Abstract
During inflation, the potential of the inflaton scalar field $\phi$,
drives the exponential expansion of the Universe. The nature of the
inflaton potential is presently unknown, but one hopes to learn more
from observations of the cosmic microwave background (CMB). Models of
topical interest of the inflaton potential can be divided into four
classes, based on observable parameters. In this thesis we explore the
possibility of reconstructing the inflaton potential from
observational data using a MonteCarlo reconstruction method. A
pipeline to estimate cosmological parameter constraints using a
MonteCarlo MarkovChain (MCMC) is also investigated. The object is to
exclude whole classes of inflaton potentials.
We find that the MonteCarlo reconstruction method is well suited
to produce vast numbers of candidates for the inflaton
potential, but present constraints on the cosmological parameters of
interest are too weak for the MonteCarlo reconstruction to be a useful
method. Furthermore we discover weaknesses with \texttt{COSMOMC}, the MCMC
method commonly used to constrain cosmological parameters. Currently,
\texttt{COSMOMC} fails when using $B$-mode polarisation data, and the time and
computing power needed to analyse noise-free CMB data is far beyond
what is needed for current observational data.
If the difficulties with the MCMC method are resolved, there is an
exciting possibility of using the MCMC method in conjunction with the
MonteCarlo reconstruction method to reconstruct the true inflaton
potential from future high precision CMB observations.