Cosmological inflation is a simple, and observationally well-supported, mechanism for generating a flat, spatially homogeneous universe with the statistical correlations in the cosmic microwave background we see today. Determining precisely how inflation happened, and how many fields were involved, are some of the main challenges of modern cosmology.

The first part of the thesis, consisting of Chapters 2 and 3, addresses this question by looking at what future measurements of local non-Gaussianity will tell us. Local non-Gaussianity has been proposed as a key observable for distinguishing between single- and multifield inflation, as a large value of this parameter would rule out the former. However, a small value would not necessarily rule out the latter. Using a new technique for generating random functions with Gaussian random fields, which we also prove the validity of, we generate random potentials for as many as 100 fields for inflation. We look at the observables of these models and in particular compute the local non-Gaussianity. An overwhelming majority of these models give local non-Gaussianity compatible with single-field inflation, despite significant multifield effects on superhorizon scales, indicating that this observable may not be sufficient to distinguish between these types of models.

The second part of the thesis, consisting of Chapters 4 and 5, addresses another aspect of this question by looking at other types of inflationary solutions than slow-roll, slow-turn. Slow-roll, slow-turn is an easily realised solution, but requires a very flat potential over large distances in field-space. The fine-tuning needed for this remains an Achilles heel of the inflationary paradigm. However, there are inflationary solutions which can be realised in steep potentials. Hyperinflation' is a particularly interesting one of these, and we investigate this solution in detail. Using the techniques developed to study hyperinflation, we then show that there exists a new, completely general two-field attractor solution that is characterised by rapidly turning fields. This rapid-turn attractor' does not require any particular background geometry, and explains how several recently studied two-field inflation models are related to each other.