*A dynamical mechanism for neutralizing the cosmological constant.*[Laurea magistrale], Università di Bologna, Corso di Studio in Physics [LM-DM270], Documento ad accesso riservato.

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## Abstract

The cosmological constant problem is a profound challenge in theoretical physics, reflecting the substantial discrepancy between experimental observations and Quantum Field Theory predictions. Various theoretical attempts to address this issue fall into two categories: Fixed-Λ and Adjustable-Λ theories, respectively those in which vacuum energy is more-or-less uniquely determined by the underlying physics, and those in which Λ is not uniquely determined but is adjustable with some mechanism. This work focuses on a notable Adjustable-Λ theory proposed by Brown and Teitelboim (BT). Their model introduces a non-propagating four-form field coupled with a two-dimensional membrane. The BT framework is crucial as it involves charged two-dimensional fundamental objects, objects which are natural in String theory, offering a potential effective field theory emerging from the String theory framework. The BT model is unstable due to membrane nucleation processes from vacuum, representing a non-perturbative quantum effect. These decays are characterized as tunneling processes, described by instanton solutions. Despite its conceptual elegance, the BT model is problematic. Achieving a neutralized Λef f ∼ Λexp necessitates working with extremely small membrane charges, leading to the so-called gap problem. As a result, large-jump transitions are kinematically prohibited, requiring subsequent small-jumps decays to gradually approach a nearly Minkowski vacuum. This implies that, before the final transition, the Universe resides in an exponentially expanding de Sitter era, leading to the dilution of both matter and radiation, thus giving rise to the so-called empty Universe problem. To address these issues, the Bousso-Polchinski (BP) model introduces multiple membranes with incommensurate charges, each coupled with a distinct four-form field. This resolves the gap problem, enabling large single-jump transitions and avoiding the empty Universe problem. However, the price to pay, to select the current vacuum on probabilistic grounds, achieving sufficiently stable daughter nearly Minkowski Universes, is the violation of the weak gravity conjecture. In the final chapter, the BT mechanism is extended to a model with N distinct membranes with incommensurate charges coupled with a single 3-form field. This extension offers a viable solution to both the gap problem and the empty Universe problem, as for the BP model. Moreover, the requirement for nearly Minkowski vacua to be long-lived does not necessarily contradict the weak gravity conjecture. Considering the possible embedding of this model in higher-dimensional theories, like string theory, enables us to apply a generalized Dirac quantization condition. As a result the charges become quantized with commensurate ratio. This fact reveals some analogies with the quantized BT model. While inheriting gap problem, the dynamics of this model, driven by potentially large charges, avoids empty Universe problem.