| Summary: | In this thesis we investigate scalar and scalar-tensor field theories and their relation to low energy modifications of Einstein’s General Relativity (GR), as well as their mathematical validity and self-consistency. We begin by outlining the cosmological constant problem, and how large quantum corrections lead to unnatural space-time curvatures. Going into depth, we present a rearrangement of GR which emphasises the global structure within the Einstein equations. Preceding in this manner, we examine global modifications of GR which semi-classically act to insulate the highly Ultra-Violet (UV) sensitive loop corrections to the vacuum energy from the curvature of space-time. We explore the consequences of a manifestly local variant of this model, studying the UV sensitivity to place bounds on resulting cosmological profiles, the effect of phase transitions on fine-tuning, and its compatibility with inflation.
Taking a different approach, we examine other local modifications of GR, which introduce new degrees of freedom. We summarise the need for screening mechanisms which are an important feature of any local modification of GR, in order to remain within constraints imposed by observation. Presenting a high energy extension of a massive Galileon theory, we investigate if it exhibits so-called Vainshtein screening; Vainshtein screened theories are commonly incompatible with Wilsonian UV completion. Using this theory as a toy model, we examine what can go wrong when integrating out a heavy field, as well as what kind of role mass term deformations might play in a wider class of theories, and at what scale Vainshtein screening potentially breaks down.
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