Thomas-Whitehead (TW) gravity is a gauge theory of gravitation based on projective geometry. The theory maintains projective symmetry through the TW connection, an affine connection over the volume bundle of the spacetime manifold. TW gravity obtains dynamics through Lovelock expansions in the action while preserving general relativity as a weak field limit. In this paper we clarify the process of lifting tensor and spinor fields from spacetime to the volume bundle and demonstrate that a choice of lifting amounts to a gauge fixing condition. This leads to a natural extension of previous work, where we now realize these prior constructions have been restricted to a particular gauge. In pursuit of generality, we also introduce torsion to the TW connection, leading to new dynamics. In particular, the appearance of torsion induces interaction terms involving gravitational coupling with Yang-Mills fields and Dirac spinors. An explicit realization of this is a geometrically sourced chiral mass term arising from the torsion dynamics.
We study gravitational waves with torsion as exact vacuum solutions of three-dimensional gravity with propagating torsion. The new solutions are a natural generalization of the plane-fronted gravitational waves in general relativity with a cosmological constant, in the presence of matter.
The possibility to distinguish Dirac from Majorana fermion by gravitational interaction and torsion coupling is discussed. The scattering of both Dirac and Majorana particles are the same in the spherically symmetric gravitational field up to the first order perturbation of the fermion-gravity interaction. The scattering behaviors of Dirac and Majorana fermion are also the same by axial vector torsion but different by vector torsion. We get the conclusion that the scattering by vector torsion field can distinguish the Dirac from Majorana neutrino.
We review how the large $c$ expansion of General Relativity leads to an effective theory in the form of Twistless Torsional Newton-Cartan gravity. We show how this is a strong field expansion around the static sector of General Relativity and illustrate this through two examples.
A linear Lorentz connection has always two fundamental derived characteristics: curvature and torsion. The latter is assumed to vanish in general relativity. Three gravitational models involving non-vanishing torsion are examined: teleparallel gravity, Einstein-Cartan, and new general relativity. Their dependability is critically examined. Although a final answer can only be given by experience, it is argued that teleparallel gravity provides the most consistent approach.
We discuss the quantum dynamics of the Dirac fermion particle in a gauge gravitational field. The minimal as well as the Pauli-type nonminimal coupling of a fermion with external fields is studied, bringing into consideration the notions of the translational and the Lorentz gravitational moments. The anomalous gravitomagnetic and gravitoelectric moments are ruled out on the basis of the covariance arguments. We derive the general Foldy-Wouthuysen transformation for an arbitrary configuration of the gauge gravitational field without assuming it weak. Making use of the Foldy-Wouthuysen Hamiltoni…
Possible geometric frameworks for a unified theory of gravity and electromagnetism are investigated: General relativity is enlarged by allowing for an arbitrary complex linear connection and by constructing an extended spinor derivative based on the complex connection. Thereby the spacetime torsion not only is coupled to the spin of fermions and causes a four-fermion contact interaction, but the non-metric vector-part of torsion is also related to the electromagnetic potential. However, this long-standing relation is shown to be valid only in a special U(1) gauge, and it is a formal consequenc…
The dynamics of a gravitational torsion kink as a plane symmetric thick domain wall solution of Einstein-Cartan (EC) field equation is given. The spin-torsion energy has to be as high as the gravitational kink potential otherwise torsion will not contribute as an appreciable effect to domain wall.Cartan torsion also contributes to the orthonal pressure of the domain wall.
Gravitational stability of torsion and inflaton field in a four-dimensional spacetime de Sitter solution in scalar-tensor cosmology where Cartan torsion propagates is investigated in detail. Inflaton and torsion evolution equations are derived by making use of a Lagrangean method. Stable and unstable modes for torsion and inflatons are found to be dependent of the background torsion and inflaton fields. Present astrophysical observations favour a stable mode for torsion since this would explain why no relic torsion imprint has been found on the Cosmic Background Radiation in the universe.
We present a review of some recent models of gravitation theory with propagating torsion based on the use of a torsion-dilaton field and propose one more model of this type which promises to be more realistic. A proper universal self-consistent minimal action principle yields the properties of this model and predicts the interactions of torsion-dilaton field with the real matter. The new model may be compatible with the string models with dilaton field and gives a novel interpretation of the dilaton as a part of the space-time torsion. A relation with some recent models of dilatonic gravity is…
Fluctuations on de Sitter solution of Einstein-Cartan field equations are obtained in terms of the matter density primordial density fluctuations and spin-torsion density and matter density fluctuations obtained from COBE data. Einstein-de Sitter solution is shown to be unstable even in the absence of torsion.The spin-torsion density fluctuation is simply computed from the Einstein-Cartan equations and from COBE data.
Braneworld models are interesting theoretical and phenomenological frameworks to search for new physics beyond the standard model of particles and cosmology. In this work, we discuss braneworld models whose gravitational dynamics are governed by teleparallel $f(T)$ gravities. Here, we emphasize a codimension two axisymmetric model, also known as a string-like brane. Likewise, in the 5D domain-walls models, the $f(T)$ gravitational modification leads to a phase transition on the perfect fluid source providing a brane-splitting mechanism. Furthermore, the torsion changes the gravitational pertur…
Spin-2, spin-1 and spin-0 modes in linearised teleparallelism are obtained where the totally skew-symmetric complex contortion tensor generates scalar torsion waves and the symmetric contortion in the last two indices generates gravitational waves as gravitational perturbations of flat spacetime with contortion tensor. A gedanken experiment with this gravitational-torsion wave hitting a ring of spinless particles is proposed which allows us to estimate the contortion of the Earth by making use of data from LISA GW detector. This value coincides with previous value obtained by Nitsch in telepar…
Homogeneous isotropic spatial flat cosmological models with two torsion functions in vacuum are built and investigated in the framework of de Sitter gauge theory of gravity. It is shown that by certain choices of parameters of gravitational Lagrangian the cosmological equations have some exact constant solutions that turn out to be stable de Sitter critical points of dynamical systems and can explain observable acceleration of cosmological expansion. The role of the space-time torsion provoking the acceleration of cosmological expansion is shown.
According to the teleparallel equivalent of general relativity, curvature and torsion are two equivalent ways of describing the same gravitational field. Despite equivalent, however, they act differently: whereas curvature yields a geometric description, in which the concept of gravitational force is absent, torsion acts as a true gravitational force, quite similar to the Lorentz force of electrodynamics. As a consequence, the right-hand side of a spinless-particle equation of motion (which would represent a gravitational force) is always zero in the geometric description, but not in the telep…
We take a Dirac field non-minimally coupled to the gravitational field within the framework of the Poincaré gauge theory of gravity with torsion and curvature. We study the subcase of "weak" gravity, that is, the gravitational Lagrangian depends only linearly on the curvature and quadratically on the torsion. We include all pieces in curvature and torsion that are of odd parity. The second field equation of gravity is derived by varying the Lorentz connection. We solve it with respect to the torsion and decompose the first field equation of gravity and the Dirac equation into Einsteinian piece…
The mantra about gravitation as curvature is a misnomer. The curvature tensor for a standard of rest does not describe acceleration in a gravitational field but the \underline{gradient} of the acceleration (e.g. geodesic deviation). The gravitational field itself (Einstein 1907) is essentially an accelerated reference system. It is characterized by a field of orthonormal four-legs in a Riemann space with Lorentz metric. By viewing vectors at different events having identical leg-components as parallel (teleparallelism) the geometry in a gravitational field defines torsion. This formulation of …
Motivated by the analogy between a weak field expansion of general relativity and Maxwell's laws of electrodynamics, we explore physical consequences of a parity violating $θ$ term in gravitoelectromagnetism. This is distinct from the common gravitational $θ$ term formed as a square of the Riemann tensor. Instead it appears as a product of the gravitoelectric and gravitomagnetic fields in the Lagrangian, similar to the Maxwellian $θ$ term. We show that this sector can arise from a quadratic torsion term in nonlinear gravity. In analogy to the physics of topological insulators, the torsion-indu…
A exact de Sitter-like cosmological solution of quadratic gravitation with torsion has been found. In the limit of constant energy and pressure, it becomes a exact de Sitter spacetime. It exists in a wide class of quadratic gravity theories and is the same in vacuum for all the models in this class, no matter how the coefficients of the quadratic terms in the Lagrangian are. It describes an accelerating universe and gives a cosmological constant which is of the order of magnitude of the observed value. In vacuum the universe is a de Sitter spacetime without torsion. When matter presents, howev…
Dipole fields are common in electromagnetism and may be viewed as the result of a positive and negative charge (or pole) which are close together. A dipole field in gravity is not expected to exist because negative mass has never been observed. However, an exact solution to the gravitational field equations with torsion is presented that does correspond to a dipole gravitational field, even though there is no negative mass. The theory is based on a non-symmetric metric tensor, and it is found there is a singularity in the metric tensor at the origin but no event horizon. Gravitational dipoles …
Dynamical (propagating) torsion can be observed by using conventional gravitational wave detectors such as LIGO, Virgo, LISA and bar detectors. We discuss specific signatures of different types of torsion, in particular those of vector and mixed symmetric torsion (skew symmetric torsion cannot be detected in this way). These signatures are specific to torsion and therefore they can be unambiguously distinguished from those of gravitational waves.
Poincaré gauge theory of gravity offers opportunities to solve some principal problems of general relativity theory and modern cosmology. In the frame of this theory the gravitational interaction can have the repulsion character in the case of usual gravitating matter with positive values of energy density and pressure satisfying energy dominance condition. Cosmological consequences of gravitational repulsion are considered in the case of homogeneous isotropic models in connection with the problem of cosmological singularity and dark energy problem of general relativity theory. Regular Big Ban…
The general covariance principle, seen as an active version of the principle of equivalence, is used to study the gravitational coupling prescription in the presence of curvature and torsion. It is concluded that the coupling prescription determined by this principle is always equivalent with the corresponding prescription of general relativity. An application to the case of a Dirac spinor is made.
In this short review, we discuss the approach of the commutator algebra of covariant derivative to analyse the gravitational theories, starting from the standard Einstein's general theory of relativity and focusing on the Rastall theory. After that, we discuss the important role of the torsion in this mathematical framework. In the Appendix of the paper we analyse the importance of the nascent gravitational wave astronomy as a tool to discriminate among the general theory of relativity and alternative theories of gravity.
We recall some of the obstacles which arise when one tries to reconcile the general theory of relativity with quantum theory. We consider the possibility that gravitation theories which include torsion, and not only curvature, provide better insight into a quantum theory of gravity. We speculate on how the Dirac equation and Einstein gravity could be thought of as limiting cases of a gravitation theory which possesses torsion.
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…
We analyse a non-relativistic approximation of the Dirac equation for slow fermions, coupled to the chameleon field and torsion in the spacetime with the Schwarzschild metric, taken in the weak gravitational field of the Earth approximation. We follow the analysis of the Dirac equation in the curved spacetime with torsion, proposed by Kostelecky (Phys. Rev. D69, 105009 (2004)), and apply the Foldy--Wouthuysen transformations. We derive the effective low-energy gravitational potentials for slow fermions, coupled to the gravitational field of the Earth, the chameleon field and to torsion with mi…
A geometric torsion (GT) underlying a $2$-form in a $(4$$+$$1)$-dimensional $U(1)$ gauge theory is revisited with a renewed perspective for a non-perturbation (NP) gravity in $d$$=$$4$. In the context we provide evidences to a holographic correspondence between a bulk GT and a boundary NP gravity. Interestingly the Killing symmetries in General Relativity (GR) are shown to provide a subtle clue to the quantum gravity. The NP gravity is shown to incorporate a $(B_{2}$$ \wedge $$F_{2})$ coupling, sourced by a non-Newtonian potential, to an exact geometry in GR. Remarkably the NP correction is id…
The Horndeski Lagrangian brings together all possible interactions between gravity and a scalar field that yield second-order field equations in four-dimensional spacetime. As originally proposed, it only addresses phenomenology without torsion, which is a non-Riemannian feature of geometry. Since torsion can potentially affect interesting phenomena such as gravitational waves and early Universe inflation, in this paper we allow torsion to exist and propagate within the Horndeski framework. To achieve this goal, we cast the Horndeski Lagrangian in Cartan's first-order formalism, and introduce …
The teleparallel version of Lewis-Papapetrou space-time is investigated. For this space-time the true discussion of the geometric and physical properties is given. We show that the value of space-like torsion-axial vector does not depend on the choice of tetrad field. Consequently, the spin procession of the Dirac particle and the corresponding Hamiltonian do. The energy and momentum densities for such space-time are calculated. We show that when choosing two sets of tetrad fields the dependence and independence of the aforementioned quantities on the tetrad field depend on the Lorentz factor,…
In the framework of the teleparallel equivalent of general relativity, we study the dynamics of a gravitationally coupled electromagnetic field. It is shown that the electromagnetic field is able not only to couple to torsion, but also, through its energy-momentum tensor, to produce torsion. Furthermore, it is shown that the coupling of the electromagnetic field with torsion preserves the local gauge invariance of Maxwell's theory.
We give a complete formulation of Poincare gauge theory, starting from the fibre bundle formulation to the resultant Riemann-Cartan spacetime. We also introduce several diverse gravity theories descendent from the Poincare gauge theory. Especially, the cosmological effect of the simple scalar-torsion (0^+) mode in Poincare gauge theory of gravity is studied. In the theory, we treat the geometric effect of torsion as an effective quantity, which behaves like dark energy and study the effective equation of state (EoS) of the model. We construct the extra dimension theory of teleparallel gravity …
It is shown that all torsion-free vacuum solutions of the model of dS gauge theory of gravity are the vacuum solutions of Einstein field equations with the same positive cosmological constant. Furthermore, for the gravitational theories with more general quadratic gravitational Lagrangian ($F^2+T^2$), the torsion-free vacuum solutions are also the vacuum solutions of Einstein field equations.
The gravitational weak field of a global monopole in the Einstein-Cartan theory of gravity is investigated.To obtain this solution we assume that Cartan torsion takes the form of the Newtonian gravitational potential.From the geodesics it is possible to show that the torsionic monopole produces a repulsive gravitational force.
The role played by torsion in gravitation is critically reviewed. After a description of the problems and controversies involving the physics of torsion, a comprehensive presentation of the teleparallel equivalent of general relativity is made. According to this theory, curvature and torsion are alternative ways of describing the gravitational field, and consequently related to the same degrees of freedom of gravity. However, more general gravity theories, like for example Einstein-Cartan and gauge theories for the Poincare and the affine groups, consider curvature and torsion as representing …
Several exact cosmological solutions of a metric-affine theory of gravity with two torsion functions are presented. These solutions give a essentially different explanation from the one in most of previous works to the cause of the accelerating cosmological expansion and the origin of the torsion of the spacetime. These solutions can be divided into two classes. The solutions in the first class define the critical points of a dynamical system representing an asymptotically stable de Sitter spacetime. The solutions in the second class have exact analytic expressions which have never been found …
In the context of the metric-affine Chern-Simons gravity endowed with projective invariance, we derive analytical solutions for torsion and nonmetricity in the homogeneous and isotropic cosmological case, described by a flat Friedmann-Robertson-Walker metric. We discuss in some details the general properties of the cosmological solutions in the presence of a perfect fluid, such as the dynamical stability and the emergence of big bounce points, and we examine the structure of some specific solutions reproducing de Sitter and power law behaviours for the scale factor. Then, we focus on first-ord…
The simplest gauge gravitation theory in Riemann-Cartan space-time leading to the solution of the problem of cosmological singularity and dark energy problem is investigated with purpose to solve the dark matter problem. It is shown that the interaction of the vacuum torsion field with proper angular moments of gravitating objects can lead to appearance at astrophysical scale (galaxies, galactic clusters) additional force of gravitational attraction, which in the frame of standard theory is connected with dark matter.
I review a string-inspired cosmological model, with gravitational anomalies present at very early epochs, which includes a totally antisymmetric torsion, that in (3+1)-dimensions is equivalent to a pseudoscalar (Kalb-Ramond, string-model independent) axion field. Upon condensation of primordial gravitational waves (GW), that are created at a pre-inflationary era, the model leads to inflation of the so-called running-vacuum-model (RVM) type, which is realised without the need for external inflaton fields, being due to the non-linearities that characterise the gravitational theory. The model pro…
In the Einstein-Cartan space $U_4$, an axial vector torsion together with a scalar field connected to a local scale factor have been considered. By combining two particular terms from the SO(4,1) Pontryagin density and then modifying it in a SO(3,1) invariant way, we get a Lagrangian density with Lagrange multipliers. Then under FRW-cosmological background, where the scalar field is connected to the source of gravitation, the Euler-Lagrange equations ultimately give the constancy of the gravitational constant together with only three kinds of energy densities representing mass, radiation and c…
Noncommutative spectral geometry offers a purely geometric explanation for the standard model of strong and electroweak interactions, including a geometric explanation for the origin of the Higgs field. Within this framework, the gravitational, the electroweak and the strong forces are all described as purely gravitational forces on a unified noncommutative space-time. In this study, we infer a constraint on one of the three free parameters of the model, namely the one characterising the coupling constants at unification, by linearising the field equations in the limit of weak gravitational fi…
Scalar-tensor gravity theories with a nonminimal Gauss-Bonnet coupling typically lead to an anomalous propagation speed for gravitational waves, and have therefore been tightly constrained by multimessenger observations such as GW170817/GRB170817A. In this paper we show that this is not a general feature of scalar-tensor theories, but rather a consequence of assuming that spacetime torsion vanishes identically. At least for the case of a nonminimal Gauss-Bonnet coupling, removing the torsionless condition restores the canonical dispersion relation and therefore the correct propagation speed fo…
We propose a gravitational model which allows the independent dynamical behaviour of the torsion and nonmetricity fields to be displayed in the framework of Metric-Affine gauge theory of gravity. For this task, we derive a new exact black hole solution referred to this model which extends the role of torsion of the main well-known exact solutions based on Weyl-Cartan geometry and constitutes the first known isolated gravitational system characterized by a metric tensor with independent spin and dilation charges.
It is shown that among the R+beta S^{abc}S_{abc} models, only the one with beta=1/2 has nonvanishing torsion effect in the Robertson--Walker universe filled with a spin fluid, where S_{abc} denotes torsion. Moreover, the torsion effect in that model is found to be able to replace the big-bang singularity by a big bounce. Furthermore, we find that the model can be obtained under a Kaluza--Klein-like ansatz, by assuming that the gravitational gauge group is the de Sitter group.
Using the Fujikawa and the heat-kernel methods we make a complete and detailed computation of the global, gauge and gravitational anomalies present in the Standard Model defined on a curved space time with torsion. We find new contributions coming from curvature and torsion terms to the leptonic number anomaly (so that $B-L$ is not conserved any more), to the $U(1)_Y$ gauge and to the mixed $U(1)_Y$-gravitational anomalies, but the gauge anomaly cancellation conditions on the hypercharges remain the same. We also find that the condition, usually related to the cancellation of the mixed $U(1)_Y…
Static spherically symmetric solution in a background spacetime with torsion is derived explicitly. The torsion considered here is identified with the field strength of a second rank antisymmetric tensor field namely the Kalb-Ramond field and the proposed solution therefore has much significance in a string inspired gravitational field theory.
Recent theoretical work has shown that spin $1/2$ particles moving through unpolarized matter which sources torsion fields experience a new type of parity-even and time-reversal-odd optical potential if the matter is spinning in the lab frame. This new type of optical potential can be sought experimentally using the helicity dependence of the total cross sections for longitudinally polarized neutrons moving through a rotating cylindrical target. In combination with recent experimental constraints on short-range P--odd, T--even torsion interactions derived from polarized neutron spin rotation i…
A star of mass greater than a critical mass is believed to undergo gravitational collapse to form a singularity, owing to Hawking-Penrose singularity theorem which is based on the Raychaudhuri equation in the absence of torsion. We argue that the spin-aspect of matter can lead to the evasion of singularity, caused by its mass-aspect, via torsion in asymptotically safe gravity.
Using a recently found black hole solution in the framework of the Poincar{é} gauge theory of gravity, we study gravitational lensing for a system where the lens is a static spherically symmetric black hole. By analyzing the equations of motion for light rays in a space-time with torsion, we derive the deflection angle as the light emitted from a source pass through near the black hole and numerically solve the resulting integral. We also study the effects of torsion on the position of images. The results show that the presence of torsion slightly alters both the deflection angle and position …
Torsion gravitational effects in the quantum interference of charged particles are investigated. The influence of axial torsion in the Schiff-Banhill effect (SB) inside a metallic shell is given. The effect of torsion on the surface of the earth on (SB) experiment is estimated. Torsion gravity effects on the Sagnac phase-shift of neutron interferometry are also computed.
In a modest attempt to present potentially new paradigms in Cosmology, including its inflationary epoch, and initiate discussions, I review in this article some novel, string-inspired cosmological models, which entail a purely geometrical origin of the Dark sector of the Universe but also of its observed matter-antimatter asymmetry. The models contain gravitational (string-model independent, Kalb-Ramond (KR)) axion fields coupled to primordial gravitational anomalies via CP-violating interactions. The anomaly terms are four-space-time-dimensional remnants of the Green-Schwarz counterterms appe…
The present paper continues the work of the authors [arXiv:1306.6887 [gr-qc]]. Here, we study generally covariant metric-torsion theories of gravity presented more concretely, setting that their Lagrangians are \emph{manifestly} generally covariant scalars. It is assumed that Lagrangians depend on metric tensor, curvature tensor, torsion tensor and its first and second covariant derivatives, besides, on an arbitrary set of other tensor (matter) fields and their first and second covariant derivatives. Thus, both the standard minimal coupling with the Riemann-Cartan geometry and non-minimal coup…
We derive the most general effective low-energy potential to order O(1/m) for slow Dirac fermions with mass m, coupled to gravitational, chameleon and torsion fields in the Einstein-Cartan gravity. The obtained results can be applied to the experimental analysis of gravitational, chameleon and torsion interactions in terrestrial laboratories. We discuss the use of rotating coordinate systems, caused by rotations of devices, for measurements of the torsion vector and tensor components, caused by minimal torsion--fermion couplings (Ivanov and Wellenzohn, Phys. Rev. D92, 065006 (2015)). Using the…
