# The reconstruction of tachyon inflationary potentials

## TL;DR

This paper reconstructs tachyon inflationary potentials based on observational data, deriving bounds on field excursions, analyzing three potential classes, and exploring reheating constraints with varying equations of state.

## Contribution

It introduces a method to reconstruct tachyon potentials from observational parameters and examines reheating constraints for different model scenarios.

## Key findings

- Observations favor concave tachyon potentials.
- Derived lower bounds on field excursions in tachyon inflation.
- Reheating constraints vary with the equation of state parameter.

## Abstract

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 $w_{re}=2/3$.