f(T) gravity mimicking dynamical dark energy. Background and perturbation analysis

Abstract: We investigate f(T) cosmology in both the background, as well as in the perturbation level, and we present the general formalism for reconstructing the equivalent one-parameter family of f(T) models for any given dynamical dark energy scenario. Despite the completely indistinguishable background behavior, the perturbations break this degeneracy and the growth histories of all these models differ from one another. As an application we reconstruct the f(T) equivalent for quintessence, and we show that the deviation of the matter overdensity evolution is strong for small scales and weak for large scales, while it is negligible for large redshifts.

• The paper demonstrates that f(T) gravity models can replicate any dynamical dark energy background by solving a specific differential equation.
• The perturbation analysis uncovers distinct signatures in f(T) models that set them apart from standard quintessence scenarios.
• The findings highlight that growth of structure data provides a crucial test for validating f(T) gravity as an alternative dark energy framework.

Analysis of $f(T)$ Gravity as a Framework for Dark Energy

The paper "$f(T)$ gravity mimicking dynamical dark energy. Background and perturbation analysis" explores the application of $f(T)$ gravity theories, an extension of teleparallel gravity, to model the dynamics of dark energy. The authors, Dent, Dutta, and Saridakis, seek to determine if $f(T)$ gravity can effectively replicate the properties of dynamical dark energy scenarios at a cosmological level, particularly how they can mimic such scenarios both in the background and perturbation level. This paper explores constructing a family of $f(T)$ models that can match any given dynamical dark energy background, while explaining how perturbation analyses can differentiate between standard dark energy models and their $f(T)$ equivalents.

Background and Methodology

The motivation behind investigating $f(T)$ gravity arises from its ability to lift some of the limitations faced by other modified gravity theories, notably $f(R)$ gravity. $f(T)$ gravity is derived from the teleparallel equivalent of General Relativity (TEGR), where the action is constructed using the torsion scalar $T$. The $f(T)$ extension involves generalizing the Lagrangian of teleparallel gravity to a function $T + f(T)$, thereby introducing modifications that might explain cosmic acceleration without invoking a cosmological constant or exotic matter components directly.

The authors construct the equivalent $f(T)$ models for any given dynamical dark energy scenario. They adopt a method where the problem is reduced to solving a differential equation that leads to a family of $f(T)$ solutions parameterized by a constant. The key aspect here is that, while these models reproduce identical background expansion histories as quintessence and other dark energy models, their perturbation behavior diverges due to the intrinsic properties of $f(T)$ theories, thus providing a potentially observable signature.

Results and Discussion

The research analyzes specific potential models of quintessence such as the Pseudo-Nambu-Goldstone-Boson (PNGB), an exponential potential, and a power-law potential, considering their ability to trace observational data. For these models, the paper demonstrates how $f(T)$ gravity can be tuned to replicate the background behavior of quintessence. However, distinct features arise when analyzing perturbations: Quasi-static analysis on sub-horizon scales shows that variations exist among the $f(T)$ models depending on scale and redshift.

The perturbation analysis further reveals that the degeneracy at the background level is lifted when one includes the growth of structure data, offering a means to observationally distinguish between $f(T)$ gravity (and its parameterized versions) and quintessence or other scalar field models. This makes $f(T)$ gravity an appealing candidate for observational tests that target the growth of structure.

Implications and Future Work

The implications of this paper are significant for theoretical and observational cosmology as it opens pathways to testing alternative theories of gravity against dark energy models, leveraging the interplay between background dynamics and perturbation theory. The authors suggest that characteristic differences in growth rates provide essential insights that complement other measurements such as the cosmic microwave background, baryon acoustic oscillations, and type Ia supernovae.

Future work could explore more complex models within the $f(T)$ framework, including the incorporation of other forms of matter and radiation, and possible coupling with other fields. Detailed observational studies and simulations would also be vital in assessing the viability of the $f(T)$ models, particularly in light of new data from upcoming astronomical surveys.

In conclusion, the paper presents $f(T)$ gravity as a compelling alternative for mimicking dynamical dark energy models, with perturbation analyses offering a differentiating tool that could be crucial for future tests of cosmological models. This study reinforces the importance of maintaining a holistic view of cosmic structure formation and evolution when probing the fundamental nature of dark energy.