Inflationary cosmology is the leading explanation of the very early universe.
Many different models of inflation have been constructed which fit current
observational data. In this work theoretical and numerical methods for
constraining the parameter space of a wide class of such models are described.
First, string-theoretic models with large non-Gaussian signatures are
investigated. An upper bound is placed on the amplitude of primordial
gravitational waves produced by ultra-violet Dirac-Born-Infeld inflation. In
all but the most finely tuned cases, this bound is incompatible with a lower
bound derived for inflationary models which exhibit a red spectrum and
detectable non-Gaussianity. By analysing general non-canonical actions, a class
of models is found which can evade the upper bound when the phase speed of
perturbations is small. The multi-coincident brane scenario with a finite
number of branes is one such model. For models with a potentially observable
gravitational wave spectrum the number of coincident branes is shown to take
only small values. The second method of constraining inflationary models is the
numerical calculation of second order perturbations for a general class of
single field models. The Klein-Gordon equation at second order, written in
terms of scalar field variations only, is numerically solved. The slow roll
version of the second order source term is used and the method is shown to be
extendable to the full equation. This procedure allows the evolution of second
order perturbations in general and the calculation of the non-Gaussianity
parameter in cases where there is no analytical solution available.Comment: PhD Thesis, Queen Mary, Univ of London, Supervisor: James E. Lidsey.
(211 pages, 35 figures