Prof. Steve Thomas Project Abstracts

BSc Project Abstracts

Kaluza-Klein theory and the origin of symmetries
In recent years the concept that our world may have hidden extra spatial dimensions has played a vital role in fundamental theories that unify the known forces, most notably superstring theory. This idea originates from the work of Kaluza and Klein in the 1920's who showed that a theory in four dimensions that contains gravity and electromagnetism may be explained by a pure gravity theory in one dimension higher. The project will introduce the student to the basic Kaluza-Klein hypothesis, with simple examples based on scalar field theory which will illustrate the physical consequences of compactification. These techniques will then be applied to higher dimensional gravity theories, which gives a clue to the higher dimensional origin of gauge symmetries in four dimensions

Large extra dimensions
This project concerns the recent proposal that we may be living in a world where there could be macroscopically large extra spatial dimensions beyond the three that we are familiar with. This possibility has arisen in so called 'brane-world' models where our 3+1 dimensional Universe is thought of as a kind of membrane moving through a higher dimensional volume. In such models the strong, weak and electromagnetic forces are confined to live in our brane but gravitational forces can penetrate the extra dimensions.
The student will investigate the behavior of Newtonian gravity in different dimensions as a way of understanding the interplay between the perceived strength of gravity and the size of any additional spatial directions. Then, within the framework of General Relativity, brane-world models first described by Randall and Sundrum will be investigated as will the current experimental bounds placed on them arising from LHC data.

From Classical Strings to Photons and Gravitons
The project starts with manipulating equations describing the geometry of string worldsheets and their embedding in space-time. This is followed by working through aspects of formal quantum mechanics and special relativity. It builds up to the worldsheet quantum theory construction of space-time physical states such as photons and gravitons. Zwiebach's string theory book provides the main reference.

Inflationary Cosmology
Inflation has been proposed as a ‘paradigm’ whereby the Universe undergoes a period of exponential expansion during which spatial regions as small as 10^{-25cm} get blown up to something of the order of a few cms in size in only 10^{-32} sec! Such a model explains some long-standing problems in standard Friedman-Roberston-Walker big bang cosmology, namely the so-called horizon and flatness problems as well as (potentially) solving the singularity problem. At the same time it also explains the near scale-invariant spectrum of perturbations that we can observe today through their imprints on the CMB radiation. One particular type of perturbation predicted is a primordial spectrum of gravitational waves whose affect is to polarise, in a very particular way, the microwave light from the CMB. One particular type of perturbation predicted is a primordial spectrum of gravitational waves whose affect is to produce B-mode polarisation of the CMB. In a recent experiment, this polarisation has been detected by the BICEP2 collaboration using telescopes based in the South Pole, although it is still unclear if the signal is primordial or due to dust in our galaxy. This project covers some fundamental aspects of inflationary cosmology. Beginning from the FRW Big Bang model in general relativity, the student will then work through the details of inflation and the conditions required for it to occur. This will primarily involve so called slow roll inflation models and some simple examples will be studied. Classical field evolution and quantum fluctuations will be investigated with the latter giving rise to various perturbation spectra that the student will derive. The resulting cosmological observables will also be derived and predictions tested against current precision CMB data. There is scope within the project to use Mathematica or MatLab as numerical tools.

MSci Review Project Abstracts

Kaluza-Klein theory and the origin of symmetries
In recent years the concept that our world may have hidden extra spatial dimensions has played a vital role in fundamental theories that unify the known forces, most notably superstring theory. This idea originates from the work of Kaluza and Klein in the 1920's who showed that a theory in four dimensions that contains gravity and electromagnetism may be explained by a pure gravity theory in one dimension higher. The project will introduce the student to the basic Kaluza-Klein hypothesis, with simple examples based on scalar field theory which will illustrate the physical consequences of compactification. These techniques will then be applied to higher dimensional gravity theories, which gives a clue to the higher dimensional origin of gauge symmetries in four dimensions

Inflationary Cosmology
Inflation has been proposed as a ‘paradigm’ whereby the Universe undergoes a period of exponential expansion during which spatial regions as small as 10^{-25cm} get blown up to something of the order of a few cms in size in only 10^{-32} sec! Such a model explains some long-standing problems in standard Friedman-Roberston-Walker big bang cosmology, namely the so-called horizon and flatness problems as well as (potentially) solving the singularity problem. At the same time it also explains the near scale-invariant spectrum of perturbations that we can observe today through their imprints on the CMB radiation. One particular type of perturbation predicted is a primordial spectrum of gravitational waves whose affect is to produce B-mode polarisation of the CMB. In a recent experiment, this polarisation has been detected by the BICEP2 collaboration using telescopes based in the South Pole, although it is still unclear if the signal is primordial or due to dust in our galaxy. This project covers some fundamental aspects of inflationary cosmology. Beginning from the FRW Big Bang model in general relativity, the student will then work through the details of inflation and the conditions required for it to occur. This will primarily involve so called slow roll inflation models and some simple examples will be studied. Classical field evolution and quantum fluctuations will be investigated with the latter giving rise to various perturbation spectra that the student will derive. The resulting cosmological observables will also be derived and predictions tested against current precision CMB data. There is scope within the project to use Mathematica or MatLab as numerical tools.

MSci Research/Investigative Project Abstracts

From classical strings to photons and gravitons
The project starts with manipulating equations describing the geometry of string worldsheets and their embedding in space-time. This is followed by working through aspects of formal quantum mechanics and special relativity. It builds up to the worldsheet quantum theory construction of space-time physical states such as photons and gravitons. These investigations can also be extended to the case of D-branes. There is also scope to study numerically, solutions describing classical open strings, closed strings as well as D-branes via use of Mathematica or Matlab software packages. Zwiebach's string theory book provides the main reference.

Inflationary Cosmology
Inflation has been proposed as a ‘paradigm’whereby the Universe undergoes a period of exponential expansion during which spatial regions as small as 10^{-25cm} get blown up to something of the order of a few cms in size in only 10^{-32} sec! Such a model explains some long-standing problems in standard Friedman-Roberston-Walker big bang cosmology, namely the so-called horizon and flatness problems as well as (potentially) solving the singularity problem. At the same time it also explains the near scale-invariant spectrum of perturbations that we can observe today throughtheir imprints on the CMB radiation. One particular type of perturbation predicted is a primordial spectrum of gravitational waves whose affect is to produce B-mode polarisation of the CMB. In a recent experiment, this polarisation has been detected by the BICEP2 collaboration using telescopes based in the South Pole, although it is still unclear if the signal is primordial or due to dust in our galaxy. This project covers some fundamental aspects of inflationary cosmology. Beginning from the FRW Big Bang model in general relativity, the student will then work through the details of inflation and the conditions required for it to occur. This will primarily involve so called slow roll inflation models and examples will be studied motivated by both particle physics and string theory. Other kinds of inflation such as ‘chaotic’ and ‘eternal’ inflation will also be covered, by way of comparison. Classical field evolution and quantum fluctuations will be investigated with the latter giving rise to various perturbation spectra that the student will derive. The resulting cosmological observables will also be derived and predictions tested against current precision CMB data. There is scope within the project to use Mathematica or MatLab as numerical tools.

Prof. Steve Thomas Project Abstracts