Recently it has been shown that in compactifications of heterotic string theory, all moduli can be stabilized perturbatively in the following case: if the compactification has intrinsic torsion, allowing for a superpotential linear in the Kahler moduli; and furthermore if anomalous U(1) symmetries are present such that they produce a particular D-term structure known as "aligned D-terms". In this talk, the speaker will discuss some approaches to realizing inflation in such a context, beginning with some illustrative toy examples before exploring various scenarios, such as aligned natural inflation and axion monodromy inflation. He will also compare the benefits and drawbacks of each approach, and review some general issues that need to be resolved.
