The role of primordial symmetries in the determination of the non-gaussian properties of our Universe

Abstract

In this thesis, we show how future cosmological observations can provide us access to unveil the mechanism responsible for the origin of the structure in our universe. The primordial perturbations sourced by quantum vacuum fluctuations in the early universe, are stretched to cosmological scales during inflation, thus generating the seeds for the structure formation. Observations of the temperature anisotropies in the cosmic microwave background have revealed that the primordial spectrum of perturbations is adiabatic and almost scale-invariant. These non-trivial features are remarkably in agreement with the predictions of cosmic inflation. Furthermore, observations are consistent with a highly Gaussian distribution of primordial perturbations. On the other hand, a generic prediction of cosmic inflation is the production of primordial gravitational waves that can later be detected as polarization in the cosmic microwave background. Nevertheless, deviations from Gaussianity known as non-Gaussianities nor primordial gravitational waves have been detected yet. Both observables carry exquisite information about the mechanism that nature chose to produce the structures that we see today in the universe. Throughout this work, we face problems related to the aforementioned observables. We study the production of primordial local non-Gaussianity in canonical single-field models of inflation, and we delve into the implications of detecting sizable primordial gravitational waves on the attempts of incorporating cosmic inflation in a quantum theory of gravitation. In particular, by using a new class of symmetries, we derive a novel soft-theorem for the 3-point function that generalizes the well-known Maldacena s consistency relation, being valid for attractor and non-attractor models of inflation. This relation allows one to derive the violation of the consistency relation found in ultra slow-roll, where the curvature perturbations grow on super-horizon scales. Then, we study the observability of primordial local non-Gaussianity, where we show that, independently of whether inflation is attractor or non-attractor, the size of the observable primordial local non-Gaussianity vanishes. Also, we show how to overcome the well-known swampland distance conjecture by taking advantage that it only applies to geodesic distances. We build a multi-field model of inflation, characterized for having a non-geodesic inflationary trajectory, that allows us to establish a relation between geodesic and non-geodesic field displacements. Together with the Lyth bound, such relation allows us to explain a signal of primordial gravitational waves, with large values of the tensor-to-scalar ratio r, without invoking super-Planckian field displacements. We also show how to constrain the parameter space of multi-field models by extending the distance conjecture to the theory of perturbations and combining it with non-Gaussianity bounds. Our results allow claiming that a detection of local primordial non-Gaussianity would rule out single-field canonical models of inflation and that detection of sizable primordial gravitational waves would not necessarily imply super-Planckian inflaton field displacements, thus allowing inflation to be incorporated into a theory of quantum gravity.