Natural inflation and moduli stabilization in heterotic orbifolds
  We study moduli stabilization in combination with inflation in heterotic
orbifold compactifications in the light of a large Hubble scale and the favored
tensor-to-scalar ratio $r \approx 0.05$. To account for a trans-Planckian field
range we implement aligned natural inflation. Although there is only one
universal axion in heterotic constructions, further axions from the geometric
moduli can be used for alignment and inflation. We argue that such an alignment
is rather generic on orbifolds, since all non-perturbative terms are determined
by modular weights of the involved fields and the Dedekind $\eta$ function. We
present two setups inspired by the mini-landscape models of the $\mathbb
Z_{6-\text{II}}$ orbifold which realize aligned inflation and stabilization of
the relevant moduli. One has a supersymmetric vacuum after inflation, while the
other includes a gaugino condensate which breaks supersymmetry at a high scale.
