We address the issue of how many e -folds we would naturally expect if inflation occurred at an energy scale of order 10 ^ { 16 } GeV .
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 V ( \phi ) = m ^ { 2 } \phi ^ { 2 } / 2 with m = 2 \times 10 ^ { 13 } GeV and cutoff at M _ { { Pl } } = 2.4 \times 10 ^ { 18 } GeV , we find an expectation value of 2 \times 10 ^ { 10 } e -folds on the set of Friedmann–Robertson–Walker trajectories .
For cosine inflation V ( \phi ) = \Lambda ^ { 4 } [ 1 - \cos ( \phi / f ) ] with f = 1.5 \times 10 ^ { 19 } GeV , we find that the expected total number of e -folds is 50 , which would just satisfy the observed requirements of our own Universe ; if f is larger , more than 50 e -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 .