Tachyon inflation in the Large-$N$ formalism

We study tachyon inflation within the large-$N$ formalism, which takes a prescription for the small Hubble flow slow--roll parameter $epsilon_1$ as a function of the large number of $e$-folds $N$. This leads to a classification of models through their behaviour at large $N$. In addition to the perturbative $N$ class, we introduce the polynomial and exponential classes for the $epsilon_1$ parameter. With this formalism we reconstruct a large number of potentials used previously in the literature for Tachyon Inflation. We also obtain new families of potentials form the polynomial class. We characterize the realizations of Tachyon Inflation by computing the usual cosmological observables up to second order in the Hubble flow slow--roll parameters. This allows us to look at observable differences between tachyon and canonical single field inflation. The analysis of observables in light of the Planck 2015 data shows the viability of some of these models, mostly for certain realization of the polynomial and exponential classes.