|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 multicoincident
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.