f(T) teleparallel gravity and cosmology (1511.07586v2)

Abstract: Over the past decades, the role of torsion in gravity has been extensively investigated along the main direction of bringing gravity closer to its gauge formulation and incorporating spin in a geometric description. Here we review various torsional constructions, from teleparallel, to Einstein-Cartan, and metric-affine gauge theories, resulting in extending torsional gravity in the paradigm of f(T) gravity, where f(T) is an arbitrary function of the torsion scalar. Based on this theory, we further review the corresponding cosmological and astrophysical applications. In particular, we study cosmological solutions arising from f(T) gravity, both at the background and perturbation levels, in different eras along the cosmic expansion. The f(T) gravity construction can provide a theoretical interpretation of the late-time universe acceleration, and it can easily accommodate with the regular thermal expanding history including the radiation and cold dark matter dominated phases. Furthermore, if one traces back to very early times, a sufficiently long period of inflation can be achieved and hence can be investigated by cosmic microwave background observations, or alternatively, the Big Bang singularity can be avoided due to the appearance of non-singular bounces. Various observational constraints, especially the bounds coming from the large-scale structure data in the case of f(T) cosmology, as well as the behavior of gravitational waves, are described in detail. Moreover, the spherically symmetric and black hole solutions of the theory are reviewed. Additionally, we discuss various extensions of the f(T) paradigm. Finally, we consider the relation with other modified gravitational theories, such as those based on curvature, like f(R) gravity, trying to enlighten the subject of which formulation might be more suitable for quantization ventures and cosmological applications.

• The paper introduces f(T) gravity as an alternative to GR by using a non-linear function of the torsion scalar to model cosmic acceleration and inflation.
• It details a methodology that yields second-order field equations, offering a mathematically simpler framework compared to f(R) gravity.
• The study explores implications for late-time acceleration, inflationary dynamics, and bouncing cosmologies while addressing challenges like Lorentz invariance.

Analysis of $f(T)$ Teleparallel Gravity and Cosmology

The paper "$f(T)$ teleparallel gravity and cosmology" presents an in-depth review of the developments and applications of $f(T)$ gravity, a modification of teleparallel gravity that has gained significant interest as an alternative to General Relativity (GR). This extended framework modifies the Einstein-Hilbert action to incorporate a function of the torsion scalar $T$, which is a fundamental aspect of the teleparallel equivalent of GR.

Background and Motivation

The universe's accelerated expansion, primarily observed in the late-time acceleration and the cosmic inflation period, has posed significant challenges to GR-based cosmological models. The standard approach often involves introducing dark energy or modifying gravity itself. Within this context, $f(T)$ gravity arises as an appealing paradigm due to its capability to describe these cosmological phenomena while leading to second-order field equations, which are mathematically simpler than the fourth-order equations seen in $f(R)$ gravity modifications.

Theoretical Framework

In this framework, the fundamental objects are the vierbeins, which provide a natural connection with the spacetime metric, and the torsion tensor, which unlike in GR, is non-zero and accounts for gravity. The action in $f(T)$ gravity is built from the torsion scalar $T$, similar to how the action in GR is constructed from the Ricci scalar $R$. The paper highlights that although $f(T)$ gravity reduces to GR in the limit $f(T) = T$, the introduction of a non-linear function $f(T)$ gives rise to a much richer mathematical structure and physical implications.

Cosmological Implications

The paper reviews $f(T)$ cosmology, focusing on its ability to interpret cosmological observations without additional exotic matter components. Key aspects addressed include:

• Late-Time Acceleration: $f(T)$ gravity models can naturally explain the current accelerated expansion of the universe. By choosing appropriate functions for $f(T)$, the theory can mimic dark energy-like behavior or provide quintessence and phantom regimes.
• Inflationary Dynamics: Early universe inflation is also explored within this framework, showing that $f(T)$ gravity can naturally accommodate an inflationary phase, addressing problems like the horizon and flatness issues without invoking an inflaton field.
• Bouncing Cosmologies: The potential for $f(T)$ modifications to result in non-singular bouncing cosmologies is explored, offering models that resolve the Big Bang singularity problem and facilitate a smooth transition from contraction to expansion phases.

Theoretical and Observational Challenges

One core challenge in $f(T)$ theories is the frame-dependent nature seen in non-covariant formulations, leading to issues with Lorentz invariance. The paper emphasizes recent advancements towards a covariant formulation, where a non-trivial spin connection is introduced to address these issues, ensuring frame independence.

Furthermore, the theoretical exploration is complemented by phenomenological analyses, where $f(T)$ models are scrutinized against observational data from supernovae, cosmic microwave background, and baryon acoustic oscillations, among others. These studies are crucial for constraining the model parameters and ensuring consistency with known cosmic histories.

Future Directions

The research underscores several promising avenues for $f(T)$ gravity, including further exploration of its perturbative structure, potential quantum implications, and its interaction with matter fields and other fundamental forces. Moreover, specific focus on analytical techniques for determining the functional form of $f(T)$ that best fits observational data remains a pivotal area of continued investigation.

In sum, the paper provides a comprehensive overview of $f(T)$ gravity, elucidating its viability and scope as a modified gravity theory that reconciles various cosmological phenomena efficiently while encouraging ongoing research and development within this intriguing field.