The conformal limit of inflation

Abstract

In this thesis, we study the origin of the primordial fluctuations in the Cosmic Microwave Background by assuming that they originated from quantum fluctuations in the early universe, which stretched to cosmic size during a period of inflationary expansion. We shall consider the case of slow-roll inflation, a single field rolling down a flat potential. The main predictions of such models are characterized by two slow-roll parameters and η. Recent measurements of the temperature and the polarization fluctuations in the CMB suggest that these parameters satisfy . η/3. This inequality will become much stronger in the absence of the detection of primordial B-modes. Therefore, the natural question to ask is what characterizes this η limit, or more generically, what characterizes the → 0 limit. We will refer to this limit as the decoupling limit. As we will see, a new hierarchy in the way of organizing the slow-roll expansion will arise. In addition, the isometries of the background will reduce to that of a de Sitter space-time. When the physical wavelength of the perturbations becomes super Hubble size, the de Sitter-isometries acting on the inflaton perturbation correlation functions will reduce to those of a Euclidean conformal field theory. In this limit, the inflaton perturbation correlation functions become fully fixed by the conformal symmetries. For this reason, we will refer to this limit as the conformal limit of inflation. Last but not least, in conformal limit, the equilateral non-Gaussianities can be approximated by the spectral tilt of the potential, fNL ∼ αs.