little sibling of the big rip.

gr-qc↗

arXiv2016

Classical and quantum cosmology of Born-Infeld type models

We discuss Born-Infeld type fields (tachyon fields) in classical and quantum cosmology. We first partly review and partly extend the discussion of the classical solutions and focus in particular on the occurrence of singularities. For quantization, we employ geometrodynamics. In the case of constant potential, we discuss both Wheeler-DeWitt quantization and reduced quantization. We are able to give various solutions and discuss their asymptotics. For the case of general potential, we transform the Wheeler-DeWitt equation to a form where it leads to a difference equation. Such a difference equation was previously found in the quantization of black holes. We give explicit results for the cases of constant potential and inverse squared potential and point out special features possessed by solutions of the difference equation.

gr-qc↗

arXiv2016

Quantum-gravitational effects on gauge-invariant scalar and tensor perturbations during inflation: The de Sitter case

We present detailed calculations for quantum-gravitational corrections to the power spectra of gauge-invariant scalar and tensor perturbations during inflation. This is done by performing a semiclassical Born-Oppenheimer type of approximation to the Wheeler-DeWitt equation, from which we obtain a Schroedinger equation with quantum-gravitational correction terms. As a first step, we perform our calculation for a de Sitter universe and find that the correction terms lead to an enhancement of power on the largest scales.

gr-qc↗