Global Embedding of Fibre Inflation Models
  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.
