| Summary: | The cosmological constant problem is one of the biggest theoretical hurdles of the modern age. It comes out of two great theories in physics: General Relativity (GR) and Quantum Field Theory (QFT). QFT predicts the existence of vacuum energy and GR predicts that it will gravitate like a cosmological constant, Λ_{vac}. Through observations we find that the Universe is undergoing an accelerated expansion which can be sourced by a constant term, Λ_{obs}, whose value is set by observations. Therefore it would be tempting to compare Λobs with Λ_{vac}, but through this we find that the predicted value of the vacuum energy is far, far
greater than that of observation. In fact, at a lower estimate it represents a fine-tuning of∼ 10^{36} orders of magnitude. However, this is not the full extent of the problem. Even if we accept a fine-tuning in Λ_{vac}, its value is unstable to higher order perturbations, leading to
repeated fine-tunings and re-tunings. This is known as radiative instability of the vacuum, and it is the true source of the cosmological constant problem.
This thesis chooses to focus on self-tuning as a method for alleviating this problem. Self-tuning refers to the practice of modifying GR by adding extra fields which act to force Λ_{vac} ∼ Λ_{obs}, removing the need for fine-tuning. In this thesis we review a variety of self-tuning mechanisms
to allow the reader to get a basic idea of the different approaches adopted.
The bulk of the thesis focuses on self-tuning with a massive scalar-tensor theory on an Anti-de Sitter (AdS) background, the idea for which originated by examining a range of allowed modifications to GR and placing some self-tuning conditions upon them. Here, we construct an explicit model and analyse the resultant field equations to check whether it can or cannot self-tune. We then perform a numerical analysis on the resultant cosmological equations to understand the dynamics of the system; focusing specifically on whether our model can self-tune regardless of initial conditions. Finally, we conduct a rudimentary analysis on the stability of this model to further understand whether we can consistently self-tune without fine-tuning.
Overall this work serves as an initial point of exploration in self-tuning on an AdS background. As we later discuss, there are many exciting future directions this model can take beyond this thesis.
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