Abstract. An upper bound on the amplitude of the primordial gravitational wave spectrum generated during ultra-violet DBI inflation is derived. The bound is insensitive to the form of the inflaton potential and the warp factor of the compactified dimensions and can be expressed entirely in terms of observational parameters once the volume of the five-dimensional sub-manifold of the throat has been specified. For standard type IIB compactification schemes, the bound predicts undetectably small tensor perturbations with a tensor-scalar ratio r < 10 −7 . This is incompatible with a corresponding lower limit of r > 0.1(1 − n s ), which applies to any model that generates a red spectral index n s < 1 and a potentially detectable non-Gaussianity in the curvature perturbation. Possible ways of evading these bounds in more general DBItype scenarios are discussed and a multiple-brane model is investigated as a specific example.

Isocurvature perturbations naturally occur in models of inflation consisting of more than one scalar field. In this paper we calculate the spectrum of isocurvature perturbations generated at the end of inflation for three different inflationary models consisting of two canonical scalar fields. The amount of non-adiabatic pressure present at the end of inflation can have observational consequences through the generation of vorticity and subsequently the sourcing of B-mode polarisation. We compare two different definitions of isocurvature perturbations and show how these quantities evolve in different ways during inflation. Our results are calculated using the open source Pyflation numerical package which is available to download.

We calculate the conditions required to produce a large local trispectrum during two-field slow-roll inflation. This is done by extending and simplifying the 'heat-map' approach developed by Byrnes et al. The conditions required to generate a large trispectrum are broadly the same as those that can produce a large bispectrum. We derive a simple relation between τ NL and f NL for models with separable potentials, and furthermore show that g NL and τ NL can be related in specific circumstances. Additionally, we interpret the heatmaps dynamically, showing how they can be used as qualitative tools to understand the evolution of non-Gaussianity during inflation. We also show how f NL , τ NL and g NL are sourced by generic shapes in the inflationary potential, namely ridges, valleys and inflection points.

We numerically solve the Klein-Gordon equation at second order in cosmological perturbation theory in closed form for a single scalar field, describing the method employed in detail. We use the slow-roll version of the second order source term and argue that our method is extendable to the full equation. We consider two standard single field models and find that the results agree with previous calculations using analytic methods, where comparison is possible. Our procedure allows the evolution of second order perturbations in general and the calculation of the non-linearity parameter fNL to be examined in cases where there is no analytical solution available.3 The k ranges in M PL are:

A class of non-canonical inflationary models is identified, where the leading-order contribution to the non-Gaussianity of the curvature perturbation is determined by the sound speed of the fluctuations in the inflaton field. Included in this class of models is the effective action for multiple coincident branes in the finite n limit. The action for this configuration is determined using a powerful iterative technique, based upon the fundamental representation of SU(2). In principle the upper bounds on the tensor–scalar ratio that arise in the standard, single-brane DBI inflationary scenario can be relaxed in such multi-brane configurations if a large and detectable non-Gaussianity is generated. Moreover models with a small number of coincident branes could generate a gravitational wave background that will be observable in future experiments.