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Quantum Phenomena in the Realm of Cosmology and Astrophysics

Quantum Phenomena in the Realm of Cosmology and Astrophysics

10 Part I. Introduction

10 Part I. Introduction matter are estimated in the analysis of the Planck collaboration as Ω M = 31.75%, and the cosmological constant is assumed to make up about Ω Λ = 68.25%. The equation of state of the universe in the ΛCDM model can be given considering these contributions as 1 ω = − , (1.35) 1 + Ω M /Ω Λ a−3 which for the above values results in ω ≃ −0.68. The cosmological constant postulated in the ΛCDM model doesn’t contain any information on its micro-physical background or origin, it is a phenomenological quantity motivated by observed features of the universe and requires yet to be derived and justified from a microphysical theory. Some constraints on its physical nature can be obtained from experiments, but since the only information comes from indirect observations of its consequences, our knowledge about the origin of the effect stands on shaky grounds. Many theories put forward as its explaination are in accordance with observations, since the parameters to compare with the data are few, and this leads to a large degeneracy of models. Correspondingly, there has been an animated discourse and prosperous growth of the number of theories about the possible explaination to the phenomenon, and a fair evaluation of the models at hand and their success is definitely necessary, and may be provided by cosmography. 1.2. Contents In this dissertation, we thus address some of the major concerns of modern cosmology. On the theoretical side, we successfully develop a model to explain dark energy by connecting it to a quantum theoretical phenomenon which has led to puzzles in quantum field theories. Among the abundance of models trying to explain this kinematic feature of the universe, one of them is to consider the vacuum fluctuations of quantum fields, an energy density constant in space as the origin of this expansion. The vacuum energy is a divergent quantity however, and is thus usually discarded as a possible explaination for dark energy. The huge discrepancy between an infinite value of the vacuum energy, or a very large finite value achieved by some kind of renormalization technique, and the tiny constant energy density driving the cosmic expansion, is termed the hirarchy problem. By balancing contributions of different quantum fields, a small finite value of the vacuum energy can be achieved, which can correctly account for the expansion of the universe. In this way, we find an explaination to the question of dark energy as well as manage to resolve the hirarchy problem in this context.

1. Basic Foundations and Outlook 11 To complement this part of the work, we investigate the issue of the accelerated re-expansion of the universe from an observational point of view and improve conventional methods of data analysis to be able to extract the universe’s kinematical properties from experimental results in the most independent way, in order to give the constraints that any viable theory of cosmology has to fulfill. We investigate observational data of the luminosity of type Ia supernovae events in order to obtain numerical fits for the parameters of the so-called cosmographic series, consisting of the Hubble parameter H 0 , the acceleration parameter q 0 , and further higher-order parameters describing the kinematical evolution of the universe. The conventional approach utilizes Taylor expansions of the relevant quantities for data fitting. We extend the existing analyses for several orders in the expansion, and suggest improvements to conventional cosmography by constructing alternatives to the commonly used redshift variable z, as well as by proposing a new method of expansion substituting the usual Taylor approach. Our results confirm the validity of the introduced modifications, as well as yield constraints on the kinematical properties of our universe, affirming the ΛCDM model to be in accordance with observations. Yet another connection of a quantum phenomenon to large scale scenarios is the theory of the occurrence of a Bose-Einstein condensate in compact objects. We will investigate the impact of the occurrence of a BEC on the properties of objects such as white dwarfs, where conditions allow for the formation of BECs due to a favourable combination of temperature and density. Thus it is of interest to investigate the condensation of bosonic particles under the influence of hard-sphere scattering and gravitational interactions in the framework of a Hartree-Fock theory at finite temperatures. Results can be compared to observations through the computed density profiles and masses of the objects. We will draw conclusions and ultimately summarize the work presented in the respective project at the end of each part, and comment on its significance and possible further extensions.

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