Problematic aspects of Kaluza-Klein models with Einstein internal spaces

Abstract: We consider Kaluza-Klein (KK) models where internal spaces are compact Einstein spaces. These spaces are stabilized by background matter (e.g., monopole form-fields). We perturb this background by a compact matter source (e.g., the system of gravitating masses) with the zero pressure in the external/our space and an arbitrary pressure in the internal space. We show that in the case of curved Einstein spaces, the Einstein equations are compatible only if the matter source is smeared over the internal space and perturbed metric components do not depend on coordinates of extra dimensions. The latter means the absence of KK modes corresponding to the metric fluctuations. There are two possibilities to satisfy the gravitational tests. First, the gravitating source (e.g. our Sun) should have the black string equation of state in the internal space. This result does not depend on the size of the internal space. Second, if the equation of state in the internal space is arbitrary (e.g. dust like), then the size of the internal space should be small enough and radion is very massive particle.

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Torsional instantons effects in quantum gravity and phenomenological implications

Abstract: We show that in the first order gravity theory coupled to axions, there exist new kind of instanton configurations (solutions of Euclidean equations of motion) whose instanton number can be interpreted as the torsional Nieh-Yan topological index. These torsional pseudoparticles turn out to be the Giddings-Strominger wormholes. Importantly, these instantons are shown to induce tunneling between degenerate topological vacua in gravity theory, leading to a rich vacuum structure exactly similar to the famous theta vacuum of gauge theories. This nonperturbative quantum vacuum is characterised by a topological vacuum angle, which can be identified with the Barbero-Immirzi parameter. We conclude with a discussion on how this nonperturbative vacuum structure in quantum gravity, hitherto unnoticed, could have important implications in the context of cosmology and various parity violating phenomena in particle physics. In particular, based on this framework, we propose a possible solution to the cosmological constant

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Massive stars at low-metallicity

Abstract: Low-metallicity environments such as the early Universe and compact star-forming dwarf galaxies contain many massive stars. These stars influence their surroundings through intense UV radiation, strong winds and explosive deaths. A good understanding of low-metallicity environments requires a detailed theoretical comprehension of the evolution of their massive stars. I have modelled massive rotating single stars with an initial metal composition appropriate for the dwarf galaxy I Zwicky 18. I present their evolutionary behaviour, and discuss the observational predictions. My most important result is that the fast rotator stars, which may be abundant at this metallicity, are found to undergo efficient mixing induced by rotation resulting in quasi chemically-homogeneous evolution. These homogeneously-evolving models reach surface temperatures of up to 90 kK during core hydrogen burning. This, together with their moderate mass-loss rates, make them transparent wind ultraviolet intense stars (TWUIN star). TWUIN stars are a newly predicted type of hot and luminous massive object with weak winds. Their expected numbers might explain the observed He-II ionising photon flux in I Zwicky 18 and other low-metallicity He-II-emitting galaxies.

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Rotating quantum states

Abstract: In the canonical quantization of fields on curved space-time, the definition of the vacuum state is of fundamental importance. We consider the definition of vacuum states for scalar and fermion fields on rotating Minkowski and anti-de Sitter space-times. The construction of the vacuum state for a fermion field is much less constrained than for a scalar field. We explore the consequences of this freedom for the definition of rotating thermal states.

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Understanding Hawking temperature from quantum entanglement

Abstract: One of the strong connection between the quantum information theory and the black hole physics is based on the conjecture of interpreting entanglement entropy as the black hole entropy, which passed various numerical tests. In the present talk, we add yet another strong supportive evidence to this conjecture, that is we numerically show that the temperature of entanglement is same as the Hawking temperature of black hole for massless free scalar fields. Also we show the validity of the first law of black hole mechanics using entanglement entropy and temperature.

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Singularity type IV avoidance by tunneling of the wave function of the universe approach

Abstract: We use Generalized Chaplygin Gas to model the evolution of the universe. For a certain choice of parameter, this model turns out to exhibit singular behavior in the cosmological scale factor. These singularities can be avoided using methods of Quantum Cosmology. In this work we study the type?IV singularity that occurs at a finite time and scale factor in future.. This singularity arises on the maximum of a distinct double well shape potential. In quantum cosmology avoiding such singularity is pursued by the tunneling of the wave function of the universe approach. The calculations are carried out in the semiclassical approximation. The objective of this research is to determine and interpret the prediction of the tunneling.

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Extended phase space approach to quantization of gravity I: its premises and the choice of quantization scheme

Abstract: In this talk I shall discuss the ideas that lead to extended phase space approach to quantization of gravity and its basic statements. The main goal of this approach is to take into account such feature of gravitational theory as a possible absence of asymptotic states in a gravitating system with non-trivial topology. The approach is considered as an alternative to Dirac canonical quantization as well as to the Batalin-Fradkin-Vilkovisky approach that is also formulated in extended phase space and has been applied successfully to systems with asymptotic states. For the simplest isotropic model I shall describe Hamiltonian dynamics in extended phase space which is completely equivalent to Lagrangian dynamics of the model. The comparison with the Batalin-Fradkin-Vilkovisky formulation will be given. To quantize the model, the Schrödinger equation is derived from a path integral in Lagrangian form. The arguments in favor of this form of the path integral will be considered. In the conclusion I shall discuss the structure of the general solution to the Schrödinger equation and its interpretation. It will be also shown that solutions to the Wheeler-DeWitt equation for this model can be found among solutions to the Schrödinger equation.

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Extended phase space approach to quantization of gravity II: possible applications

Abstract: In my second talk devoted to extended phase space approach to quantization of gravity I shall discuss some applications of this approach to demonstrate its advantages and viability. Among others, I shall consider canonical transformations in extended phase space involving gauge degrees of freedom; the BRST charge as a generator of gauge transformation for all gravitational degrees of freedom; a possible role of a subsystem, related to the observer and described by the gauge-fixing term in the effective action, in cosmological evolution; the description of quantum gravitational phenomena in various reference frames and its possible relation to black hole complementarity.

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Changing Observables in Hamiltonian General Relativity

Abstract: Is change missing in canonical General Relativity? Hamiltonian-Lagrangian implies that there is Hamiltonian change just when there is no time-like Killing vector field. Change has seemed missing partly due to Dirac's belief that a first-class constraint, especially a primary, generates a gauge transformation. Pons showed that Dirac's argument stops too soon: working to second order in time brings in first-class secondaries and hence the gauge generator G, a tuned sum of first-class constraints used by Anderson and Bergmann (1951) and recovered by Mukunda, Castellani et al. from the 1980s. I observe that trouble happens immediately: a first-class primary constraint generates an illegal change of initial data in GR, Maxwell and Yang-Mills. Dirac's subtractive derivation misses it by cancellation. Confusion between the electric field E(dA) and canonical momenta p (auxiliary fields in the canonical Lagrangian p \dot{q}-H) also obscures the problem. The gauge generator G changes the action by at most a boundary term, but an isolated first-class constraint does not. The gauge generator G generates spatio-temporal coordinate transformations (not just spatial ones) for the space-time metric (not just the spatial metric), as one would want in GR.

But are there locally varying _observables_? With first-class constraints exposed as not generating gauge transformations, Poisson brackets should be taken with the gauge generator G, as noted by Pons, Salisbury and Sundermeyer. Heeding Einstein's point-coincidence argument excludes primitive point individuation. Kuchar's waiver of the vanishing Poisson brackets condition for the Hamiltonian constraint to permit change has a principled extension that yields 4-dimensional Lie derivatives. Mere covariance, not invariance, suffices for coordinate transformations in General Relativity, to which one can point, in contrast to electromagnetic gauge transformations. Hence the space-time metric and its concomitants (connection, curvature, etc.) and the electromagnetic field strength are locally varying observables for Einstein-Maxwell theory in Hamiltonian form as well.

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Naked Singularities in the canonical quantized LTB-Model

Abstract: The final state of a spherically symmetric star always admits a singularity at its center if only gravitational effects are considered. This singularity is covered by an event horizon in most cases. However, the existence of singularities in final theory of Quantum Gravity is so far unclear. For some initial conditions to the matter distribution it is possible that the formed singularity might be temporary visible. This case is called a naked singularity and is of central interest in this thesis. Their existence implies the breakdown of General Relativity itself, since it manifests that future is unpredictable from initial data alone. Anything could form in the central singularity due to the presence of an infinitely large energy density. It was shown that initial conditions leading to naked singularities are physically meaningful and cannot be neglected. The following question arises: Are singularities an artifact of General Relativity itself and can be resolved by taking quantum mechanical effects into account? Here we show, that for a specific model containing a naked singularity, we obtain an everywhere vanishing wave function. This result can be interpreted as the avoidance of the classically allowed naked singularity. Furthermore, our toy model shows certain similarities to the Friedmann-Lemaitre-Robertson-Walker metric (FLRW metric). We show that a specific perturbation around this solution is also quantum mechanically forbidden. Our results demonstrate that canonical quantization is at least in our case capable of contributing to the ongoing debate on singularity avoidance. However, we consider only one case of a naked singularity and a result the general case of (naked) singularities still remains unclear.

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The Conformal Immirzi Parameter and a Shape Dynamical Loop Gravity

Abstract: The Barbero-Immirzi parameter of loop quantum gravity is a one parameter ambiguity of the theory whose physical significance is as-of-yet unknown. It is an inherent characteristic of the quantum theory since it appears in the spectra of geometric operators. The parameter’s appearance in the area and volume spectra suggest that it plays a role in determining the fundamental length scale of space.

The main theme of this thesis is that the Barbero-Immirzi parameter arising in loop quantum gravity can consistently be interpreted as a Weyl rescaling of the geometry.

An interesting realization is that promoting the Barbero-Immirzi parameter to be a general conformal transformation leads to a system which can be identified as analogous to the linking theory of shape dynamics. A three dimensional gravitational gauge connection is then constructed within the linking theory in a manner analogous to loop quantum gravity. This new connection-based shape dynamics is then quantized to form a hybrid quantum shape dynamical loop gravity.

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Quantum Cosmology of Tachyon Models

Abstract: The talk will start with an introduction into the classical cosmology of universes filled with tachyons and other Born-Infeld type fields. In particular we analyze the cases with a constant potential and with an inverse square potential. Furthermore we discuss how such models can be treated in the framework of quantum cosmology.

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Contact Geometry of the Restricted Three-Body Problem

Abstract: The existence of closed obits in the Three-Body Problem can also be proven by using methods of Contact Geometry. This goal will be archived by using theorems of Symplectic Field Theory. In order to do so one needs a Liouville vector field that is transverse to the considered energy hypersurface. However, in the general case this existence is not proven for all energy values . Here I show the existence of such a transverse Liouville vector field for energies below the energy corresponding to the first Lagrange point. Furthermore, it can also be proven for energies slightly above this value. Using this as a starting point I prove the existence of closed orbits in that energy range. Even if the existence of closed orbits can be proven by considering other methods, the Three-Body Problem gives a nice application to the methods of Contact Geometry.

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The Pais-Uhlenbeck-Oscillator and its Application in Quantum Cosmology

Abstract: The Pais-Uhlenbeck-Oscillator, which is somehow the simplest model for higher order derivative theories, is discussed. After a classical description, quantization is applied and possible applications in Quantum Cosmology are sketched.

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Local cohomology, master equation and renormalization of higher-derivative and nonlocal quantum gravity

Abstract: The major problem of quantum gravity is that it is a nonrenormalizable theory. Extensions of the Einstein-Hilbert action may solve this problem, but have other weaknesses. For example, higher-derivative quantum gravity is renormalizable, but not unitary. At present, the only known solutions that are both unitary and renormalizable are nonlocal. Both the higher-derivative and nonlocal extensions of quantum gravity have features that are quite interesting and worth of investigation, because they may shed light on the ultimate theory. In this talk we reconsider them under a modern perspective. First, we prove the renormalizability of higher-derivative quantum gravity using the Batalin-Vilkovisky formalism. Then we relax the assumption of locality by adding infinitely many higher-derivative terms to the Action and arranging them appropriately. At last, we review the approach to nonlocal theories and illustrate how our results apply to them.

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Phase-field concept of matter: The dynamic universe without space and time

Abstract: The phase-field theory is applied to gravitating elementary masses in a network of vector-components of the phase-field. Being a monistic theory with the phase-field as the only "substance" it describes the dual elements space and mass by space- and gradient-energy of the field. In the framework of a realistic nonlocal field theory, time and space coordinates are formulated as background independent dynamic variables intrinsic to the field. The field controls the distribution of masses in space and the evolution in time. The equations of motion are derived from first principles of thermodynamics. Application to a large number of fields predicts scale separation in space and repulsive action of masses distant beyond a marginal distance. The predicted marginal distance is compared to the size of the voids in the observable universe.

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Soft singularity crossing and transformation of matter properties

Alexander Kamenshchik (Uni Bologna/Landau Inst. Moscow)

We investigate particular cosmological models, based either on tachyon fields or on perfect fluids, for which soft future singularities arise in a natural way. Our main result is the description of a smooth crossing of the soft singularity in models with an anti-Chaplygin gas or with a particular tachyon field in the presence of dust. Such a crossing is made possible by certain transformations of matter properties. Some of these cosmological evolutions involving tachyons are compatible with SNIa data. We compute numerically their dynamics involving a first soft singularity crossing, a turning point and a second soft singulatity crossing during recollapse, ending in a Big Crunch singularity.

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