Perturbations of bounce inflation scenario from $f(T)$ modified gravity revisited

TL;DR

This paper revisits the generation of perturbations in bounce inflation models within $f(T)$ gravity, highlighting the challenges and potential solutions for avoiding instabilities in such theories.

Contribution

It provides a detailed analysis of perturbations in $f(T)$ bounce inflation models, including conditions to prevent pathologies and exploring extensions with scalar fields.

Findings

Pure $f(T)$ theory cannot produce bounce inflation without instabilities.

Adding a scalar field helps extend the model but does not fully eliminate pathologies.

Relaxing certain continuity conditions may allow healthier models.

Abstract

In this work, we revisit the perturbations that are generated in the bounce inflation scenario constructed within the framework of $f(T)$ theory. It has been well known that pure $f(T)$ theory cannot give rise to bounce inflation behavior, so aside from the gravity part, we also employ a canonical scalar field for minimal extension. We calculate the perturbations in $f(T)$ theory using the well-established ADM formalism, and find various conditions to avoid their pathologies. We find that it is indeed very difficult to obtain a healthy model without those pathologies, however, one may find a way out if a potential requirement, say, to keep every function continuous, is abandoned.