Weakly broken Galileon symmetry in cosmology

One of the main challenges of modern cosmology consists of confirming, or even disproving, inflation. In the simplest models, a single scalar field drives the acceleration of the early Universe thanks to a flat potential or derivative self-interactions. In the latter case, however, in order to avoid possible instabilities, only single derivatives acting on the field are usually considered in the Lagrangians. In the present work, using an effective field theory point of view, we explore theories of single-field inflation where higher derivative operators become relevant, affecting in a novel way the dynamics and therefore the observations. For instance, concerning the scalar spectrum, they allow for measurable equilateral non-Gaussianity, whose amplitude can differ signifi- cantly from the predictions of other existing models. Moreover, we show that the stability and the consistency of such theories are ensured by an approximate Galileon symmetry. Indeed, being generi- cally possible to build an invariant theory under Galileon transformations in flat space-time, it is instead well known that such a symmetry is un- avoidably broken by gravity. In principle, this might ruin the nice and in- teresting properties of the Galileons in flat backgrounds, such as the non- renormalization theorem. However, we find that this does not happen if the Galileon invariance is broken only weakly, in a well defined sense, by a suit- able coupling to gravity, providing therefore an extension of the quantum non-renormalization properties in curved space-times. Hence, besides discussing the phenomenological consequences and the observational predictions for inflation, we apply such Galileon theories to the context of the late-time acceleration of the Universe. In the last part, in order to probe non-standard primordial scenarios, they are also employed in a cosmology where the Big Bang singularity is smoothed down and the Universe emerges from a Minkowski space-time, in a well defined extension at all times of the Galilean Genesis scenario.