Reconstructing the inflaton potential

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