I will describe in details the construction of finite and
super-renormalizable theories, which have applications for gravity and cosmology. They will be related to the R + R^2, Starobinsky
inflationary model, which represents a fully consistent example of a one-parameter inflationary scenario. This model has a graceful exit from inflation and provides a mechanism for subsequent creation and final thermalization of the standard matter. Moreover, it produces a very good fit of the observed spectrum of primordial perturbations. In this talk I show explicitly that the R^2 inflationary spacetime is an exact solution of a range of weakly non-local (quasi-polynomial)gravitational theories, which provide an ultraviolet completion of the Stelle quadratic theory in quantum field theory framework. These theories are ghost-free, super-renormalizable or finite at quantum level, and perturbatively unitary. Their spectrum consists of the graviton and the scalaron that is responsible for driving the inflation. Further, I will give a special account to the cosmological
implications of this theory by considering perturbations during
inflation. The highlight of the non-local model is the prediction of a modified, in comparison to a local R^2 model, value for the ratio of tensor and scalar power spectra r, depending on only few parameters of the theory. The relevant parameters are under control to be
successfully confronted with existing observational data.

Facultad de Ciencias

Seminario de Física Teórica
Universidad de Zaragoza