The reconstruction of tachyon inflationary potentials

We derive a lower bound on the field excursion for the tachyon inflation, which is determined by the amplitude of the scalar perturbation and the number of e-folds before the end of inflation. Using the relation between the observables like n_s and r with the slow-roll parameters, we reconstruct three classes of tachyon potentials. The model parameters are determined from the observations before the potentials are reconstructed, and the observations prefer the concave potential. We also discuss the constraints from the reheating phase preceding the radiation domination for the three classes of models by assuming the equation of state parameter w_re during reheating is a constant. Depending on the model parameters and the value of w_re, the constraints on N_re and T_re are different. As n_s increases, the allowed reheating epoch becomes longer for w_re=-1/3, 0 and 1/6 while the allowed reheating epoch becomes shorter for w_re=2/3.