Leonardo Trombetta (SNS & INFN, Pisa)
Infrared effects in de Sitter spacetime: Nonperturbative treatments
The study of interacting quantum fields in de Sitter spacetime is of interest for a variety of reasons. In inflationary models, interactions could lead to non-Gaussianities in the cosmic microwave background. Quantum effects could also contribute to the dark energy, and explain, at least partially, the present acceleration of the Universe.
In this geometry, the exponential expansion of the background greatly amplifies the quantum fluctuations of light (m << H) fields leading to a secular growth of the correlation functions at late times. Moreover, there is also an effective growth of the couplings constants, causing the usual perturbative expansion to eventually break down as well. These issues can be traced to the absence of a de Sitter invariant vacuum state for massless free fields, around which the perturbation theory is built.
I will discuss several nonperturbative approaches that are used to understand this problem, focusing on a massless scalar field theory with self-interactions, where it is possible to perform certain resummations that suggest a dynamical mass generation mechanism is in place. Although this seems to solve (some of) the problems, the agreement among the different methods is still under discussion. Whether these infrared (IR) divergences have physical consequences or not remains an open question.