Inflation, the currently favoured solution to the grievous initial conditions problems of the Big Bang model of the universe, is a very general framework that can be constructed from any number of underlying theories. As inflation is meant to solve a problem of initial conditions, it is generally preferred that it not introduce its own initial conditions problem. The purpose of this thesis is to explore the sensitivity to initial conditions of solutions to two toy models of inflation. The models in and of themselves are not intended to explain inflation, but rather seek to begin to explore, in a controlled way, interesting properties that a full inflationary theory might have.
The first model is one with a single scalar inflaton, but two compact extra dimensions. We find this model has two inflationary solutions that can be well understood analytically. These solutions are power laws in time. One is found to be marginally insensitive to its initial conditions, and the other is found to be highly sensitive to its initial conditions. We also find a solution to this model that exhibits 4D quasi-de Sitter space, but is difficult to understand analytically, and its sensitivity to initial conditions is not yet well known.
The second model examines an n-scalar field Lagrangian that includes kinetic terms first-order in the derivatives of the fields (similar to certain ferromagnetic Lagrangians). It is found that this model can realize slow-roll inflation with arbitrarily steep potentials. A solution is constructed that can realize an exact de Sitter equation of state without saying anything about the slope of its potential. This solution is found to be marginally insensitive to its initial conditions for a certain range of parameters. Corrections from higher order terms in the Lagrangian are found to introduce a parameter space for which this solution is in fact highly insensitive to its initial conditions.
We therefore make progress in understanding higher-dimensional inflation, slow-roll inflation with steep potentials, and the sensitivity of solutions in both those cases to their initial conditions. / Thesis / Master of Science (MSc)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/20259 |
| Date | January 2016 |
| Creators | Hayman, Peter |
| Contributors | Burgess, Cliff, Physics and Astronomy |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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