Aspects of inflation and the very early universe

Abstract: Until recently our knowledge of the primordial curvature perturbation was relatively modest. Ever since COBE delivered its map of data we know the scalar spectrum of primordial perturbations is approximately flat, with the power being only slightly stronger at larger scales. Most inflationary models predict an approximately scale-invariant spectrum, which therefore cannot be used as a distinctive signature. To distinguish between different inflationary microphysics we need to study higher point statistics of the primordial perturbation, which can encode non-gaussian data. In the first part of this thesis we study the bispectrum in all single-field models with a well-defined quantum field theory during a quasi-de Sitter inflationary phase. Any single-field models without ghost-like instabilities fall into this description: from canonical, to Dirac-Born-Infeld inflation and galileon inflation theories. We investigate the scale and shape- dependences of the bispectrum to next-order in the slow-roll approximation. We illustrate our results by applying them to different models and argue these corrections must be taken into account to keep the theoretical error below the observational precision set by the Planck satellite. We then explore the ability of using bispectrum shapes to distinguish between inflationary models more efficiently. We further extend the study of the bispectrum of single-field models beyond the slow-roll approximation, demanding the spectral index to be close to, but not exactly, unity. In the second part of this thesis we explore the process by which the universe is repopulated with matter particles at the end of a Dirac-Born-Infeld inflation phase. We place some mild bounds on the reheating temperature of these models. We argue that the constraints arising from the preheating analysis are complementary to those derived from the primordial perturbation.