Natural inflation and moduli stabilization in heterotic orbifolds

We study moduli stabilization in combination with inflation in leterotic orbHold compactifications in the light of a large Hubble scale and the favored tensor-to-scalar ratio r approximate to 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 orbitolds, 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 Z(6-II) orbifold which realize aligned inflation and stabilization of the relevant moduli. One has a supersynametric vacuum after inflation, while the other includes a gaugino condensate which breaks supersymmetry at a high scale.