Quantisatión of cosmological perturbatións in the eddington-born-infeld theory

Abstract

In this thesis we studied the origin of cosmological perturbations in the early Uníverse, which were seeds of temperature anisotropies and structures observed today, such as galaxies, clusters, etc. Initially, we reviewed the well-known theory of inflation in General Relativity, including the motivations, main assumptions, gauge freedoms, quantumtheory and predictions. We showed that inflation predicts a nearly scale-free power spectrum for primordial scalar quantum fluctuations, which grow in time and generate inhomogeneities today. This result is in agreement with observations (see Komatsu et al.(2011)). It also predicts a nearly scale-free power spectrum for tensor perturbations. In addition, we studied this issue in a modified gravity called Eddington-Born-Infeld theory(Bañados and Ferreira (2010)), which introduces significant modifications to General Relativity in regions with high curvature, e.g. during the early Universe. We discussed the motivations, gauge freedoms, quantum theory and predictions. We found a scale-freepower spectrum for scalar and tensor primordial quantum perturbations, although sorne numerical estimations do not fit the experimental values.