Cosmological perturbations in f(T) gravity (1008.1250v2)

Abstract: We investigate the cosmological perturbations in f(T) gravity. Examining the pure gravitational perturbations in the scalar sector using a diagonal vierbien, we extract the corresponding dispersion relation, which provides a constraint on the f(T) ansatzes that lead to a theory free of instabilities. Additionally, upon inclusion of the matter perturbations, we derive the fully perturbed equations of motion, and we study the growth of matter overdensities. We show that f(T) gravity with f(T) constant coincides with General Relativity, both at the background as well as at the first-order perturbation level. Applying our formalism to the power-law model we find that on large subhorizon scales (O(100 Mpc) or larger), the evolution of matter overdensity will differ from LCDM cosmology. Finally, examining the linear perturbations of the vector and tensor sectors, we find that (for the standard choice of vierbein) f(T) gravity is free of massive gravitons.

• The paper presents a detailed linear perturbative analysis of scalar, vector, and tensor modes to establish stability criteria for viable f(T) models.
• It derives constraints on the f''(T) parameter, ensuring consistency with cosmic acceleration and reducing to general relativity when f(T) is constant.
• Numerical results reveal deviations from ΛCDM predictions in matter perturbation growth, offering actionable insights for observational cosmology.

Cosmological Perturbations in $f(T)$ Gravity: A Technical Overview

The paper "Cosmological perturbations in $f(T)$ gravity" explores an area of theoretical cosmology that extends the framework of teleparallel gravity, known for its unique utilization of torsion rather than curvature in describing gravitational phenomena. This paper aligns with a broader effort to address the accelerated expansion of the universe through modifications of general relativity (GR) and seeks to provide a perturbative understanding of cosmology in $f(T)$ gravity.

In the framework of $f(T)$ gravity, the teleparallel equivalent of general relativity (TEGR) is generalized from the torsion scalar $T$ to a function $T+f(T)$. This is similar to $f(R)$ gravity, where the Ricci scalar $R$ in the Einstein-Hilbert action is generalized to a function $f(R)$. The advantage of $f(T)$ theories over $f(R)$ is their preservation of second-order field equations, avoiding higher-order derivatives that often lead to pathologies. The authors aim to thoroughly inspect the stability and perturbation dynamics in $f(T)$ models, which is crucial for both theoretical consistency and observational compatibility.

Perturbative Analysis

The paper comprehensively analyzes the scalar, vector, and tensor perturbations at the linear level in $f(T)$ cosmology, with the perturbations explored in the synchronous and Newtonian gauges for various sectors. The key focus of the scalar perturbation analysis is to determine the stability of potential $f(T)$ models. Stability is scrutinized through the derived dispersion relation, revealing constraints on $f(T)$ models to prevent instability. Notably, $f(T)$ models reduce to general relativity when $f(T)$ is constant, maintaining expected cosmic dynamics at both background and perturbative levels.

The perturbed equations are meticulously derived, revealing that $f''(T) \approx 0$ when anisotropic stress is neglected. This constraint aligns well with observational compatibility, ensuring consistent dynamics with observed cosmic acceleration phenomena without additional exotic contributions to gravitational dynamics.

Practical Implications and Observational Signatures

The paper extends its perturbative analysis through numerical computations, considering the growth of matter perturbations for specific $f(T)$ models, like the power-law model. This analysis shows notable deviations from the $\Lambda$CDM model on large subhorizon scales, emphasizing observable effects within cosmic structure formation that can be tested against data from gravitational lensing, galaxy clustering, and cosmic microwave background observations. This perspective prioritizes selecting viable $f(T)$ models compatible with empirical cosmological data.

Vector and Tensor Perturbations

Expanding the analysis, vector and tensor perturbations reinforce findings of no massive graviton emergence, aligning with GR's prediction of gravitational waves and ensuring $f(T)$ gravity does not introduce unwarranted modifications at linear order. These results underscore the mathematical consistency and physical plausibility of $f(T)$ theories within the perturbative domain.

Conclusion & Future Prospects

This paper of cosmological perturbations in $f(T)$ gravity offers significant insights into alternative gravity's role in the universe's accelerated expansion. By affirmatively connecting with GR in relevant limits, $f(T)$ gravity presents a theoretically coherent and practically applicable modification to the story of cosmic acceleration. Future research should explore higher-order perturbations and non-diagonal vierbein configurations to fully map the feasibility and predictability of $f(T)$ gravity. This paper sets the groundwork for such explorations and bridges the gap between theoretical predictions and empirical scrutiny within modified teleparallel gravity theories.