Quantum gravity with higher curvature interactions and the Standard Model

The quest for a fundamental quantum theory of gravity compatible with the Standard Model of particle physics continues to offer challenges. The asymptotic safety conjecture offers a promising direction, stipulating the non-perturbative renormalisability of gravity through an interacting ultraviolet fixed point. Strong circumstantial evidence for asymp- totic safety of gravity has accumulated over the past decades with the help of functional renormalisation. However, matter quantum fluctuations may destabilise a gravitational fixed point. Since the observable universe contains matter, it becomes important to understand whether an asymptotically safe version of gravity is compatible with matter. This thesis investigates the impact of quantised non-selfinteracting matter fields and the prospect for a combined fixed point for gravity with matter. The focus is on Standard Model matter, though asymptotic limits such as matter domination (N → ∞), where N denotes the number of matter fields, or the absence of matter (N → 0) are also investigated. A novelty of this study is introducing higher order Ricci scalar, Ricci tensor and Riemann tensor interactions beyond the Einstein-Hilbert action to ensure stability and convergence of findings. A bootstrap search strategy is performed to high polynomial order in curvature, along- side functional renormalisation and high performance computing tools to identify ultraviolet fixed points. Additionally, heat kernel and spectral sum techniques are compared, providing improved approximations for the latter. Results include new gravitational fixed points with matter and higher curvature invariants, tests of stability and convergence, universal scaling dimensions and eigenperturbations. Notably, matter influences the types of higher order interactions required for asymptotic safety. Moreover, Standard Model mat- ter may increase the dimensionality of the UV critical surface. Finally, a new scaling limit is found in the large-N regime, characterised by an enhancement of fourth√-order interactions. Results are established both numerically and analytically in a 1/√N expansion. The relevance of these findings for the asymptotic safety conjecture is discussed.