We investigate the strong coupling problem in modified teleparallel gravity theories using the effective field theory (EFT) approach, demonstrating that it is possible to shift the emergence of new degrees of freedom (DoFs) to lower orders in perturbation theory. We first focus on the case of $f(T)$ gravity, and we show that in its conformally equivalent form the scalar perturbations are non-dynamical up to the cubic action. We then propose a simple modification of the theory, which lowers the appearance of new DoFs to cubic order, compared to the quartic order in standard $f(T)$ gravity. Our work opens a new avenue to address the issue of strong coupling in modified teleparallel gravity, and suggests a new classification scheme of these theories based on the perturbative order at which new DoFs appear.
Cosmological perturbations are considered in $f(T)$ and in scalar-torsion $f(φ)T$ teleparallel models of gravity. Full sets of linear perturbation equations are accurately derived and analysed at the relevant limits. Interesting features of generalisations to other teleparallel models, spatially curved backgrounds, and rotated tetrads are pointed out.
We consider the variational principle in the covariant formulation of modified teleparallel theories with second order field equations. We vary the action with respect to the spin connection and obtain a consistency condition relating the spin connection with the tetrad. We argue that since the spin connection can be calculated using an additional reference tetrad, modified teleparallel theories can be interpreted as effectively bigravity theories. We conclude with discussion about the relation of our results and those obtained in the usual, non-covariant, formulation of teleparallel theories …
The existence and the stability conditions for some exact relativistic solutions of special interest are studied in a higher-order modified teleparallel gravitational theory. The theory with the use of a Lagrange multiplier is equivalent with that of General Relativity with a minimally coupled noncanonical field. The conditions for the existence of de Sitter solutions and ideal gas solutions in the case of vacuum are studied as also the stability criteria. Furthermore, in the presence of matter the behaviour of scaling solutions is given. Finally, we discuss the degrees of freedom of the field…
We study the matter stability in modified teleparallel gravity or $f(T)$ theories. We show that there is no Dolgov-Kawasaki instability in these types of modified teleparallel gravity theories. This give the $f(T)$ theories a great advantage over their $f(R)$ counterparts because from the stability point of view there isn't any limit on the form of functions that can be chosen.
We investigate modified theories of gravity in the context of teleparallel geometries. It is well known that modified gravity models based on the torsion scalar are not invariant under local Lorentz transformations while modifications based on the Ricci scalar are. This motivates the study of a model depending on the torsion scalar and the divergence of the torsion vector. We derive the teleparallel equivalent of $f(R)$ gravity as a particular subset of these models and also show that this is the unique theory in this class that is invariant under local Lorentz transformation. Furthermore one …
Born-Infeld strategy to smooth theories having divergent solutions is applied to teleparallel equivalent of General Relativity. Differing from other theories of modified gravity, modified teleparallelism leads to second order equations, since teleparallel Lagrangian only contains first derivatives of the vierbein. We show that Born-Infeld-modified teleparallelism solves the particle horizon problem in a spatially flat FRW universe by providing an initial exponential expansion without resorting to an inflaton field.
Finding spherically symmetric exact solutions in modified gravity is usually a difficult task. In this paper we use the Noether's symmetry approach for a modified Teleparallel theory of gravity labelled as $f(T,B)$ gravity where $T$ is the scalar torsion and $B$ the boundary term. Using the Noether's theorem, we were able to find exact spherically symmetric solutions for different forms of the function $f(T,B)$ coming from the Noether's symmetries.
We investigate modified theories of gravity in the context of teleparallel geometries with possible Gauss-Bonnet contributions. The possible coupling of gravity with the trace of the energy-momentum tensor is also taken into account. This is motivated by the various different theories formulated in the teleparallel approach and the metric approach without discussing the exact relationship between them. Our formulation clarifies the connections between different well known theories. For instance, we are able to formulate the correct teleparallel equivalent of Gauss-Bonnet modified general relat…
We review the current status of the Lorentz covariance in teleparallel and modified teleparallel theories of gravity, and discuss the controversial features of the different approaches. We also revisit the issue of the remnant Lorentz gauge symmetries in $f(T)$ gravity.
The recently proposed Nieh-Yan modified teleparallel gravity is a parity-violating gravity model that modifies the general relativity equivalent teleparallel gravity by a Nieh-Yan term. This model is healthy and simple in form. In this paper, we consider the application of this model to the Solar System and investigate its slow-motion and weak-field approximation in terms of the parametrized post-Newtonian formalism. We find that all the post-Newtonian parameters of the model are the same as those of general relativity, which makes the model compatible with the Solar System experiments.
New classes of modified teleparallel theories of gravity are introduced. The action of this theory is constructed to be a function of the irreducible parts of torsion $f(T_{\rm ax},T_{\rm ten},T_{\rm vec})$, where $T_{\rm ax},T_{\rm ten}$ and $T_{\rm vec}$ are squares of the axial, tensor and vector components of torsion, respectively. This is the most general (well-motivated) second order teleparallel theory of gravity that can be constructed from the torsion tensor. Different particular second order theories can be recovered from this theory such as new general relativity, conformal telepara…
In this paper, working in a Friedman-Lemaitre-Robertson-Walker (FLRW), first, in the flat case, we recover the generalized Friedman equation of Quantum Loop cosmology, and therefore the cosmological bounce, in the framework of modified teleparallel gravity $f(T)$-model, $T$ being the torsion scalar introduced in teleparallel gravity approach, without invoking unconventional exotic matter. Furthermore we study the associated perturbations again in a flat FLRW space-time. Then, we generalize the results to the curved FLRW space-time, where some issues related to the choice of tetrad exist, by us…
Teleparallel gravity offers a new avenue in which to construct gravitational models beyond general relativity. While teleparallel gravity can be framed in a way to be dynamically equivalent to general relativity, its modifications are mostly not equivalent to the traditional route to modified gravity. $f(T,B)$ gravity is one such gravitational theory where the second and fourth order contributions to the field equations are decoupled. In this work, we explore the all important cosmological perturbations of this new framework of gravity. We derive the gravitational propagation equation, its vec…
We investigate the gravitational waves and their properties in various modified teleparallel theories, such as $f(T), f(T,B)$ and $f(T,T_G)$ gravities. We perform the perturbation analysis both around a Minkowski background, as well as in the case where a cosmological constant is present, and for clarity we use both the metric and tetrad language. For $f(T)$ gravity we verify the result that no further polarization modes comparing to general relativity are present at first-order perturbation level, and we show that in order to see extra modes one should look at third-order perturbations. For n…
We study the matter density perturbations in modified teleparallel gravity theories, where extra degrees of freedom arise from the local Lorentz violation in the tangent space. We formulate a vierbein perturbation with variables addressing all the 16 components of the vierbein field. By assuming the perfect fluid matter source, we examine the cosmological implication of the 6 unfamiliar new degrees of freedom in modified $f(T)$ gravity theories. We find that despite the new modes in the vierbein scenario provide no explicit significant effect in the small-scale regime, they exhibit some deviat…
The possibility of static and spherically symmetric traversable wormhole solution in modified teleparallel Rastall gravity (MTRG) in a non-diagonal tetrad is investigated. Rastall assumption modifies the field equations and energy-momentum conservation law. These modifications lead to different exact asymptotically flat traversable wormhole solutions. By imposing different constraints on modified energy-momentum conservation law, different exact solutions are found and the obtained results for teleparallel Rastall gravity (TRG), with specific choices of $f(T)$, are studied. It is shown that th…
In this paper, we present the Noether symmetries of locally rotationally symmetric Bianchi type I (LRS BI), an anisotropic model, in the context of the teleparallel gravity. We study a certain modified teleparallel theory based on the action that, in particular, contains a coupling between the scalar field and field strength (magnetism part). We derive the symmetry generators and show that, by means of cyclic variables approach, we can not obtain a suitable solution for field equations. Hence by the use of B.N.S. approach, we solve the equations which carry Noether currents as well. By data an…
This paper explores the possibility of treating the exotic Chaplygin-gas (CG) fluid model as some manifestation of an $f(T)$ gravitation. To this end, we use the different cosmological CG equations of state, compare them with the equation of state for the modified teleparallel gravity and reconstruct the corresponding Lagrangian densities. We then explicitly derive the equation of state parameter of the torsion fluid $w_T$ and study its evolution for vacuum-torsion, radiation-torsion, dust-torsion, stiff fluid torsion, and radiation-dust-torsion multi-fluid systems. The obtained Lagrangians ha…
Teleparallel theory of gravity and its modifications have been studied extensively in literature. However, gravitational waves has not been studied enough in the framework of teleparallelism. In the present study, we discuss gravitational waves in general theories of teleparallel gravity containing the torsion scalar $T$, the boundary term $B$ and a scalar field $ϕ$. The goal is to classify possible new polarizations generalizing results presented in Ref.[15]. We show that, if the boundary term is minimally coupled to the torsion scalar and the scalar field, gravitational waves have the same p…
In this paper, we have presented the Noether symmetries of flat FRW spacetime in the context of a new action in Teleparallel Gravity which we construct it based on $f(R)$ version. This modified action contains a coupling between scalar field potential and magnetism. Also, we introduce an innovative approach (B.N.S. Approach) for exact solutions which carry more conserved currents than Noether approach. By data analysis of the exact solutions, obtained from Noether approach, late time acceleration and phase crossing are realized, and some deep connections with observational data such as the age…
This study is conducted to examine the validity of generalized second law of thermodynamics (GSLT) in flat FRW for modified teleparallel gravity involving coupling between a scalar field with the torsion scalar $T$ and the boundary term $B=2\nabla_μT^μ$. This theory is very useful since it can reproduce other important well-known scalar field theories in suitable limits. The validity of the first and second law of thermodynamics at the apparent horizon is discussed for any coupling. As examples, we have also explored the validity of those thermodynamics laws in some new cosmological solutions …
In the present study, we consider an extended form of teleparallel Lagrangian $f(T,ϕ,X)$, as function of a scalar field $ϕ$, its kinetic term $X$ and the torsion scalar $T$. We use linear perturbations to obtain the equation of matter density perturbations on sub-Hubble scales. The gravitational coupling is modified in scalar modes with respect to the one of General Relativity, albeit vector modes decay and do not show any significant effects. We thus extend these results by involving multiple scalar field models. Further, we study conformal transformations in teleparallel gravity and we obtai…
We study the cosmological inflation and reheating in a teleparallel model of gravity. Reheating is assumed to be due to the decay of a scalar field to radiation during its rapid oscillation. By using cosmological perturbations during inflation, and subsequent evolutions of the Universe, we calculate the reheating temperature as a function of the spectral index and the power spectrum.
We study a spin 1/2 fermion in a teleparallel f(T) domain-wall thick braneworld. By assuming a non-minimal coupling of fermion to the torsion, a geometric alternative to the Yukawa coupling is found. The torsion parameters control the width of the massless Kaluza-Klein mode and the properties of the analogue quantum-potential near the origin. The non-normalized massive fermionic modes are also analyzed.
In a higher-order modified teleparallel theory cosmological we present analytical cosmological solutions. In particular we determine forms of the unknown potential which drives the scalar field such that the field equations form a Liouville integrable system. For the determination of the conservation laws we apply the Cartan symmetries. Furthermore, inspired from our solutions, a toy model is studied and it is shown that it can describe the Supernova data, while at the same time introduces dark matter components in the Hubble function. When the extra matter source is a stiff fluid then we show…
In the context of modified teleparallel gravity, we study the generation of primordial density fluctuations in a general scalar-torsion theory whose Lagrangian density is an arbitrary function $f(T,ϕ)$ of the torsion scalar $T$ and a scalar field $ϕ$, plus the kinetic term of this latter. It is well known that generic modifications of teleparallel gravity are not invariant under six-parameter local Lorentz transformations. In order to restore the local Lorentz symmetry, we have incorporated six additional degrees of freedom in the form of Goldstone modes of the symmetry breaking through a Lore…
This paper studies the cosmology of accelerating expansion of the universe in modified teleparallel gravity theory. We discuss the cosmology of $f(T,B)$ gravity theory and its implication to the new general form of the equation of state parameter $w_{TB}$ for explaining the late-time accelerating expansion of the universe without the need for the cosmological constant scenario. We examine the numerical value of $w_{TB}$ in different paradigmatic $f(T,B)$ gravity models. In those models, the numerical result of $w_{TB}$ is favored with observations in the presence of the torsion scalar T associ…
It has been shown that at the semi-classical order, gravitational theories with quantum fluctuations can be effectively recast as modified theories of gravity with non-minimal gravity-matter couplings. We proceed from an observational perspective and see whether such quantum fluctuations can leave imprints on the late Universe. Within the teleparallel formulation, we investigate a representative model in this general class of modified gravitational theories inlaid with quantum fluctuations, and determine the cosmological parameters by using compiled late-time data sets. Furthermore, we assess …
We study the parametrized post-Newtonian (PPN) limit of higher-derivative-torsion Modified Teleparallel Gravity. We start from the covariant formulation of modified Teleparallel Gravity by restoring the spin connection of the theory. Then, we perform the post-Newtonian expansion of the tetrad field around the Minkowski background and find the perturbed field equations. We compute the PPN metric for the higher-order Teleparallel Gravity theories which allows us to show that at the post-Newtonian limit this more general class of theories are fully conservative and indistinguishable from General …
We construct $F(T,\left(\nabla{T}\right)^2,\Box {T})$ gravitational modifications, which are novel classes of modified theories arising from higher-derivative torsional terms in the action, and are different than their curvature analogue. Applying them in a cosmological framework we obtain an effective dark energy sector that comprises of the novel torsional contributions. We perform a detailed dynamical analysis for two specific examples, extracting the stable late-time solutions and calculating the corresponding observables. We show that the thermal history of the universe can be reproduced,…
In this work, we explore disformal transformations in the context of the teleparallel equivalent of general relativity and modified teleparallel gravity. We present explicit formulas in components for disformal transformations of the main geometric objects in these theories such as torsion tensor, torsion vector and contortion. Most importantly, we consider the boundary term which distinguishes the torsion scalar from the Ricci scalar. With that we show for $f(T)$ gravity that disformal transformations from the Jordan frame representation are unable to straightforwardly remove local Lorentz br…
To recreate the cosmological models, we employed the parametrization approach in modified teleparallel Gauss-Bonnet gravity. It has been interesting to apply the parametrization approach to investigate cosmological models. The real benefit of using this method is that the observational data may be incorporated to examine the cosmological models. Several cosmological parameters were examined, such as the Hubble parameter (H), the deceleration parameter (q), and the equation of state (EoS) parameter (w). The results obtained are consistent with recent cosmological findings in the conventional sc…
It is well known that one cannot apply a conformal transformation to $f(T)$ gravity to obtain a minimally coupled scalar field model, and thus no Einstein frame exists for $f(T)$ gravity. Furthermore nonminimally coupled "teleparallel dark energy models" are not conformally equivalent to $f(T)$ gravity. However, it can be shown that $f(T)$ gravity is conformally equivalent to a teleparallel phantom scalar field model with a nonminimal coupling to a boundary term only. In this work, we extend this analysis by considering a recently studied extended class of models, known as $f(T,B)$ gravity, wh…
In this paper, we study different Solar System tests in a modified Teleparallel gravity theory based on an arbitrary function $f(T,B)$ which depends on the scalar torsion $T$ and the boundary term $B$. To do this, we first find new perturbed spherically symmetric solutions around Schwarzschild for different power-law forms of the arbitrary Lagrangian. Then, for each model we calculated the photon sphere, perihelion shift, deflection of light, Cassini experiment, Shapiro delay and the gravitational redshift. Finally, we confront these computations with different known experiments from these Sol…
In the present work, we reconstruct different f(T)-gravity models corresponding to the original and entropy-corrected version of the holographic and new agegraphic dark energy models. We also obtain the equation of state parameters of the corresponding f(T)-gravity models. We conclude that the holographic and new agegraphic f(T)-gravity models behave like phantom or quintessence model. Whereas in the entropy-corrected models, the equation of state parameter can justify the transition from the quintessence state to the phantom regime as indicated by the recent observations.
Axially symmetric spacetimes play an important role in the relativistic description of rotating astrophysical objects like black holes, stars, etc. In gravitational theories that venture beyond the usual Riemannian geometry by allowing independent connection components, the notion of symmetry concerns, not just the metric, but also the connection. As discovered recently, in teleparallel geometries, axial symmetry can be realised in two branches, while only one of these has a continuous spherically symmetric limit. In the current paper, we consider a very generic $f(T,B,ϕ,X)$ family of telepara…
Teleparallel gravity theories employ a tetrad and a Lorentz spin connection as independent variables in their covariant formulation. In order to solve their field equations, it is helpful to search for solutions which exhibit certain amounts of symmetry, such as spherical or cosmological symmetry. In this article we present how to apply the notion of spacetime symmetries known from Cartan geometry to teleparallel geometries. We explicitly derive the most general tetrads and spin connections which are compatible with axial, spherical, cosmological and maximal symmetry. For homogeneous and isotr…
Horndeski gravity is the most general scalar tensor theory, with a single scalar field, leading to second order field equations and after the GW170817 it has been severely constrained. In this paper, we study the analogue of Horndeski's theory in the teleparallel gravity framework were gravity is mediated through torsion instead of curvature. We show that, even though, many terms are the same as in the curvature case, we have much richer phenomenology in the teleparallel setting because of the nature of the torsion tensor. Moreover, Teleparallel Horndenski contains the standard Horndenski grav…
In this paper, we consider wormhole geometries in the context of teleparallel equivalent of general relativity (TEGR) as well as $f(T)$ gravity. The TEGR is an alternative geometrical formulation of Einstein's general relativity, where modified teleparallel gravity or $f(T)$ gravity has been invoked as an alternative approach for explaining an accelerated expansion of the universe. We present the analytical solutions under the assumption of spherical symmetry and the existence of a conformal Killing vectors to proceed a more systematic approach in searching for exact wormhole solutions. More p…
We present a novel reconstruction method of $f(T)$ teleparallel gravity from phenomenological parameterizations of the deceleration parameter or other alternatives. This can be used as a toolkit to produce viable modified gravity scenarios directly related to cosmological observations. We test two parameterizations of the deceleration parameter considered in recent literatures in addition to one parametrization of the effective (total) equation of state (EoS) of the universe. We use the asymptotic behaviour of the matter density parameter as an extra constraint to identify the viable range of …
In the semi-classical regime, quantum fluctuations embedded in a Riemannian spacetime can be effectively recast as classical back reactions and manifest themselves in the form of non-minimal couplings between matter and curvature. In this work, we exhibit that this semi-classical description can also be applied within the teleparallel formulation. In the teleparallel formulation, quantum fluctuations generically lead to non-minimal torsion-matter couplings. Due to the equivalence between the (classical) Einstein gravity in the Riemannian description and that in teleparallel description, some e…
Inspired by the teleparallel formulation of General Relativity, whose Lagrangian is the torsion invariant T, we have constructed the teleparallel equivalent of Gauss-Bonnet gravity in arbitrary dimensions. Without imposing the Weitzenbock connection, we have extracted the torsion invariant T_G, equivalent (up to boundary terms) to the Gauss-Bonnet term G. T_G is constructed by the vielbein and the connection, it contains quartic powers of the torsion tensor, it is diffeomorphism and Lorentz invariant, and in four dimensions it reduces to a topological invariant as expected. Imposing the Weitze…
The presence of additional compact dimensions in cosmological models is studied in the context of modified teleparallel theories of gravity. We focus the analysis on eleven dimensional spacetimes, where the seven dimensional extra dimensions are compactified. In particular, and due to the importance that global vector fields play within the conceptual body of teleparallel modified gravity models, we consider the additional dimensions to be products of parallelizable spheres. The global vector fields characterizing the different topologies are obtained, as well as the equations of motion associ…
Teleparallel gravity has significantly increased in popularity in recent decades, bringing attention to Einstein's other theory of gravity. In this Review, we relate this form of geometry to the broader metric-affine approach to forming gravitational theories where we describe a systematic way of constructing consistent teleparallel theories that respect certain physical conditions such as local Lorentz invariance. We first use teleparallel gravity to formulate a teleparallel equivalent of general relativity which is dynamically equivalent to general relativity but which may have different beh…
Realization of quintom dark energy after DESI DR2 in Nieh-Yan modified teleparallel gravity
University of Science and Technology of China（中国科学技术大学）；Interdisciplinary Center for Theoretical Study, University of Science and Technology of China（中国科学技术大学交叉理论研究中心）；Peng Huanwu Center for Fundamental Theory（彭桓武基础理论中心）
