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Description
The construction of viable particle physics models of inflation is challenging due to the $\eta$-problem, which states that the large vacuum energy required for inflation generically induces a too large mass for the inflaton which spoils inflation. We discuss strategies to overcome this problem in the context of supergravity. We introduce a novel class of inflation models called 'tribrid inflation', which is taylor-made for solving the $\eta$-problem by symmetry, for instance by a Heisenberg symmetry or shift symmetry in the Kahler potential. Inflation can be realised in the matter sector of the theory, with close connection to particle physics. We also comment on how a generalization of this model class may be suitable for realising inflation in heterotic string theory, where the Heisenberg symmetry is a property of the tree-level Kahler potential of untwisted matter fields.