Vacuum energy in quantum field theory and cosmology

Resumen

The cosmological constant appearing in Einstein’s equations is a key element of the LambdaCDM standard cosmological model. This term performs, effectively, as pure vacuum energy, and is considered the easiest explanation of the positive acceleration of the current Universe. But despite the successes of the concordance model in explaining a large variety of high precision data, some tensions are also present at the observational level, and there are also some important problems arising on the theoretical side. The most severe one is the so-called “cosmological constant problem”, which is caused by the gigantic discrepancy between the predicted value of the vacuum energy density in Quantum Field Theory and the measured one. This huge difference is considered as one of the most profound (unsolved) problems of theoretical Physics and its solution probably will come hand in hand with a change of paradigm. But at this moment, there is no clear hint pointing to the aforesaid solution. In view of the current status of the problem, those phenomenological studies that are able to shed some light on the nature of the dark energy (DE) component that is dominating the current Universe, are very welcome. In this thesis are presented detailed studies (at the background and perturbations levels) on various dynamical vacuum energy models, which are motivated from the renormalization group equation formalism of Quantum Field Theory in curved spacetime. In these models, the cosmological term is not a rigid constant, it depends explicitly on the Hubble function and its time derivative. Thus, it varies with the cosmic expansion. Upon the study of the capability of these models on fitting the experimental data, we can determine whether this dynamical behavior is favored by observations or not. Is the vacuum energy density (or in more general terms, the dark energy density) dynamical? One of the main conclusions of this dissertation is that we have indeed strong evidences in favor of the variability of the DE with the cosmic time. It has been shown that this variation can also be traced through other (purely phenomenological) dynamical vacuum models, together with different parameterizations of the DE (as the XCDM and CPL), and scalar field models as the Peebles-Ratra one. The statistical confidence level with which these evidences are obtained reaches in some cases the 4 sigma level, something that is unprecedented in the literature.