Cosmological Perturbation in f(T) Gravity Revisited

TL;DR

This paper investigates cosmological perturbations in f(T) gravity with a scalar field, revealing no extra propagating degrees of freedom at second order and showing perturbations resemble those in general relativity with a modified gravitational coupling.

Contribution

It provides a detailed second-order perturbation analysis in f(T) gravity, including pseudoscalar and pseudovector modes, and clarifies the absence of additional degrees of freedom at this order.

Findings

No propagating degrees of freedom in scalar, pseudoscalar, vector, pseudovector modes.

Scalar and tensor perturbations mirror those in general relativity with a modified coupling.

f(T) gravity's nonlinear nature prevents conclusive linear stability analysis.

Abstract

We perform detailed investigation of cosmological perturbations in f(T) theory of gravity coupled with scalar field. Our work emphasizes on the way to gauge fix the theory and we examine all possible modes of perturbations up to second order. The analysis includes pseudoscalar and pseudovector modes in addition to the usual scalar, vector, and tensor modes. We find no gravitational propagating degree of freedom in the scalar, pseudoscalar, vector, as well as pseudovector modes. In addition, we find that the scalar and tensor perturbations have exactly the same form as their counterparts in usual general relativity with scalar field, except that the factor of reduced Planck mass squared $M_{\text{pl}}^2 \equiv 1/(8\pi G)$ that occurs in the latter has now been replaced by an effective time-dependentgravitational coupling $-2 (df/dT)|_{T=T_0}$, with $T_0$ being the background torsion scalar. The absence of extra degrees of freedom of f(T) gravity at second order linear perturbation indicates that f(T) gravity is highly nonlinear. Consequently one cannot conclusively analyze stability of the theory without performing nonlinear analysis that can reveal the propagation of the extra degrees of freedom.