Second-order reconstruction of the inflationary potential

On the Constant-Roll Tachyon Inflation with Large and Small ηH

We study the constant-roll tachyon inflation with large and small η. In previous studies, only the constant-roll tachyon inflation with small η is consistent with the observations. We find that the duality between the constant-roll tachyon inflation with large and small η may exist. The apparent duality suggests that the constant-roll tachyon inflationary model with large η may also be consistent with the observations. By fitting the spectral tilde ns and tensor to scalar ratio r, which is a measure of primordial gravitational waves with the observations, we get small and large η in this range −0.01629≤ηH≤−0.00079 and 3.00081≤ηH≤3.01621 at the 2σ C.L for N=60 efolds.