Poincarè gauge theory (PGT) is an alternative gravity theory, which attempts to bring the gravity into the gauge-theoretic frame, where the Lagrangian is quadratic in torsion and curvature. Recently, the cosmological models with torsion based on this theory have drawn many attentions, which try to explain the cosmic acceleration in a new way. Among these PGT cosmological models, the one with only even parity dynamical modes -- SNY model, for its realistic meaning, is very attractive. In this paper, we first analyze the past-time cosmic evolution of SNY model analytically. And based on these results we fit this model to the most comprehensive SNeIa data (Union 2) and thus find the best-fit values of model parameters and initial conditions, whose related $χ^{2}$ value is consistent with the one from $Λ$CMD at the 1$σ$ level. Also by the $χ^{2}$ estimate, we provide certain constraints on these parameters. Using these best-fit values for the Union 2 SNeIa dataset, we are able to predict the evolution of our real universe over the late time. From this prediction, we know the fate of our universe that it would expand forever, slowly asymptotically to a halt, which is in accordance with the earlier works.
We study a four-dimensional gauge theory of the Poincaré group with topological action which generalizes some well-known two-dimensional gravity models. We classify the spherically symmetric solutions and discuss the perturbative propagation of excitations around flat spacetime.
We derive a new exact static and spherically symmetric vacuum solution in the framework of the Poincaré gauge field theory with dynamical massless torsion. This theory is built in such a form that allows to recover General Relativity when the first Bianchi identity of the model is fulfilled by the total curvature. The solution shows a Reissner-Nordström type geometry with a Coulomb-like curvature provided by the torsion field. It is also shown the existence of a generalized Reissner-Nordström-de Sitter solution when additional electromagnetic fields and/or a cosmological constant are coupled t…
Analysis of regular inflationary cosmological models with two torsion functions filled with scalar field with quadratic potential and ultrarelativistic matter is carried out numerically. Properties of different stages of regular inflationary cosmological solutions are studied, restrictions on admissible values of parameters and initial conditions at transition from compression to expansion are found. The structure of extremum surface in space of physical variables is investigated.
The "dark energy" problem is investigated in the framework of the Poincare gauge theory of gravity in 4-dimensional Riemann-Cartan space-time. By using general expression for gravitational Lagrangian homogeneous isotropic cosmological models with pseudoscalar torsion function are built and investigated. It is shown that by certain restrictions on indefinite parameters of gravitational Lagrangian the cosmological equations at asymptotics contain effective cosmological constant and can lead to observable acceleration of cosmological expansion. This effect has geometrical nature and is connected …
In Poincare gauge theory of gravity, in addition to mass-energy content, spin is also a source for gravitational interactions. Although the effects of spin are negligible at low energies, they can play a crucial role at very early universe when the spin density was very high. In this paper by choosing a suitable Lagrangian for Poincare gauge theory of gravity, and suitable energy-momentum and spin density tensors, we show that the effects of spin and torsion can lead to a inflationary phase without the need for any additional fields. No fine tuning of parameters is required in this setup. We a…
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 …
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…
Black holes with torsion hair in cubic Holst-type Poincaré gauge gravity: from singular to regular geometries
Institute for Basic Science (IBS)（韩国基础科学研究所）；Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS)（宇宙理论物理中心，韩国基础科学研究所）；Center for Geometry and Physics, Institute for Basic Science (IBS)（几何与物理中心，韩国基础科学研究所）
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 …
Starting from the generalized pp waves that are exact vacuum solutions of general relativity with a cosmological constant, we construct a new family of exact vacuum solutions of Poincaré gauge theory, the generalized pp waves with torsion. The ansatz for torsion is chosen in accordance with the wave nature of the solutions. For a subfamily of these solutions, the metric is dynamically determined by the torsion.
We study the cosmological effect of the simple scalar-torsion ($0^+$) mode in Poincaré gauge theory of gravity. We find that for the non-constant (affine) curvature case, the early evolution of the torsion density $ρ_T$ has a radiation-like asymptotic behavior of $a^{-4}$ with $a$ representing the scale factor, along with the stable point of the torsion pressure ($P_T$) and density ratio $P_T/ρ_T\rightarrow 1/3$ in the high redshift regime $(z \gg 0)$, which is different from the previous result in the literature. We use the Laurent expansion to resolve the solution. We also illustrate our res…
In (1+2)-dimensional Poincaré gauge gravity, we start from a Lagrangian depending on torsion and curvature which includes additionally {\em translational} and {\em Lorentzian} Chern-Simons terms. Limiting ourselves to to a specific subcase, the Mielke-Baekler (MB) model, we derive the corresponding field equations (of Einstein-Cartan-Chern-Simons type) and find the general vacuum solution. We determine the properties of this solution, in particular its mass and its angular momentum. For vanishing torsion, we recover the BTZ-solution. We also derive the general conformally flat vacuum solution …
In this work we have studied the non-geodesical behaviour of particles with spin 1/2 in Poincaré gauge theories of gravity, via the WKB method and the Mathisson-Papapetrou equation. We have analysed the relation between the two approaches and we have argued the different advantages associated with the WKB approximation. Within this approach, we have calculated the trajectories in a particular Poincaré gauge theory, discussing the viability of measuring such a motion.
In this work the Poincare-Chern Simons and Anti de Sitter Chern Simons gravities are studied. For both a solution that can be casted as a black hole with manifest torsion is found. Those solutions resemble Schwarzschild and Schwarzschild-AdS solutions respectively.
We investigate the equation of state (EoS) of the scalar-torsion mode in Poincaré gauge theory of gravity. We concentrate on two cases with the constant curvature solution and positive kinetic energy, respectively. In the former, we find that the torsion EoS has different values in the various stages of the universe. In particular, it behaves like the radiation (matter) EoS of $w_r=1/3$ ($w_m=0$) in the radiation (matter) dominant epoch, while in the late time the torsion density is supportive for the accelerating universe. In the latter, our numerical analysis shows that in general the EoS ha…
A cosmology of Poincare gauge theory is developed, where several properties of universe corresponding to the cosmological equations with the pseudoscalar torsion function are investigated. The cosmological constant is found to be the intrinsic torsion and curvature of the vacuum universe and is derived from the theory naturally rather than added artificially, i.e. the dark energy originates from geometry and includes the cosmological constant but differs from it. The cosmological constant puzzle, the coincidence and fine tuning problem are relieved naturally at the same time. By solving the co…
Changing the set of independent variables of Poincare gauge theory and considering, in a manner similar to the second order formalism of general relativity, the Riemannian part of the Lorentz connection as function of the tetrad field, we construct theories that do not contain second or higher order derivatives in the field variables, possess a full general relativity limit in the absence of spinning matter fields, and allow for propagating torsion fields in the general case. A concrete model is discussed and the field equations are reduced by means of a Yasskin type ansatz to a conventional E…
In the framework of the gauge theory based on the Poincaré symmetry group, the gravitational field is described in terms of the coframe and the local Lorentz connection. Considered as gauge field potentials, they give rise to the corresponding field strength which are naturally identified with the torsion and the curvature on the Riemann--Cartan spacetime. We study the class of quadratic Poincaré gauge gravity models with the most general Yang--Mills type Lagrangian which contains all possible parity-even and parity-odd invariants built from the torsion and the curvature. Exact vacuum solution…
A self-consistent model which can unify Starobinsky inflation and the $Λ$CDM model in the framework of Poincaré gauge cosmology (PGC) is studied in this work, without extra inflaton and ``dark energy''. We start from the general nine-parameter PGC Lagrangian and get two Friedmann-like analytical solutions with the certain ghost- and tachyon-free conditions on the Lagrangian parameters. The scalar torsion $h$-determined solution is consistent with Starobinsky cosmology in the early-time and the pseudo-scalar torsion $f$-determined solution contains naturally a constant ``dark energy'' density, …
We obtain the Schwarzschild solution based on teleparallel gravity (TG) theory formulated in a space-time with torsion only. The starting point is the Poincar\UNICODE{0xe9} gauge theory (PGT).The general structure of TG and its connection with general relativity (GR) are presented and the Schwarzschild solution is obtained by solving the field equations of TG. Most of calculations are performed using the GRTensorII package, running on the MapleV platform.
Homogeneous isotropic models built in the framework of the Poincaré gauge theory of gravity (PGTG) based on general expression of gravitational Lagrangian without cosmological constant are analyzed. It is shown that the physical spacetime in the vacuum in the frame of PGTG can have the structure of flat de Sitter spacetime with torsion. Some physical consequences of obtained conclusion are discussed.
We apply the teleparallelism condition to the Poincaré gauge theory of gravity. The resultant teleparallelized cosmology is completely equivalent to the Friedmann cosmology derived from Einstein's general theory of relativity. The torsion is shown to play the role of the cosmological constant driving the cosmic acceleration. We then extend such theory to include the effect of spin and explore the possibility of accounting for the current accelerating universe by a spinning dark energy.
We find a new exact vacuum solution in the framework of the Poincaré Gauge field theory with massive torsion. In this model, torsion operates as an independent field and introduces corrections to the vacuum structure present in General Relativity. The new static and spherically symmetric configuration shows a Reissner-Nordström-like geometry characterized by a spin charge. It extends the known massless torsion solution to the massive case. The corresponding Reissner-Nordström-de Sitter solution is also compatible with a cosmological constant and additional U(1) gauge fields.
Ever since E.Cartan in the 1920s enriched the geometric framework of general relativity (GR) by introducing a {\it torsion} of spacetime, the question arose whether one could find a measurement technique for detecting the presence of a torsion field. Mao et al.(2007) claimed that the rotating quartz balls in the gyroscopes of the Gravity Probe B experiment, falling freely on an orbit around the Earth, should "feel" the torsion. Similarly, March et al.(2011) argue with the precession of the Moon and the Mercury and extend later their considerations to the Lageos satellite.--- A consistent theor…
We investigate two-dimensional higher derivative gravitational theories in a Riemann-Cartan framework and obtain the most general static black hole solutions in conformal coordinates. We also consider the hamiltonian formulation of the theory and discuss its symmetries, showing they are implemented by a non-linear generalizations of the 2-dimensional Poincaré algebra. Finally, we discuss the quantization in the Dirac formalism.
It is shown that cosmological equations for homogeneous isotropic models deduced in the framework of the Poincaré gauge theory of gravity by certain restrictions on indefinite parameters of gravitational Lagrangian take at asymptotics the same form as cosmological equations of general relativity theory for $ΛCDM$-model. Terms related to dark matter and dark energy in cosmological equations of standard theory for $ΛCDM$-model are connected in considered theory with the change of gravitational interaction provoked by spacetime torsion.
In the present work, we {study} static spherically symmetric solutions representing wormhole configurations in Poincarè gauge theory ({\sf PGT}). The gravitational sector of the Lagrangian is chosen as a subclass of {\sf PGT} Lagrangians for which, the spin-$0^+$ is the only propagating torsion mode. The spacetime torsion in {\sf PGT} has a dynamical nature even in the absence of intrinsic angular momentum (spin) of matter, hence, {torsion can play a principal role in the case of usual spin-less gravitating systems. We therefore} consider a spin-less matter distribution with an anisotropic ene…
Institute for Basic Science (IBS)（韩国基础科学研究所）；Cosmology, Gravity, and Astroparticle Physics Group, Center for Theoretical Physics of the Universe（宇宙学、引力与天体物理组，宇宙理论物理中心）；Center for Geometry and Physics（几何与物理中心）
A systematic analysis of the symmetries of topological 3D gravity with torsion and a cosmological term, in the first order formalism, has been performed in details - both in the hamiltonian and lagrangian formalisms. This illuminates the connection between the symmetries of curved spacetime (diffeomorphisms plus local Lorentz transformations) with the Poincare gauge transformations. The Poincare gauge symmetries of the action are shown to be inequivalent to its gauge symmetries. Finally, the complete analysis is compared with the metric formulation where the diffeomorphism symmetry is shown to…
Cosmological solutions for homogeneous isotropic models in the framework of the Poincaré gauge theory of gravity based on gravitational Lagrangian adopted in the paper by Kun-Feng Shie, James M. Nester and Hwei-Jang Yo (Phys. Rev. D \textbf{78}, 023522 (2008)) are discussed. Cosmological solutions for accelerating Universe obtained in referred paper are compared with corresponding solutions of standard $ΛCDM$-model and also with cosmological solution obtained by authors of this Comment.
Minimal coupling of a Dirac field to gravity with the most general non-propagating torsion is considered in (1+2)-dimensions. The field equations are obtained from a lagrangian by a variational principle. The space-time torsion is calculated algebraically in terms of a quadratic spinor condensate plus coupling coefficients. Firstly we give circularly symmetric rotating exact solutions that collapse to $AdS_3$ geometry in the absence of the Dirac condensate. Secondly we investigate a BTZ-like solution.
We investigate the propagation of light rays and evolution of optical scalars in gauge theories of gravity where torsion is present. Recently the modified Raychaudhuri equation in the presence of torsion has been derived. We use this result to derive the basic equations of geometric optics for several different interesting solutions of the Poincar{é} gauge theory of gravity. The results show that the focusing effects for neighboring light rays will be different than general relativity. This in turn has practical consequences in the study of gravitational lensing effects and also determining th…
A Poincaré gauge theory of (2+1)-dimensional gravity is developed. Fundamental gravitational field variables are dreibein fields and Lorentz gauge potentials, and the theory is underlain with the Riemann-Cartan space-time. The most general gravitational Lagrangian density, which is at most quadratic in curvature and torsion tensors and invariant under local Lorentz transformations and under general coordinate transformations, is given. Gravitational field equations are studied in detail, and solutions of the equations for weak gravitational fields are examined for the case with a static, \lq \…
Poincaré gauge theories provide an approach to gravity based on the gauging of the Poincaré group, whose homogeneous part generates curvature while the translational sector gives rise to torsion. In this note we revisit the stability of the widely studied quadratic theories within this framework. We analyse the presence of ghosts without fixing any background by obtaining the relevant interactions in an exact post-Riemannian expansion. We find that the axial sector of the theory exhibits ghostly couplings to the graviton sector that render the theory unstable. Remarkably, imposing the absence …
Gauge theories of gravity provide an elegant and promising extension of general relativity. In this paper we show that the Poincaré gauge theory exhibits gravity-induced birefringence under the assumption of a specific gauge invariant nonminimal coupling between torsion and Maxwell's field. Furthermore we give for the first time an explicit expression for the induced phaseshift between two orthogonal polarization modes within the Poincaré framework. Since such a phaseshift can lead to a depolarization of light emitted from an extended source this effect is, in principle, observable. We use whi…
The Hamiltonian constraint formalism is used to obtain the first explicit complete analysis of non-trivial viable dynamic modes for the Poincaré gauge theory of gravity. Two modes with propagating spin-zero torsion are analyzed. The explicit form of the Hamiltonian is presented. All constraints are obtained and classified. The Lagrange multipliers are derived. It is shown that a massive spin-$0^-$ mode has normal dynamical propagation but the associated massless $0^-$ is pure gauge. The spin-$0^+$ mode investigated here is also viable in general. Both modes exhibit a simple type of ``constrain…
We study the gauge symmetries in a Mielke-Baekler type model of gravity in 2+1 dimensions. The model is built in a Poincare gauge theory framework where localisation of Poincare symmetries lead to gravity. However, explicit construction of gauge symmetries in the model through a Hamiltonian procedure yields an apparently different set of symmetries, as has been noted by various authors. Here, we show that the two sets of symmetries are actually equivalent in a canonical sense, their difference being just a set of trivial symmetries.
We study the coupling of the gravitational action, which is a linear combination of the Hilbert-Palatini term and the quadratic torsion term, to the action of Dirac fermions. The system possesses local Poincare invariance and hence belongs to Poincare gauge theory with matter. The complete Hamiltonian analysis of the theory is carried out without gauge fixing but under certain ansatz on the coupling parameters, which leads to a consistent connection dynamics with second-class constraints and torsion. After performing a partial gauge fixing, all second-class constraints can be solved, and a SU(…
We review the basics and the current status of the Poincaré gauge theory of gravity. The general dynamical scheme of Poincaré gauge gravity (PG) is formulated, and its physical consequences are outlined. In particular, we discuss exact solutions with and without torsion, highlight the cosmological aspects, and consider the probing of the spacetime geometry.
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…
A class of Siklos waves, representing exact vacuum solutions of general relativity with a cosmological constant, is extended to a new class of Siklos waves with torsion, defined in the framework of the Poincaré gauge theory. Three particular exact vacuum solutions of this type, the generalized Kaigorodov, the homogeneous and the exponential solution, are explicitly constructed.
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 …
In the gauge theory of gravity based on the Poincare group (the semidirect product of the Lorentz group and the spacetime translations) the mass (energy-momentum) and the spin are treated on an equal footing as the sources of the gravitational field. The corresponding spacetime manifold carries the Riemann-Cartan geometric structure with the nontrivial curvature and torsion. We describe some aspects of the classical Poincare gauge theory of gravity. Namely, the Lagrange-Noether formalism is presented in full generality, and the family of quadratic (in the curvature and the torsion) models is a…
The canonical approach to black hole entropy in Poincaré gauge theory without matter is extended to include Maxwell field as a matter source. The new formalism is used to calculate asymptotic charges and entropy of Kerr--Newmann--AdS black holes with torsion. The result implies that the first law, with a nontrivial contribution of the Maxwell field, takes the same form as in general relativity.
We construct Kaluza--Klein-type models with a de Sitter or Minkowski bundle in the de Sitter or Poincaré gauge theory of gravity, respectively. A manifestly gauge-invariant formalism has been given. The gravitational dynamics is constructed by the geometry of the de Sitter or Minkowski bundle and a global section which plays an important role in the gauge-invariant formalism. Unlike the old Kaluza--Klein-type models of gauge theory of gravity, a suitable cosmological term can be obtained in the Lagrangian of our models and the models in the spin-current-free and torsion-free limit will come ba…
The stable pseudo-scalar degree of freedom of the quadratic Poincaré Gauge theory of gravity is shown to be a suitable dark matter candidate. We find the parameter space of the theory which can account for all the predicted cold dark matter, and constrain such parameters with astrophysical observations.
We derive the exact gravitational wave solutions in a general class of quadratic Poincaré gauge gravity models. The Lagrangian includes all possible linear and quadratic invariants constructed from the torsion and the curvature, including the parity odd terms. The ansatz for the gravitational wave configuration and the properties of the wave solutions are patterned following the corresponding ansatz and the properties of the plane-fronted electromagnetic wave.
Homogeneous isotropic models with two torsion functions built in the framework of the Poincare gauge theory of gravity based on general expression of gravitational Lagrangian by certain restrictions on indefinite parameters are analyzed numerically. Special points of cosmological solutions at asymptotics and conditions of their stability in dependence of indefinite parameters are found. Procedure of numerical integration of the system of gravitational equations at asymptotics is considered. Numerical solution for accelerating Universe without dark energy and dark matter is obtained. It is show…
In this work we present a gauge-invariant three-dimensional teleparallel supergravity theory using the Chern-Simons formalism. The present construction is based on a supersymmetric extension of a particular deformation of the Poincaré algebra. At the bosonic level the theory describes a non-Riemannian geometry with a non-vanishing torsion. In presence of supersymmetry, the teleparallel supergravity theory is characterized by a non-vanishing super-torsion in which the cosmological constant can be seen as a source for the torsion. We show that the teleparallel supergravity theory presented here …
The Poincaré (inhomogeneous Lorentz) group underlies special relativity. In these lectures a consistent formalism is developed allowing an appropriate gauging of the Poincaré group. The physical laws are formulated in terms of points, orthonormal tetrad frames, and components of the matter fields with respect to these frames. The laws are postulated to be gauge invariant under local Poincaré transformations. This implies the existence of 4 translational gauge potentials ${e}^α$ (``gravitons") and 6 Lorentz gauge potentials $Γ^{αβ}$ (``rotons") and the coupling of the momentum current and the s…
Using a Hamiltonian approach, we introduce black hole entropy for Kerr-AdS spacetimes with torsion as the canonical charge on horizon. In spite of a completely different geometric setting with respect to GR, the resulting thermodynamic variables, energy, angular momentum and entropy, are shown to be proportional to the corresponding GR expressions. The validity of the first law is confirmed.
