Axion inflation and gravity waves in string theory

The majority of models of inflation in string theory predict an absence of measurable gravitational waves, r<<10-3. The most promising proposals for making string theoretic models that yield measurable tensor fluctuations involve axion fields with slightly broken shift symmetry. We consider such models in detail, with a particular focus on the N-flation scenario and on axion valley/natural inflation models. We find that in Calabi-Yau threefold compactifications with logarithmic Kaehler potentials K it appears to be difficult to meet the conditions required for axion inflation in the supergravity regime. However, in supergravities with an (approximately) quadratic shift-symmetric K, axion inflation may be viable. Such Kaehler potentials do arise in some string models, in specific limits of the moduli space. We describe the most promising classes of models; more detailed study will be required before one can conclude that working models exist