# Bachelor's Thesis in Mathematical Physics and Geometry

On this page you will find information specific for the course SA114X, with specialization towards Mathematical Physics and Geometry.

### Course Structure

Recommended background knowledge for writing a bachelor's thesis in Mathematical Physics is the course SF1677. The course SF1677, Foundation of Analysis, is given during the spring semester. It is recommended that the student has taken this course before taking the course SA114X. If you are interested in writing a bachelor's thesis in Mathematical Physics and Geometry you are encouraged to contact the supervisor as soon as possible to discuss possible projects and get advice on needed background material for their particular project.

## Suggestions for projects

### MODELS OF THE UNIVERSE

Supervisor: H. Ringström

The cosmological principle is the basic starting point when modeling the universe. According to this assumption, one does (at a given a moment in time) not see any difference between two points in space (homogeneity) nor between different directions (isotropy). As a consequence, one obtains the standard models in cosmology. These models start with a big bang and then expand forever (or recollapse). Since the cosmological principle is not exactly fulfilled, it is, however, of interest to see what happens if it is relaxed. Does one obtain a big bang with arbitrarily strong gravitational fields? Are the standard models stable? It is quite hard to answer these questions in all generality, and it is thus natural to reduce the symmetry assumptions gradually. A natural first step is to study homogeneous (but not necessarily isotropic) models. Under these assumptions, Einstein's equations become a system of non-linear ODEs. In the easiest case, it is possible to study the solutions with methods from the course SF1683 (differentialekvationer och transformmetoder). In the more difficult cases, the relevant systems of equations are objects of current research.

In short, the equations to be investigated in this course are systems of non-linear ODEs (which appear in the study of the different cosmological models in general relativity). The objective of the course is that the participants should learn to analyze the asymptotic behavior of the solutions.

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