Higher-Derivative Supergravity and String Cosmology

Abstract

In this thesis we study theories with $mathcal{N}=1,D=4$ supersymmetry including higher-derivative operators for chiral multiplets. In particular, we initiate a systematic analysis of these higher-derivative operators and corrections to the scalar potential required by supersymmetry. For theories formulated in flat superspace the full scalar potential can be derived from a generalized K"ahler potential where the additional corrections arise from higher powers of the chiral auxiliary field. Consequently, the equations of motion for the auxiliary field admit several solutions. However, we demonstrate that in the context of effective field theories there exists only a single solution which is compatible with the principles of effective field theory. For supergravity we develop new tools that allow us to compute the component actions, but also simplify the determination of the linearized on-shell theory. We then classify the leading order and next-to-leading order superspace derivative operators and determine the component forms of a subclass thereof. Equipped with the higher-derivative actions in flat and curved superspace we proceed to investigate the vacuum structure of the theory. In particular, we study the properties of supersymmetric Minkowksi and $AdS_4$ vacua and also comment on non-supersymmetric vacua. In the second part of this thesis we turn to Calabi-Yau orientifold compactifications of type IIB string theory with background fluxes. We derive four-derivative terms for the volume modulus from ten-dimensional $(alpha')^3 mathcal{R}^4$-corrections and match these to a particular higher-derivative operator which we computed in the first part. Thereby, we can indirectly infer new $F^4$-type corrections to the scalar potential. Lastly, we study the relevance of this new correction for moduli stabilization and inflation. In particular, we demonstrate the possibility of stabilizing all K"ahler moduli model-independently just by $(alpha')^3$-corrections. Finally, we comment on realizations of plateau-type inflationary models via the new $F^4$-correction in the context of the Large Volume Scenario with K3-fibered compactification geometries.