Slow-roll single-field inflation constitutes the main paradigm of the
Early Universe. But this model suffers from a number of conceptual issues
that naturally lead to the consideration of multifield models of
inflation with curved field space, that have recently been under scrutiny
as realistic realizations of high-energy physics in the Early Universe.
I will show that the non-trivial internal geometry reshuffles
observational predictions from inflation, at the level of the background
(geometrical destabilisation of inflation), of linear
fluctuations (spectral index, tensor-to-scalar ratio) and can lead to
exotic type of non-Gaussianities (bispectrum, higher-order correlation
functions).
This last fact in particular motivates the thorough analysis of
non-Gaussianities in this large class of models. For that, we revisit
Maldacena's calculation of the bispectrum in a 2-field context. As a
byproduct, we also derive the effective single-field theory including
interactions, when the fluctuation perpendicular to the trajectory
(isocurvature mode) can be integrated out, and explicitly show the effect
of the curvature of the field space on the bispectrum.
Time permitting I will also mention other projects that might interest the
audience, such as multifield stochastic inflation and
multifield/multi-fluid reheating after inflation.