Stout, John Eldon2018-04-262018-04-262017-08-30Stout_cornellgrad_0058F_10482http://dissertations.umi.com/cornellgrad:10482bibid: 10361396https://hdl.handle.net/1813/56719Our knowledge of the physical world is mediated by relatively simple, effective descriptions of complex processes. By their very nature, these effective theories obscure any phenomena outside their finite range of validity, discarding information crucial to understanding the full, quantum gravitational theory. However, we may gain enormous insight into the full theory by understanding how effective theories with extreme characteristics---for example, those which realize large-field inflation or have disparate hierarchies of scales---can be naturally realized in consistent theories of quantum gravity. The work in this dissertation focuses on understanding the quantum gravitational constraints on these ``extreme'' theories in well-controlled corners of string theory. Axion monodromy provides one mechanism for realizing large-field inflation in quantum gravity. These models spontaneously break an axion's discrete shift symmetry and, assuming that the corrections induced by this breaking remain small throughout the excursion, create a long, quasi-flat direction in field space. This weakly-broken shift symmetry has been used to construct a dynamical solution to the Higgs hierarchy problem, dubbed the ``relaxion.'' We study this relaxion mechanism and show that---without major modifications---it can not be naturally embedded within string theory. In particular, we find corrections to the relaxion potential---due to the ten-dimensional backreaction of monodromy charge---that conflict with naive notions of technical naturalness and render the mechanism ineffective. The super-Planckian field displacements necessary for large-field inflation may also be realized via the collective motion of many aligned axions. However, it is not clear that string theory provides the structures necessary for this to occur. We search for these structures by explicitly constructing the leading order potential for $C_4$ axions and computing the maximum possible field displacement in all compactifications of type IIB string theory on toric Calabi-Yau hypersurfaces with $h^{1,1} \leq 4$ in the Kreuzer-Skarke database. While none of these examples can sustain a super-Planckian displacement---the largest possible is $0.3 M_\lab{pl}$---we find an alignment mechanism responsible for large displacements in random matrix models at large $h^{1,1} \gg 1$, indicating that large-field inflation may be feasible in compactifications with tens or hundreds of axions. These results represent a modest step toward a complete understanding of large hierarchies and naturalness in quantum gravity.en-USAttribution-NonCommercial 4.0 InternationalPhysicsAxionAxion MonodromyLarge Field InflationQuantum GravityString Theorydissertation or thesishttps://doi.org/10.7298/X4M043JS