Inflationary e-folding and the implications for gravitational-wave detection

We demonstrate that the approximation for the number of inflationary e-folds commonly used in the literature can lead to highly inaccurate predictions for the amplitude of primordial gravitational waves. We show that such an approximation can lead to perfectly viable inflation models being falsely ruled out by direct or indirect gravitational-wave measurements. We illustrate this point using a new class of inflation models which include the power-law potential as the simplest limit. These models are simple to construct without using the slow-roll approximation, and are consistent with constraints from Planck. Crucially, these models may suffer from an order-of-magnitude error in the prediction for the gravitational-wave amplitude if the common definition of e-folding is used. Our findings have strong implications for the classes of inflation models that can be ruled out by future space-based laser interferometers such as BBO and DECIGO.