Astrophysics

I will discuss the phenomenologically interesting scenario of matter inflation in supersymmetric hybrid inflation models. The inflaton resides in a gauge non-singlet matter multiplet and the eta-problem is solved by a "Heisenberg" symmetry. This symmetry relates the inflaton with a modulus field and we stabilize this modulus via corrections to the Kähler potential. The Heisenberg symmetry arises naturally for the untwisted matter fields in heterotic orbifolds. A way to embed matter inflation into heterotic orbifold compactifications is suggested and moduli stabilization in the extended setup is discussed. I argue that the corrections from moduli stabilization may not spoil the flatness of the inflaton potential at large radius.