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.
Highlights
Inflation [1,2,3] has been viewed as one of the most successful theory in modern cosmology
We will focus on an interesting type of bounce inflation scenario, driven by the f (T ) modified gravity theory
Teleparallel Equivalent General Relativity (TEGR), as a torsion theory, is equivalent to General Relativity, f (T ) is no longer equivalent to the extension to GR, namely f (R) theory, but act as a totally new theory, with many interesting properties not shared by GR or f (R) theories
Summary
We first consider the tensor perturbations produced from action (8). Note that since the tensor perturbations decouples with the scalar counterpart at. The second order action is: δ2T S. From this action one can see that it is very much alike that of GR, except for the coefficients in front of both kinetic term and spatial derivative terms are fT 0, with the sound speed squared being unity. From stability of tensor perturbation: fT > 0 Note that this condition is the generalization of the condition ∂L/∂ R > 0 in scalar-tensor gravity, and f R > 0 in f (R) gravity to f (T ) gravity, the breaking of which leads to the formation of generic curvature singularity at a spatial hypersurface where this derivative becomes zero [48].1. (31) 1 We thank the anonymous referee for pointing this to us
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