On Effective Field Theory (and a bit of Differential Geometry) in Cosmology

Observational Cosmology has made tremendous progress in the last couple of decades, allowing us to explore the beginning of the universe with unprecedented precision. Such exquisite measurements have now made us sensitive to non-linear corrections to the evolution of the cosmological density perturbations. In order to continue to address the mysteries of our universe with similar success, we have to be able to control these non-linearities. In this context, the effective field theory paradigm represents the ideal setup to explore and systematically study the signatures that come from interactions, and to directly map what we are learning from data into theory. I will describe two recent applications of this paradigm to Cosmology: the Effective Field Theory of Inflation and the Effective Field Theory of Cosmological Large-Scale Structure. The first example represents the general parametrization of the fluctuations around an inflationary background, the earliest probed phase of our universe, and it allows us to study its most general signatures. I will also explain how recent developments in differential geometry and topology, as well as numerical relativity, allow us to shed light on the old problem of how inflation starts from an inhomogenous and anisotropic universe. The second effective field theory example is in the context of the cosmological clustering of matter. In our universe matter perturbations are large on short distances and small on long distances: strongly coupled in the UV and weakly coupled in the IR. We formulate an effective description based on an IR fluid-like system that allows us to develop a perturbative expansion to describe weak matter clustering. I will discuss the formalism, the main results and successes so far, and how this research program is crucial for next generation cosmological experiments.​