Vacuum energy and cosmological inflation

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2022, Tutor: Joan Solà PeracaulaWe study the cosmic evolution from the perspective of the Running Vacuum Models, in which the vacuum energy density is dynamic throughout the cosmic history. In this context, we find that there is an initial period of inflation, in which the vacuum decays into radiation and there is a huge entropy production. In contrast to the standard inflaton-based mechanism of inflation, there is a smooth transition between this period and the standard ΛCDM radiation epoch. We also test the model against the Generalised Second Law, finding it is fulfilled in the current universe but not in the early stages. This is a welcome feature, however, as it may provide a possible solution to both the entropy and horizon problems, in a context where the eventual thermodynamic equilibrium of the universe is not jeopardise

Stochastic inflation in the Constant Roll regime

Màster Oficial d'Astrofísica, Física de Partícules i Cosmologia, Facultat de Física, Universitat de Barcelona. Curs: 2022-2023. Tutor: Cristiano GermaniWe investigate the inhomogeneities generated during the inflationary epoch from the point of view of the stochastic formalism, which attempts to transform a problem of quantum fluctuations into a statistical one. The formalism, that we derive in the text, is based on the use of the Arnowitt-Deser-Misner (ADM) equations, which are convenient to describe inhomogeneities in the context of inflation, as well as gradient expansion, which works at zeroth order in spatial gradients but at all orders in the amplitudes of the fluctuations, and is therefore intended to capture non-perturbative effects. Finally, the perturbations are split into long- and short-wavelength modes, where the latter act as a stochastic noise for the former when crossing a certain scale. We demonstrate that the use of certain approximations in the derivation of this formalism, which are intended to make the system of stochastic differential equations (SDEs) Markovian and described with white noises, causes the method to become restricted to the reproduction of Linear Perturbation Theory (LPT). This framework, nonetheless, is still useful since it can be used as a test for the validity of the linear approximation, signalling the coming into play of non-perturbative effects. Specifically, we solve the system of SDEs numerically for the Constant Roll (CR) inflationary scenario, and show that this regime is in accordance with LPT