We describe a framework for a generalized nonlocal gravity theory inspired by Poincaré gauge theory. Our theory provides a unified description of previous nonlocal extensions of Einstein's theory of gravitation, in particular it allows for a clear geometrical foundation. Furthermore, it incorporates recent simplifications for the ansatz of the nonlocality, which should allow for a systematic study of the impact of nonlocal concepts on observations.
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.
The minimal coupling procedure, which is employed in standard Yang-Mills theories, appears to be ambiguous in the case of gravity. We propose a slight modification of this procedure, which removes the ambiguity. Our modification justifies some earlier results concerning the consequences of the Poincaré gauge theory of gravity. In particular, the predictions of the Einstein-Cartan theory with fermionic matter are rendered unique.
The Poincaré invariance of GR is usually interpreted as Lorentz invariance plus diffeomorphism invariance. In this paper, by introducing the local inertial coordinates (LIC), it is shown that a theory with Lorentz and diffeomorphism invariance is not necessarily Poincaré invariant. Actually, the energy-momentum conservation is violated there. On the other hand, with the help of the LIC, the Poincaré invariance is reinterpreted as an internal symmetry. In this formalism, the conservation law is derived, which has not been sufficiently explored before.
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…
We prove that the Minkowski spacetime is stable at nonlinear level and to all perturbative orders in the gravitational perturbation in a general class of nonlocal gravitational theories that are unitary and finite at quantum level.
In this work we review the study of singularities in Poincaré gauge theories of gravity. Since one of the most recent studies uses the appearance of black hole regions of arbitrary dimension as an indicator of singular behaviour, we also give some explicit examples of these structures and study how particles behave around them.
We construct a Hamiltonian for the nonlocal F(R) theory in the present work. By this construction, we demonstrate the nature of the ghost degrees of freedom. Finally, we find conditions that give rise to ghost-free theories
We analyze the structure of a recent nonlocal generalization of Einstein's theory of gravitation by Mashhoon et al. By means of a covariant technique, we derive an expanded version of the nonlocality tensor which constitutes the theory. At the lowest orders of approximation, this leads to a simplification which sheds light on the fundamental structure of the theory and may prove useful in the search for exact solutions of nonlocal gravity.
The stability of the de-Sitter universe in nonlocal gravity
School of Physics and Electronic Engineering, Shanxi Normal University（山西师范大学物理与电子工程学院）；College of Physical Science and Technology, Hebei University（河北大学物理科学与技术学院）
In this work, we construct the logical framework of the Poincaré gauge gravity cosmology based on five postulations, and introduce the modified redshift relation within this framework. Then we solve a system with quadratic action and some other assumptions to get an analytic solution on background level. The evolution of the Universe on background can be reproduced from this solution without hypothesizing dark energy. Further, we use the type Ia supernova data set JLA to test the effect of the modified redshift relation under the constraints of system parameters. The results show that the cons…
A complete basis of nonlocal invariants in quantum gravity theory is built to third order in spacetime curvature and matter-field strengths. The nonlocal identities are obtained which reduce this basis for manifolds with dimensionality $2ω<6$. The present results are used in heat-kernel theory, theory of gauge fields and serve as a basis for the model-independent approach to quantum gravity and, in particular, for the study of nonlocal vacuum effects in the gravitational collapse problem.
Nonlocal gravity (NLG) is a classical nonlocal generalization of Einstein's theory of gravitation based on a certain analogy with the nonlocal electrodynamics of media. The history dependence enters NLG through a constitutive relation involving a causal kernel that should ultimately be determined via observational data. The purpose of this paper is to reformulate nonlocal gravity such that the nonlocal aspect of the constitutive relation directly connects measurable quantities as in the nonlocal electrodynamics of media. The resulting constitutive relation turns out to coincide with the recent…
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…
Nonlocal gravity models are constructed to explain the current acceleration of the universe. These models are inspired by the infrared correction appearing in Einstein Hilbert action. Here we develop the Hamiltonian formalism of a nonlocal model by considering only terms to quadratic order in Ricci tensor and Ricci scalar. We also show how to count the degree of freedom using Hamiltonian formalism in this model.
We consider cosmological properties of modified gravity with nonlocal term $ R^p\mathcal{F}(\Box)R^q$ in its Lagrangian. Equations of motion are presented. For the flat FLRW metric, and some particular values of natural numbers $p$ and $q$ cosmological solutions of the form $a(t)= C e^{- \frac γ{12}t^2}$ are found.
The field equations of the recent nonlocal generalization of Einstein's theory of gravitation are presented in a form that is reminiscent of general relativity. The implications of the nonlocal field equations are studied in the case of conformally flat spacetimes. Even in this simple case, the field equations are intractable. Therefore, to gain insight into the nature of these equations, we investigate the structure of nonlocal gravity in two-dimensional spacetimes. While any smooth 2D spacetime is conformally flat and satisfies Einstein's field equations, only a subset containing either a Ki…
It was recently found that there are classes of nonlocal gravity theories that are free of ghosts and singularities in their Newtonian limit [PRL, 108 (2012), 031101]. In these proceedings, a detailed and pedagogical derivation of a main result, the flat space propagator for an arbitrary covariant metric theory of gravitation, is presented. The result is applied to analyse f(R) models, Gauss-Bonnet theory, Weyl-squared gravity and the potentially asymptotically free nonlocal theories.
It is shown that the gauge field in Poincare-gauge theory of gravity consists in two parts: the translational gauge field (t -field), which is generated by the energy-momentum current of external fields, and the rotational gauge field (r -field), which is generated by the sum of the angular and spin momentum currents of external fields. In connection with this the physical field generating by rotating masses should exist.
A higher dimensional modified gravity theory with an action that includes dimensionally continued Euler-Poincaré forms up to second order in curvatures is considered. The variational field equations are derived. Matter in the universe at large scales is modeled by a fluid satisfying an equation of state with dimensional dichotomy. We study solutions that describe higher dimensional steady state cosmologies with constant volume for which the three dimensional external space is expanding at an accelerated rate while the (compact) internal space is contracting. We showed that the second order Eul…
In order to explain the late-time cosmological acceleration, we propose a new pure geometric gravity based on Deser-Woodard theory, in which the expansion of a matter-dominated universe can be accelerating. This new theory behaves as well as general relativity in solar system and gravitational waves, which is an important improvement over Deser-Woodard nonlocal gravity. Especially, for the simplest case, theoretical considerations determine all the parameters that appear in the Lagrangian.
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 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…
Nonlocal gravity (NLG) is a classical nonlocal generalization of Einstein's theory of gravitation developed in close analogy with the nonlocal electrodynamics of media. It appears that the nonlocal aspect of the universal gravitational interaction could simulate dark matter. Within the Newtonian regime of NLG, we investigate the deviation of the gravitational force from the Newtonian inverse square law as a consequence of the existence of the effective dark matter. In particular, we work out the magnitude of this deviation in the solar system out to 100 astronomical units. Moreover, we give an…
The gauge approach to the theory of gravity has been widely discussed as an alternative to standard general relativity. The Poincar{é} group, as a symmetry group of all relativistic theories in the absence of gravitation, constitutes the most natural candidate for a gauge group. Although the Poincar{é} gauge theory of gravity has been elaborated over the years and cast into a beautiful formal framework, some fundamental problems have remained unsolved. One of them concerns the inclusion of matter. The minimal coupling procedure, which is employed in standard Yang--Mills theories, appears to be…
It is shown explicitly that in the framework of Bohmian quantum gravity, the equations of motion of the space-time metric are Einstein's equations plus some quantum corrections. It is observed that these corrections are not covariant. So that in the framework of Bohmian quantum gravity the general covariance principle breaks down at the individual level. This principle is restored at the statistical level.
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 …
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.
A nonlocal form of the effective gravitational action could cure the unboundedness of euclidean gravity with Einstein action. On sub-horizon length scales the modified gravitational field equations seem compatible with all present tests of general relativity and post-Newtonian gravity. They induce a difference in the effective Newton's constant between regions of space with vanishing or nonvanishing curvature scalar (or Ricci tensor). In cosmology they may lead to a value $Ω<1$ for the critical density after inflation. The simplest model considered here appears to be in conflict with nucleosyn…
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…
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.
Here, we derive the metric for the spacetime around rotating object for the gravity action having nonlocal correction of $R\Box^{-2} R $ to the Einstein-Hilbert action. Starting with the generic stationary, axisymmetric metric, we solve the equations of motion in linearized gravity limit for the modified action including energy-momentum tensor of the rotating mass. We also derive the rotating metric from the static metric using the Demanski-Janis-Newmann algorithm. Finally, we obtain the constraint on the value of $M$ by calculating the frame dragging effect in our theory and comparing it with…
We demonstrate that Einstein's general relativity theory arises as a special case in the framework of the Poincaré gauge theory of gravity under the assumption of a suitable nonminimal coupling of matter to the Riemann-Cartan geometry of spacetime.
The strong gravitational field near massive blackhole is an interesting regime to test General Relativity(GR) and modified gravity theories. The knowledge of spacetime metric around a blackhole is a primary step for such tests. Solving field equations for rotating blackhole is extremely challenging task for the most modified gravity theories. Though the derivation of Kerr metric of GR is also demanding job, the magical Newmann-Janis algorithm does it without actually solving Einstein equation for rotating blackhole. Due to this notable success of Newmann-Janis algorithm in the case of Kerr met…
We give an introductory overview of the classical Poincaré gauge theory of gravity formulated on the spacetime manifold that carries the Riemann-Cartan geometry with nontrivial curvature and torsion. After discussing the basic mathematical structures at an elementary level in the framework of the standard tensor analysis, we formulate the general dynamical scheme of Poincaré gauge gravity for the class of Yang-Mills type models, and consider a selected number of physically interesting consequences of this theory.
Recently the non-local gravity theory has come out to be a good candidate for an effective field theory of quantum gravity and also it can provide rich phenomenology to understand late-time accelerating expansion of the universe. For any valid theory of gravity, it has to surmount solar system tests as well as strong field tests. Having motivations to prepare the framework for the strong field test of the modified gravity using Extreme Mass Ratio Inspirals(EMRIs), here we try to obtain the metric for Kerr-like blackhole for a non-local gravity model known as RR model and calculate the shift in…
With the help of Weil polynomials on the Lie algebra of the Poincaré group in D dimensions, we construct a Lagrangian form for higher dimensional gravity on a principal fibre bundle whose base space is an even-dimensional Riemann-Cartan spacetime and whose structure group is the Poincaré group.
Foundations of the Poincaré-gauge theory of gravity are developed. It is shown that the Poincaré-gauge field consists of two components: the translational gauge field ($t$-field), which is generated by the energy-momentum current of external fields, and the rotational gauge field ($r$-field), which is generated by the sum of the angular and spin momentum currents of external fields. Therefore, a physical field generated by the angular momentum of a rotating mass should exist.
Contrary to recent claims in the literature, a simple test for reflection positivite, which we call perturbative reflection positivity in the coincidence limit, is shown to be satisfied for nonlocal field theories. Particular attention is given to weakly nonlocal gravity and gauge theories.
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.
Within the framework of the minimum quadratic Poincare gauge theory of gravity in the Riemann-Cartan spacetime the dynamics of homogeneous anisotropic Bianchi types I-IX spinning-fluid cosmological models is investigated. A basic equation set for these models is obtained and analyzed. In particular, exact solutions for the Bianchi type-I spinning-fluid and Bianchi type-V perfect-fluid models are found in analytic form.
Defining a new r-matrix compatible with the scalar product at the basis of the Chern-Simons action for a particle coupled to (2+1) Lorentzian gravity with cosmological constant, I show how deformed symmetries of $κ$-de Sitter and, in the vanishing cosmological limit, of $κ$-Poincaré kind, arise naturally as quantum-deformation of three dimensional gravity. I obtain moreover the non-commutative spacetime associated to these kinds of symmetries.
We study the causal structure of a class of weakly nonlocal gravitational theories (eventually coupled to matter) that are compatible with perturbative unitarity and finiteness at quantum level. In particular, we show that in nonlocal quantum gravity a Shapiro's time advance never occurs. Moreover, we provide a recipe to construct a general ultraviolet complete gravitational theory coupled to matter (with or without supersymmetry) compatible with causality. Therefore, nonlocal gravity is consistent with causality, as well as string theory.
We analyse the parity violation issue in the Poincaré gauge theory of gravity for the two classes of models which are built as natural extensions of the Einstein-Cartan theory. The conservation laws of the matter currents are revisited and we clarify the derivation of the effective Einstein field equation and the structure of the effective energy-momentum current for arbitrary matter sources.
We consider a nonlocal gravity model motivated by nonperturbative Quantum Gravity studies. This model, if correct, suggests the existence of strong IR relevant effects which can lead to an interesting late time cosmology. We implement the IR modification directly in the effective action. We show that, upon some assumptions on initial conditions, this model describes an observationally viable background cosmology being also consistent with local gravity tests.
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…
We discuss the choice of the Lagrangian in the Poincaré gauge theory of gravity. Drawing analogies to earlier de Sitter gauge models, we point out the possibility of deriving the Einstein-Cartan Lagrangian {\it without} cosmological term from a {\it modified} quadratic curvature invariant of {\it topological} type.
We consider a new modified gravity model with nonlocal term of the form $R^{-1} \mathcal{F}(\Box) R. $ This kind of nonlocality is motivated by investigation of applicability of a few unusual ansätze to obtain some exact cosmological solutions. In particular, we find attractive and useful quadratic ansatz $\Box R = q R^{2}.$
We address the stability issue of Ricci-flat and maximally symmetric spacetimes in nonlocal gravity to all perturbative orders in the gravitational perturbation. Assuming a potential at least cubic in curvature tensors but quadratic in the Ricci tensor, our proof consists on a mapping of the stability analysis in nonlocal gravity to the same problem in Einstein-Hilbert theory. One of the consequences is that only the graviton field can propagate and the theory is ghost-free at all perturbative orders. All the results known in Einstein gravity in vacuum with or without a cosmological constant c…
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…
It is shown that gravity on the line can be described by the two dimensional (2D) Hilbert-Einstein Lagrangian supplemented by a kinetic term for the coframe and a translational {\it boundary} term. The resulting model is equivalent to a Yang-Mills theory of local {\it translations} and frozen Lorentz gauge degrees. We will show that this restricted Poincaré gauge model in 2 dimensions is completely integrable. {\it Exact} wave, charged black hole, and `dilaton' solutions are then readily found. In vacuum, the integrability of the {\it general} 2D Poincaré gauge theory is formally proved along …
Nonlocal gravity is the recent classical nonlocal generalization of Einstein's theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial theorem for the Newtonian regime of nonlocal gravity theory is derived and its consequences for "isolated" astronomical systems in virial equilibrium at the present epoch are investigated. In particular, for a sufficiently isolated nearby galaxy in virial equilibrium, the galaxy's baryonic diameter---namely, the diameter of the smallest sphere that …
The recent classical nonlocal generalization of Einstein's theory of gravitation is presented within the framework of general relativity via the introduction of a preferred frame field. The nonlocal generalization of Einstein's field equations is derived. The linear approximation of nonlocal gravity (NLG) is thoroughly examined and the solutions of the corresponding field equations are discussed. It is shown that nonlocality, with a characteristic length scale of order 1 kpc, simulates dark matter in the linear regime while preserving causality. Light deflection in linearized nonlocal gravity …
Based on the ultraviolet asymptotic freedom of nonlocal quantum gravity, we show that the trans-Planckian energy regime is unattainable in laboratory experiments. As physical implications, it turns out that the violation of causality, typical of nonlocal field theories, can never be detected in particle accelerators, while the asymptotic freedom of the theory provides an elegant solution to the so called trans-Planckian cosmological problem.
