Global Embedding of Fibre Inflation Models

Abstract: We present concrete embeddings of fibre inflation models in globally consistent type IIB Calabi-Yau orientifolds with closed string moduli stabilisation. After performing a systematic search through the existing list of toric Calabi-Yau manifolds, we find several examples that reproduce the minimal setup to embed fibre inflation models. This involves Calabi-Yau manifolds with $h^{1,1}= 3$ which are K3 fibrations over a $\mathbb{P}^1$ base with an additional shrinkable rigid divisor. We then provide different consistent choices of the underlying brane set-up which generate a non-perturbative superpotential suitable for moduli stabilisation and string loop corrections with the correct form to drive inflation. For each Calabi-Yau orientifold setting, we also compute the effect of higher derivative contributions and study their influence on the inflationary dynamics.