AbstractIn this work we explore the correspondence between the physical processes associated with inflationary models inspired by string theory and the subsequent non-Gaussian signatures imprinted in the primordial density perturbations. Specifically, we have chosen multiple-DBI inflation as a representative model to understand the effect of multiple-field dynamics and non-canonical kinetic terms on the resultant form of non-Gaussianity.
We begin by introducing inflation as a mechanism to naturally lay down the initial conditions necessary for the hot big bang. Since the primordial density perturbations provide the best way to constrain inflationary models, we then review cosmological perturbation theory and provide the predictions of standard single-field, slow-roll inflation. Thereafter, we briefly review extensions to this model and introduce non-Gaussianity as a way to observationally discern between these otherwise degenerate scenarios.
Thereafter, we study the effect of non-trivial sound speeds on local-type non-Gaussianity during multiple-field inflation. To this end, we use the δN formalism and a sum separable Hubble parameter to derive an analytic expression for the local-type non-linearity parameter in the two-field case, valid beyond slow variation. We find that non-trivial sound speeds can, in principle, curve the trajectory in such a way that significant local-type non- Gaussianity is produced. Deviations from slow variation, such as rapidly varying sound speeds, enhance this effect. To illustrate our results we consider inflation in the tip regions of two warped throats and find large local-type non-Gaussianity produced towards the end of the inflationary process.
We then consider the equilateral contribution to the bi-spectrum by first calculating the full third-order action for the field fluctuations using the Arnowitt-Deser-Misner formalism. We then derive the corresponding three-point function for the field fluctuations at horizon-exit, to leading order in slow variation and small sound speeds. Thereafter, we again use the δN formalism and a separable Hubble parameter to present the combined local and equilateral contributions to the bi-spectrum of the curvature perturbation. We then revisit the case of inflation in two cutoff throats and find that the corresponding equilateral contribution is prohibitively large in this case.
As an application of the above, we then explore further the parameter space of multiple- DBI inflation and, in particular, the dependence of large local-type non Gaussianity on initial conditions. To this end, we consider an alternative model of inflation in two cutoff throats that allows analytical solutions for the trajectories. We begin by considering the canonical limit of the model in which local-type non-Gaussianity is produced by the curvature of the potential. We find that such behaviour is highly dependent on the initial values of the fields. We then consider inflation in the tip regions of two cutoff throats and find that the production of large local-type non-Gaussianity through rapidly varying sound speeds is similarly dependent on initial conditions. Moreover, the equilateral contribution remains prohibitively large in such cases.
Finally, we summarise our results and identify directions for future research, before providing a wider outlook for the inflationary paradigm in light of recent results from Planck.
|Date of Award||Feb 2014|
|Supervisor||David Wands (Supervisor)|