f(T) teleparallel gravity and cosmology

By Yi-Fu Cai, Salvatore Capozziello, M. De Laurentis, Emmanuel N. Saridakis. Reports on progress in physics. Physical Society, 2015

1,402 citations recorded by the source corpus.

Over recent 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, alternative to a cosmological constant, 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, for a certain class of f (T) models, 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 at even earlier moments 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 illuminate the subject of which formulation, or combination of formulations, might be more suitable for quantization ventures and cosmological applications.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/97b1b7227151805970958b84cc490e0e69ab8789

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Nuclear and High Energy Physics

Citations in the corpus

Teleparallel Palatini theories (2018, background): “Further, it turned out that the f(Q) background cosmologies are equivalent to those in the extensively studied f(T̊) models [23, 37, 38], and amongst many other classes of modified gravity cosmologies, they are captured by the “vector distortion” parameterisation [69, 70].”
Born–Infeld inspired modifications of gravity (2017, methodology): “The same would apply to theories based on the teleparallel equivalent of GR as for instance in [165] that can be classified as belonging to the f(T ) extensions of teleparallel theories [92].”
Holographic dark energy (2016, background): “In addition, it has been proved that modified gravity (MG) models can be expressed in terms of the DE/DM interaction in the Einstein frame [284, 285, 286, 287, 288].”
Cosmological perturbations in modified teleparallel gravity models (2018, background): “[15, 16, 17]) additional scalar fields in the action (see [7] and Section 9).”
Bouncing cosmology in f(Q) symmetric teleparallel gravity (2020, background): “As a consequence of this equivalence, neither TEGR nor GR are able to solve the above mentioned problems of the large-scale structure; in analogy to modified metric theories of gravity such as f(R) theories, modified teleparallel actions aims to solve the cosmological and astrophysical issues by int”
Modified Gravity and Cosmology (2021, methodology): “In particular, considering nonlinear extensions we can obtain f(T) gravity as [27]”
On the covariance of teleparallel gravity theories (2017, background): “It is relatively benign when dealing with the teleparallel equivalent of general relativity7, but strikes back in the form of new degrees of freedom with any attempts at generalisation like that of f (T) [17].”
Teleparallel theories of gravity: illuminating a fully invariant approach (2018, background): “Similarly, it was suggested to generalize the Lagrangian density of teleparallel gravity from • T → f ( • T), where • T is the so-called torsion scalar with respect to the teleparallel connection that we will define later (see [10] and references within for an overview of f (T) teleparallel gravity)”
Structure formation in f(T) gravity and a solution for H0 tension (2018, background): “In particular, we can define the effective dark energy density as [17]”