Abstract
We address the issue of how many -folds we would naturally expect if inflation occurred at an energy scale of order . We use the canonical measure on trajectories in classical phase space, specialized to the case of flat universes with a single scalar field. While there is no exact analytic expression for the measure, we are able to derive conditions that determine its behavior. For a quadratic potential with and cutoff at , we find an expectation value of -folds on the set of Friedmann-Robertson-Walker trajectories. For cosine inflation with , we find that the expected total number of -folds is 50, which would just satisfy the observed requirements of our own Universe; if is larger, more than 50 -folds are generically attained. We conclude that one should expect a large amount of inflation in large-field models and more limited inflation in small-field (hilltop) scenarios.
- Received 22 May 2014
DOI:https://doi.org/10.1103/PhysRevD.90.063517
© 2014 American Physical Society