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Inflationary cosmology is the leading explanation of the very early universe.Many different models of inflation have been constructed which fit currentobservational data. In this work theoretical and numerical methods forconstraining the parameter space of a wide class of such models are described.First, string-theoretic models with large non-Gaussian signatures areinvestigated. An upper bound is placed on the amplitude of primordialgravitational waves produced by ultra-violet Dirac-Born-Infeld inflation. Inall but the most finely tuned cases, this bound is incompatible with a lowerbound derived for inflationary models which exhibit a red spectrum anddetectable non-Gaussianity. By analysing general non-canonical actions, a classof models is found which can evade the upper bound when the phase speed ofperturbations is small. The multi-coincident brane scenario with a finitenumber of branes is one such model. For models with a potentially observablegravitational wave spectrum the number of coincident branes is shown to takeonly small values. The second method of constraining inflationary models is thenumerical calculation of second order perturbations for a general class ofsingle field models. The Klein-Gordon equation at second order, written interms of scalar field variations only, is numerically solved. The slow rollversion of the second order source term is used and the method is shown to beextendable to the full equation. This procedure allows the evolution of secondorder perturbations in general and the calculation of the non-Gaussianityparameter in cases where there is no analytical solution available.

Constraining Inflationary Scenarios with Braneworld Models and Second Order Cosmological Perturbations