Singularity Avoidance in Bianchi Type I Models in Quantum Cosmology

Abstract: In this thesis the possibility of avoiding cosmological singularities in Bianchi type I models in the framework of quantum geometrodynamics is investigated. Therefore three different models are considered: one with a positive cosmological constant, one with matter that fulfills the barotropic equation of state p=ωρ, and one with a generalized Chaplygin gas. Those exhibit Big Bang, Big Rip and Big Brake singularities, respectively. In all cases the classical behaviour as well as the behaviour of the solution of the corresponding Wheeler-DeWitt equation is analyzed and compared to the isotropic flat FLRW case. It is found that the there are solutions fulfilling the DeWitt criterion for singularity avoidance, that in some cases the classical behaviour is modified by the anisotropy (i.e. introducing new or changing present singularities) and that the additional degrees of freedom can lead to dispersive behaviour of the wave packets.

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Geometry transition in covariant LQG: black to white

Abstract: Black holes may end their lifes by becoming white holes, as the result of a non-perturbative quantum-gravitational process. To the best of our knowledge, the transition is not forbidden by any physical principle and quantum theory should be in a position to describe relevant physics. In particular, estimates of characteristic timescales are within reach with currently available tools. We use the EPRL model to define a transition amplitude. The EPRL model represents the current state-of-the-art of the spinfoam quantization program, which provides a tentative definition for the regularized path-integral of gravity in the context of Loop Quantum Gravity. We will review the conceptual setup of this ongoing project, present results for the characteristic timescales and discuss implications for the information paradox.

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Quantum gravity: the effective way

Abstract: In this talk I will review recent progress in using effective field theoretical (EFT) methods to deal with quantum gravity. I will show that EFT techniques enable us to make model independent calculations and to identify features of the underlying, unknown, theory of quantum gravity. Equipped with these tools, we reconsider problems such as the calculations of quantum gravitational corrections to black hole metrics, stars or Newton's potential and comment on applications to gravitational waves and other astrophysical probes of quantum gravity.

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Radiative Symmetry Breaking in Classically Conformal Extensions of the Standard Model

Abstract: We will examine the dynamical breakdown of the electroweak symmetry in classically conformal extensions of the Standard Model known as Higgs Portal Models. In such extensions, the validity of perturbation theory for arbitrary field values can be guaranteed (or improved) with the renormalisation group (RG). To achieve this, we will discuss a new method to RG improve the effective potential with an arbitrary number of scalar fields. The method amounts to solving the renormalisation group equation for the effective potential with the boundary conditions chosen on the hypersurface where quantum corrections vanish. We will show how this procedure opens the possibility of studying the effective potential of different Higgs Portal Models across a large range of energy scales and, in particular, how it clarifies the issue of stability of the improved potential.

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Integrable Cosmological Models with Liouville Scalar Fields

Abstract: An alternative method is proposed for homogeneous cosmological models with a Liouville field, which is a scalar field with an exponential potential. The key of the method is to use an integral of motion to eliminate the lapse function as the redundant degree of freedom. Applying this method in isotropic (Friedmann-Lemaître) as well as anisotropic (Bianchi-I) universes, explicit equations of time-independent classical trajectories in minisuperspace are derived, which makes their correspondence with the Wheeler--DeWitt quantum cosmological theory more directly.
The completeness and orthogonality of cosmological wave functions in quantum context are carefully reconsidered, so is the Hermiticity of the phantom model, which as a result admits a discrete spectrum unusually. The orthonormal eigenfunctions of the Wheeler--DeWitt equation pushes one step further to the calculation of observables of physical quantities.
The physical wave packets are established based on two definitions of norm, one is non-relativistic, the other is introduced from the techniques of pseudo-Hermitian quantum mechanics. Numerical results of both cases are given and discussed.

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3-forms and the recent speed up of the Universe

Abstract: In this talk, we consider 3-form dark energy (DE) models with interactions in the dark sector. We aim to distinguish the phenomenological interactions that are defined through the dark matter (DM) and the DE energy densities. We identify the non-interacting 3-form DE model which generically leads to an abrupt late-time cosmological event which is known as the little sibling of the Big Rip (LSBR). We classify the interactions which can possibly avoid this late-time abrupt event. we make also some preliminary analysis constraint of our model, for example, in light of the SDSS III data on the measurement of the linear growth rate of structure.

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Inducing the Einstein action in QCD-like theories

Abstract: We evaluate the induced value of Newton’s constant which would arise in QCD. The ingredients are modern lattice results, perturbation theory and the operator product expansion. The resulting shift in the Planck mass is positive. A scaled-up version of such a theory may be part of a quantum field theory treatment of gravity.

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Abstract: Cosmic strings are interesting objects both from an experimental and a theoretical point of view. In this talk, we discuss two scenarios:

(i) The stress-energy tensor of a string without internal structure satisfies a simple equation of state (?stringy matter?). We demonstrate that spherical deformations of the Reissner-Nordström-(A)dS metric give rise to such stringy matter, which in turn can be interpreted as a continuous distribution of cosmic strings.

(ii) For stationary spacetimes admitting a non-degenerate closed conformal Killing-Yano 2-form (e.g. the Kerr-NUT-(A)dS geometry), we construct a special stationary string configuration from the principal null congruence and the timelike Killing vector. In the special case of the Kerr metric (and higher-dimensional generalizations thereof) these strings extend from the black hole horizon to spatial infinity and extract angular-momentum from the black hole. We interpret this as the action of an asymptotic torque.

References

[1] J.B. and V. P. Frolov, "Stationary black holes with stringy hair," arXiv:1711.06357 [gr-qc], to appear in Phys. Rev. D (2018)
[2] J.B. and V. P. Frolov, "Principal Killing strings in higher-dimensional Kerr-NUT-(A)dS spacetimes," arXiv:1801.00122 [gr-qc].

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Dark Energy: Theoretical Approaches, Observational Constraints, and Cosmic Future Singularities

Abstract: In this thesis we will try to get a fundamental understanding of dark energy, starting by fully deriving the cosmological background model from a FLRW spacetime. In order to understand the observations that we want to discuss later on, we need to discuss both the matter species in our universe aswell as the concept of cosmic distances. The derivation of the equation of state of dark energy concludes the first section of this thesis. We follow up by discussing multiple examples of observations to find out, that they require dark energy to exist. This leads to constraints on the cosmic parameters and we will try to understand how these constraints are obtained. In the last section of this thesis we are going to discuss the fate of our universe under the existence of (phantom) dark energy before we fit a scalar field to our previous calculations to create a model for phantom dark energy.

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Beyond General Relativity: exponential gravity as a particular case

Abstract: In this talk I will review the basis of some types of modified gravities, their pros and cons, the possibility of reproducing late-time acceleration and their viability. A particular case will be analysed, based on exponential terms in the gravitational action, such a model may be capable of reproducing both inflation as the late-time acceleration. I will discuss the constraints coming from different sources of data, both at the inflationary epoch as at late times by using Sne Ia, BAO and Hubble data. As will be shown, exponential gravity may be kept as a promising candidate for dark energy and inflation.

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New boundary variables for classical and quantum gravity on a null surface

Abstract: In my talk, I present new canonical boundary variables for classical and quantum gravity on a null surface. These variables are found by considering general relativity as a Hamiltonian system in domains with inner null boundaries. The presence of such lightlike boundaries requires then additional boundary terms in the action. Using Ashtekar?s original SL(2,C) selfdual variables, I will explain that the natural such boundary term is nothing but a kinetic term for a spinor (defining the null flag of the boundary) and a spinor-valued two-form, which are both intrinsic to the boundary. The relevance of this new boundary term for the definition of quasi-local observables and for quantum gravity in particular will be explained. I will show, in particular, that in quantum gravity the oriented area of a two-dimensional cross section of the null boundary turns into the difference of two number operators. The resulting area spectrum is discrete and agrees with the results from loop quantum gravity. The entire derivation happens at the level of the continuum theory, and no spin-networks or SU(2) gauge variables are ever required for deriving this result.

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A partially ordered introduction to Causal Set theory

Abstract: In causal set theory space-time is described as a partially ordered set. While this makes identifying geometric properties a little more cumbersome, it does provide a Lorentz invariant discretisation. One interesting side effect of this discretisation are non-local effects in field theories that could be searched for in experiments. Another feature of this discrete description is that we can use computer simulations to explore the path integral over geometries. In this lecture I will introduce the basic set up of causal set theory, tell you a little bit about non-local signatures and then show some results of computer simulations.

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The chronon in M-theory

Abstract: In this seminar we discuss some aspects of chronon physics in an M-theory model. We start considering the possibility that quantum fluctuations are stretched on very large distances allowing a quantum mechanical treatment of physics on certain macroscopic scales. A crucial element of our analysis is the relativity of time. Indeed, the presence of a 5D black hole (with its gravitational field) leads us to a scenario where small quantum fluctuations produced near the black hole become very large for an asymptotic observer in harmony with the relativity of time. In the deep IR region, gravity shows new phenomena (related to an orbifold of time) which cannot be described through a field theory on the brane and, in this sense, these phenomena resemble the action-at-a-distance of Newtonian gravity when interpreted from the standpoint of S-brane physics. If an observer on the brane tries to analyze quantum gravity in his ground state, the gauge fixing procedure shows that all the matter fields and all the interactions of the Standard Model become redundant: the only physical degree of freedom for quantum gravity in this case is the time (namely the chronon) with its two dimensions (parametrized by the dilaton and the radion). Remarkably, the dynamics of the chronon is governed by a modified Schroedinger equation and, in this sense, the Schroedinger equation is the most fundamental equation of physics. A dilatonic signal traveling in the bulk can bring information from the future (of a different dilatonic time dimension) to our present dilatonic time. The selection of the dilatonic time dimension is related to the value of the chameleonic radion which is stabilized by some UV dynamics. Therefore, a modification of the environment produces a small shift in the radionic coordinate and this selects a totally different dilatonic time dimension (this mechanism is reminiscent of a butterfly effect). A number of consequences of this approach will be discussed.

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