Conference

We use the power-counting formalism of effective field  theory to study the size of loop corrections in theories of slow-roll inflation, with the aim of more precisely identifying the limits of validity of the usual classical inflationary treatments. Although most slow-roll models lie within the semiclassical domain, we find the consistency of the Higgs-Inflaton scenario to be more delicate due to the proximity between the Hubble scale during inflation and the upper bound allowed by unitarity on the new-physics scale.

Single field inflation with derivative interactions provides a class of scenarios with interesting theoretical and observational properties. I will discuss properties of correlation functions in generic single field models and the implications of those relationships for inflationary observables, as well as for eternal inflation

We investigate the feasibility of explosive particle production via parametric resonance or tachyonic preheating in multi-field inflationary models by means of lattice simulations. We observe a strong suppression of resonances in the presence of four-leg interactions between the inflaton fields and a scalar matter field, leading to insufficient preheating when more than two inflatons couple to the same matter field. This suppression is caused by a dephasing of the inflatons that increases the effective mass of the matter field. Including three-leg interactions leads to tachyonic preheating, which is not suppressed by an increase in the number of fields. If four-leg interactions are sub-dominant, we observe a slight enhancement of tachyonic preheating. Thus, in order for preheating after multi-field inflation to be efficient, one needs to ensure that three-leg interactions are present. If no tachyonic contributions exist, we expect the old theory of reheating to be applicable.

Modifications of the initial-state of the inflaton field can induce a departure from Gaussianity and leave a testable imprint on the higher order correlations of the CMB and large scale structures in the Universe. I will discuss general vacuum state modifications in the case of a canonical single-field action, after adding a dimension 8 higher order derivative term, and DBI models of inflation. Observed bounds on local and equilateral non-Gaussianities, even though they correspond to template shapes that are far from optimal, can lead to constraints that are already competing to those derived from the power spectrum alone, due to enhancement effects. We emphasize that the construction and application of especially adapted templates could lead to significant improvements in the CMB bispectrum constraints on modified initial states.

"A Hamiltonian action of a Lie group on a symplectic manifold $(M,\omega)$ gives rise to a gauge theoretic deformation of the Cauchy-Riemann equations, called the symplectic vortex equations. Counting solutions of these equations over the complex plane leads to a quantum version of the Kirwan map. In joint work with Christopher Woodward, we interpret this map as a weak morphism of cohomological field theories."

This talk will discuss, illustrated by a toy example, how to construct "higher-algebraic" quantum field theories using groupoids. In particular, the groupoids describe configuration spaces of connections, together with their gauge symmetries, on spacetime, space, and boundaries of regions in space. The talk will describe a higher-algebraic "sum over histories", and how this construction is related to usual QFT's, and particularly the relation to the case of the Chern-Simons theory.