We explore the mechanics of inflation within simplified extra-dimensional models
involving an inflaton interacting with a Einstein-Maxwell system in two extra
dimensions. The models are complicated enough to include a stabilization
mechanism for the extra-dimensional radius, but simple enough to solve the full
six-dimensional field equations. After performing a consistent truncation, which
guarantees our six-dimensional equations are equivalently satisfied by the four dimensional
equations of motion, we explore (numerically and analytically) the
power-law solutions evident in our initial parameter search. After a comprehensive
search for potential power-law scaling solutions in both six and four dimensions,
we find two that give rise to interesting inflationary dynamics. They both
can generically exist outside of the usual four dimensional effective theory, and
yet, we still trust them since our truncation is consistent. One of these is a dynamical
attractor whose features are relatively insensitive to initial conditions, but
whose slow-roll parameters cannot be arbitrarily small; the other is not an attractor
but can roll much more slowly, until eventually transitioning to another solution
due to its unstable nature. We present a numerical and analytic discussion of these
two solutions. Four of the appendices contain calculations in more explicit detail
than are performed in the main text, while a fifth contains a representative Mathematica
worksheet and the sixth contains the general results of the systematic sweep
for scaling solutions. / Thesis / Master of Science (MSc) / When looking out at the night sky, we see a universe that is extremely flat and
looks the same no matter what direction we stare. However, these present-day observations
require the universe to have begun under very specific circumstances,
which is not something that naturally occurs; think about what is necessary to hit a
hole-in-one with a golf club: a very precise and specific shot is required. The theory
of Cosmological Inflation—a period of rapid expansion in the early universe—is
the current leading theory proposed to explain these observations. In our exploration,
we aim to study inflation from a higher-dimensional perspective in which
two extra spatial dimensions are added to our usual three. Ultimately, we find
three classes of solutions, two of which exist outside of the regimes usually studied,
that have the potential both to explain current observations, and also be useful
tools in future explorations.
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/20253 |
| Date | January 2016 |
| Creators | Enns, Jared |
| Contributors | Burgess, Cliff, Physics and Astronomy |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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