Scale Invariance in the Early Universe

Scale invariance provides a well-motivated guiding principle for the physics of the early Universe. It emerges as an approximate symmetry in several high-energy regimes and is exactly realized at the fixed points of the renormalization-group flow, where no intrinsic mass or length scale is present. Within this perspective, scale-invariant theories offer a natural setting in which physical mass scales arise dynamically through symmetry breaking. Motivated by these considerations, this thesis investigates the implications of scale-invariant gravity in the context of inflationary cosmology. We study a classically scale-invariant model based on an $R^2$ modification of the gravitational action coupled to a real scalar field and analyze its inflationary dynamics. We examine the evolution of the background and linear cosmological perturbations, clarifying the role of scale symmetry and the corresponding Noether current. We derive constraints on the model parameters and connect the resulting inflationary dynamics to current observational data. Finally, we explore the implications of scale-invariant inflation for primordial magnetogenesis, investigating a mechanism for breaking electromagnetic conformal invariance during inflation and its phenomenological consequences.