Brook, Mark N.
(2010)
Cosmology meets condensed matter.
PhD thesis, University of Nottingham.
Abstract
This thesis is concerned with the interface of cosmology and condensed matter.
Although at either end of the scale spectrum, the two disciplines have more in common than one might think. Condensed matter theorists and high-energy field theorists study, usually independently, phenomena embedded in the structure of a quantum field theory. It would appear at first glance that these phenomena are disjoint, and this has often led to the two fields developing their own procedures and strategies, and adopting their own nomenclature.
We will look at some concepts that have helped bridge the gap between the two subjects, enabling progress in both, before incorporating condensed matter techniques to our own cosmological model. By considering ideas from cosmological high-energy field theory, we then critically examine other models of astrophysical condensed matter phenomena.
In Chapter 1, we introduce the current cosmological paradigm, and present a somewhat historical overview of the interplay between cosmology and condensed matter. Many concepts are introduced here that later chapters will follow up on, and we give some examples in which condensed matter physics has had a very real effect on informing cosmology. We also reflect on the most recent incarnations of the condensed matter / cosmology interplay, and the future of these developments.
Chapter 2 presents the Einstein-Klein-Gordon system of equations and their non-relativistic and nonlinear counterparts, the Schrodinger-Poisson, and nonlinear Schrodinger (Gross Pitaevskii)-Poisson systems. We give a more technical overview of the various applications of these systems of equations, as well as discussing the role and interpretation of condensates in the field of cosmology.
In Chapter 3 we discuss more qualitatively the fluid-mechanical methods used in a wave-mechanical approach to structure formation, and in formulations of condensed matter models. Taking a lead from the condensed matter side, we look at some of the details of the Gross-Pitaevskii equation, particularly with regard to quantum vortices, and then put this quantum-mechanical system into a cosmological environment by coupling it to the Poisson equation, in an effort to pin down some of the parameters that may be consistent with the existence of vortices in a cosmological Bose-Einstein condensate.
In Chapter 4 we turn to high-energy field theory and elucidate further some of the relationships with condensed matter physics that are present. We also critically examine a Bose-Einstein dark matter model in light of these considerations.
Chapter 5 rounds off with a discussion and suggestions for further work based upon models we have discussed, as well as some ideas for models that have not yet been mentioned.
An appendix discusses techniques for moving from the relativistic Einstein-Klein-Gordon equations to the Schrodinger-Poisson system.
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