The article communicates gravitational baryogenesis in non-minimal $f(T)$ gravity and $f(T,B)$ teleparallel gravity where $T$ denote the torsion scalar and $B$ a boundary term. These extended teleparallel theories of gravity differ from the usual $f(T)$ gravity and therefore could provide key insights in expounding the baryon asymmetry of the universe. Furthermore, such a study also put constraints on the model parameters of these extended teleparallel theory of gravity. I present different baryogenesis interactions proportional to $\partial_{i}T$, $\partial_{i}f(T)$, $\partial_{i}(T+B)$ and $\partial_{i}f(T+B)$ and find that both of these teleparallel theories of gravity yield viable estimates of the baron-to-entropy ratio compatible with observations except for the baryogenesis interaction proportional to $\partial_{i}(T+B)$. It is therefore encouraging to exercise these extended theories of gravity in other cosmological areas to under their efficiency and applicability in characterizing the current state of the universe.
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 …
In this paper, we consider the possibilities of generating baryon number asymmetry in thermal equilibrium within the frameworks of teleparallel and symmetric teleparallel gravities. Through the derivative couplings of the torsion scalar or the non-metricity scalar to baryons, the baryon number asymmetry is indeed produced in the radiation dominated epoch. For gravitational baryogenesis mechanisms in these two frameworks, the produced baryon-to-entropy ratio is too small to be consistent with observations. But the gravitational leptogenesis models within both frameworks have the possibilities t…
We analyze the relation between teleparallelism and local Lorentz invariance. We show that generic modifications of the teleparallel equivalent to general relativity will not respect local Lorentz symmetry. We clarify the reasons for this and explain why the situation is different in general relativity. We give a prescription for constructing teleparallel equivalents for known theories. We also explicitly consider a recently proposed class of generalized teleparallel theories, called f(T) theories of gravity, and show why restoring local Lorentz symmetry in such theories cannot lead to sensibl…
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 …
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.
Generalised Proca theories of gravity represent an interesting class of vector-tensor theories where only three propagating degrees of freedom are present. In this work, we propose a new teleparallel gravity analog to Proca theories where the generalised Proca framework is extended due to the lower order nature of torsion based gravity. We develop a new action contribution and explore the example of the Friedmann equations in this regime. We find that teleparallel Proca theories offer the possibility of a much larger class of models in which do have an impact on background cosmology.
The basics of teleparallel gravity and its extensions are reviewed with particular emphasis on the problem of Lorentz-breaking choice of connection in pure-tetrad versions of the theories. Various possible ways to covariantise such models are discussed. A by-product is a new form of $f(T)$ field equations.
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 the context of extended Teleparallel gravity theories with a 3+1 dimensions Gauss-Bonnet analog term, we address the possibility of these theories reproducing several well-known cosmological solutions. In particular when applied to a Friedmann-Lemaître-Robertson-Walker geometry in four-dimensional spacetime with standard fluids exclusively. We study different types of gravitational Lagrangians and reconstruct solutions provided by analytical expressions for either the cosmological scale factor or the Hubble parameter. We also show that it is possible to find Lagrangians of this type without…
Conformal symmetries appear in many parts of physics and play a unique role in exploring the Universe. In this work, we consider the possibility of constructing conformal theories of gravity in the Symmetric Teleparallel Gravity framework, where gravitation is expressed through non-metricity rather than curvature or torsion. We demonstrate that it is possible to formulate a family of conformal theories with second-order field equations and have the metric tensor as the fundamental variable. Moreover, we consider the addition of a scalar field to the theory, and compare the results to the Telep…
We study teleparallel gravity in five-dimensional spacetime with particular discussions on Kaluza-Klein (KK) and braneworld theories. We directly perform the dimensional reduction by differential forms. In the braneworld theory, the teleparallel gravity formalism in the Friedmann-Lemaître-Robertson-Walker cosmology is equivalent to GR due to the same Friedmann equation, whereas in the KK case the reduction of our formulation does not recover the effect as GR of 4-dimensional spacetime.
Teleparallel geometry offers a platform on which to build up theories of gravity where torsion rather than curvature mediates gravitational interaction. The teleparallel analogue of Horndeski gravity is an approach to teleparallel geometry where scalar-tensor theories are considered in this torsional framework. Being teleparallel gravity of lower order in dynamics, this turns out to be more general than metric Horndeski gravity. In other words, the class of teleparallel Horndeski gravity models is much broader than the standard metric one. In this work, we explore constraints on this wide rang…
We analyze the construction of conformal theories of gravity in the realm of teleparallel theories. We first present a family of conformal theories which are quadratic in the torsion tensor and are constructed out of the tetrad field and of a scalar field. For a particular value of a coupling constant, and in the gauge where the scalar field is restricted to assume a constant value, the theory reduces to the teleparallel equivalent of general relativity, and the tetrad field satisfies Einstein's equations. A second theory is formulated out of the tetrad field only, and is not equivalent to the…
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…
The covariant formulation of teleparallel gravity theories must include the spin connection, which has 6 degrees of freedom. One can, however, always choose a gauge such that the spin connection is put to zero. In principle this gauge may affect counting of degrees of freedom in the Hamiltonian analysis. We show for general teleparallel theories of gravity, that fixing the gauge such that the spin connection vanishes in fact does not affect the counting of degrees of freedom. This manifests in the fact that the momenta of the Lorentz transformations which generate the spin connection are fully…
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 the context of extended Teleparallel gravity theories with a 3+1 dimensions Gauss-Bonnet analog term, we address the possibility of these theories reproducing several well-known cosmological bouncing scenarios in a four-dimensional Friedmann-Lemaître-Robertson-Walker geometry. We shall study which types of gravitational Lagrangians are capable of reconstructing bouncing solutions provided by analytical expressions for symmetric, oscillatory, superbounce, the matter bounce and singular bounce. Some of the Lagrangians discovered are both analytical at the origin having Minkowski and Schwarzsc…
We investigate the Lagrange multiplier formulation of teleparallel theories, including f(T) gravity, in which the connection is not set to zero a priori and compare it with the pure frame theory. We show explicitly that the two formulations are equivalent, in the sense that the dynamical equations have the same content. One consequence is that the manifestly local Lorentz invariant f(T) theory cannot be expected to be free of pathologies, which were previously found to plague f(T) gravity formulated in the usual pure frame approach.
Teleparallel geometry utilizes Weitzenböck connection which has nontrivial torsion but no curvature and does not directly follow from the metric like Levi-Civita connection. In extended teleparallel theories, for instance in $f(T)$ or scalar-torsion gravity, the connection must obey its antisymmetric field equations. So far only a few analytic solutions were known. In this note we solve the $f(T,ϕ)$ gravity antisymmetric vacuum field equations for a generic rotating tetrad ansatz in Weyl canonical coordinates, and find the corresponding spin connection coefficients. By a coordinate transformat…
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 …
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…
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…
It is well known that the teleparallel equivalent of general relativity yields the same vacuum solutions as general relativity does, which ensures that this particular teleparallel model is in good agreement with experiments. A less known result concerns the existence of a wider class of teleparallel models which also admits these solutions when the spacetime is diagonalizable by means of a coordinate change. However, it is stated in Ref. [Phys. Rev. D 67, 044016 (2003).] that the teleparallel equivalent of general relativity is the only teleparallel model which admits black holes. To show tha…
Teleparallel gravity and its popular generalization $f(T)$ gravity can be formulated as fully invariant (under both coordinate transformations and local Lorentz transformations) theories of gravity. Several misconceptions about teleparallel gravity and its generalizations can be found in the literature, especially regarding their local Lorentz invariance. We describe how these misunderstandings may have arisen and attempt to clarify the situation. In particular, the central point of confusion in the literature appears to be related to the inertial spin connection in teleparallel gravity models…
Symmetric teleparallel gravity (STG) offers an interesting avenue to formulate a theory of gravitation that relies neither on curvature nor torsion but only on non-metricity Q. Given the growing number of observations of gravitational waves (GWs) and their use to explore gravitational theories, in this work we investigate the GWs in various extensions of STG, focusing on their speed and polarization. For the simple STG, for theories that arise from the generalized irreducible decomposition of STG, and for f(Q) gravity, we obtain the same speed and polarizations with general relativity. For sca…
We consider the most general class of teleparallel theories of gravity quadratic in the torsion tensor, and carry out a detailed investigation of its Hamiltonian formulation in the time gauge. Such general class is given by a three-parameter family of theories. A consistent implementation of the Legendre transform reduces the original theory to a one-parameter theory determined in terms of first class constraints. The free parameter is fixed by requiring the Newtonian limit. The resulting theory is the teleparallel equivalent of general relativity.
Recently Kaniel & Itin proposed a gravitational model with the wave type equation [\square+λ(x)]\vartheta^α=0 as vacuum field equation, where \vartheta^αdenotes the coframe of spacetime. They found that the viable Yilmaz-Rosen metric is an exact solution of the tracefree part of their field equation. This model belongs to the teleparallelism class of gravitational gauge theories. Of decisive importance for the evaluation of the Kaniel-Itin model is the question whether the variation of the coframe commutes with the Hodge star. We find a master formula for this commutator and rectify some corre…
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…
There is a growing interest in modified gravity theories based on torsion, as these theories exhibit interesting cosmological implications. In this work, inspired by the teleparallel formulation of general relativity, we present its extension to Lovelock gravity known as the most natural extension of general relativity in higher-dimensional space-times. First, we review the teleparallel equivalent of general relativity and Gauss-Bonnet gravity, and then we construct the teleparallel equivalent of Lovelock gravity. In order to achieve this goal we use the vielbein and the connection without imp…
We determine the possible gravitational wave polarizations in two general classes of teleparallel gravity theories, using the metric and symmetric teleparallel geometries. For this purpose we apply the Newman-Penrose formalism, and find that depending on the choice of parameters, the $\mathrm{E}(2)$ class of the theories is one of $\mathrm{N}_2, \mathrm{N}_3, \mathrm{III}_5, \mathrm{II}_6$, corresponding to two to six polarizations, where all of them include the two tensor polarizations known from general relativity. We also find classes of theories apart from general relativity which yield th…
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.
Despite the fact that General Relativity (GR) has been very successful, many alternative theories of gravity have attracted the attention of a significant number of theoretical physicists. Among these theories, we have theories with conformal symmetry. Here, the use of Weyl geometry to deal with conformal teleparallel gravity is reviewed in great detail. As an application, a model that can be set to be equivalent to the Teleparallel Equivalent of General Relativity (TEGR) and is invariant under diffeomorphisms, local Lorentz transformations (LLT) and Weyl transformations (WT) is created. Some …
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 discuss conformal issues of pure and extended teleparallel gravity. In particular, we present formulations of conformal transformation in teleparallel gravity. Furthermore, we propose conformal scalar and gauge field theories in teleparallel gravity and study conformal torsion gravity. We explicitly demonstrate that a power-law acceleration (including the $Λ$CDM universe) as well as the de Sitter expansion of the universe can be realized in extended teleparallel gravity with a conformal scalar field, and that pure teleparallel gravity with a conformal scalar field can lead to the $Λ$CDM mod…
Lorentz-violating theories of gravity typically contain constrained vector fields. We show that the lowest-order coupling of such vectors to $\mathrm{U}(1)$-symmetric scalars can naturally give rise to baryogenesis in a manner akin to the Affleck-Dine mechanism. We calculate the cosmology of this new mechanism, demonstrating that a net $B-L$ can be generated in the early Universe, and that the resulting baryon-to-photon ratio matches that which is presently observed. We discuss constraints on the model using solar system and astrophysical tests of Lorentz violation in the gravity sector. Gener…
We study tensor perturbations around the most general cosmologically symmetric backgrounds in a class of teleparallel gravity theories known as New General Relativity. These theories comprise a one-parameter class, which is fully consistent with observations at the post-Newtonian level, and which contains the teleparallel equivalent of General Relativity as a special case. We find that for a particular class of cosmological background geometries these theories exhibit gravitational wave birefringence and dispersion, i.e., the dispersion relation for gravitational waves depends on their polariz…
The Palatini formalism is developed for gravitational theories in flat geometries. We focus on two particularly interesting scenarios. First, we fix the connection to be metric compatible, but we follow a completely covariant approach by imposing the constraints with suitable Lagrange multipliers. For a general quadratic theory we show how torsion naturally propagates and we reproduce the Teleparallel Equivalent of General Relativity as a particular quadratic action that features an additional Lorentz symmetry. We then study the much less explored theories formulated in a geometry with neither…
We apply the Hamiltonian formulation of teleparallel theories of gravity in 2+1 dimensions to a circularly symmetric geometry. We find a family of one-parameter black hole solutions. The BTZ solution fixes the unique free parameter of the theory. The resulting field equations coincide with the teleparallel equivalent of Einstein's three-dimensional equations. We calculate the gravitational energy of the black holes by means of the simple expression that arises in the Hamiltonian formulation and conclude that the resulting value is identical to that calculated by means of the Brown-York method.
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.
A class of theories of gravitation that naturally incorporates preferred frames of reference is presented. The underlying space-time geometry consists of a partial parallelization of space-time and has properties of Riemann-Cartan as well as teleparallel geometry. Within this geometry, the kinematic quantities of preferred frames are associated with torsion fields. Using a variational method, it is shown in which way action functionals for this geometry can be constructed. For a special action the field equations are derived and the coupling to spinor fields is discussed.
The teleparallel formulation of gravity theories reveals close structural analogies to electrodynamics, which are more hidden in their usual formulation in terms of the curvature of spacetime. We show how every locally Lorentz invariant teleparallel theory of gravity with second order field equations can be understood as built from a gravitational field strength and excitation tensor which are related to each other by a constitutive relation, analogous to the axiomatic construction of theories of electrodynamics. We demonstrate how the previously studied models of $f(\mathbb{T})$ and $f(T_\tex…
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…
Gauge symmetries in teleparallel gravity, together with the identities among the dynamical equations they provide, are analyzed in relation to the way they condition the coupling between matter and gravity. Particularly, the coupling of fermionic matter seems to be excluded in a wide range of teleparallel theories.
We derive the post-Newtonian limit of a general class of teleparallel gravity theories, whose action is given by a free function of three scalar quantities obtained from the torsion of the teleparallel connection. This class of theories is chosen to be sufficiently generic in order to include the $f(T)$ class of theories as well as new general relativity as subclasses. To derive its post-Newtonian limit, we first impose the Weitzenböck gauge, and then introduce a post-Newtonian approximation of the tetrad field around a Minkowski background solution. Our results show that the class of theories…
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…
We study conditions on a generic connection written in terms of first-order derivatives of the vielbein in order to obtain (possible) equivalent theories to Einstein Gravity. We derive the equations of motion for these theories which are based on the new connections. We recover the Teleparallel Gravity equations of motion as a particular case. The analysis of this work might be useful to Double Field Theory to find other connections determined in terms of the physical fields.
Symmetric teleparallel gravity theories, in which the gravitational interaction is attributed to the nonmetricity of a flat, symmetric, but not metric-compatible affine connection, have been a topic of growing interest in recent studies. Numerous works study the cosmology of symmetric teleparallel gravity assuming a flat Friedmann-Lemaître-Robertson-Walker metric, while working in the so-called "coincident gauge", further assuming that the connection coefficients vanish. However, little attention has been paid to the fact that both of these assumptions rely on the freedom to choose a particula…
