Phenomenology analysis of duration inflation for Tachyon field in loop quantum cosmology

TL;DR

This paper analyzes tachyonic inflation in loop quantum cosmology, showing that slow-roll inflation with specific parameters is necessary to achieve sufficient e-folding, emphasizing the importance of the entire inflationary phase for cosmological expansion.

Contribution

It investigates the phenomenology of duration inflation in tachyonic models within LQC, highlighting the role of potentials and initial conditions in achieving enough e-foldings.

Findings

Super inflation is affected by potentials and initial conditions.

Super inflation alone cannot produce enough e-foldings.

Slow-roll inflation is essential for sufficient e-foldings.

Abstract

Assuming that the e-folding number is just determined by the change of the scale factor, the tachyonic inflation theory in LQC has been discussed. Considering the tachyon field with exponential potential and inverse quadratic potential, we find that the evolutionary pictures of super inflation are affected by the potentials and the initial conditions. However it cannot provide enough e-folding number, no matter which condition is chosen. Therefore a slow-rolling inflation is necessary. The e-folding number for slow-rolling inflation depends on the values of the parameter $\alpha$ of the exponential potential and the initial conditions. To get enough e-folding number, $\alpha$ should be small. Based on the slow-rolling inflation happens immediately when the super inflation ends, and the scale factor is continuously growing during the whole inflation stage, we consider an e-folding number provided by the whole inflationary stage, and we find that it is easier to get enough e-folding number when the scale factor increases during all the inflation phase.