We revisit an emergent gravity scenario in $(4+1)$ dimensions underlying a propagating geometric torsion ${\cal H}_3$ with a renewed interest. We show that a pair-symmetric $4$th order curvature tensor is sourced by a two-form Neveu-Schwarz (NS) in a $U(1)$ gauge theoretic formulation. Interestingly the new space-time curvature governs a torsion free geometry sourced by a two-form NS field and shares the properties of the Riemann tensor. On the other hand, a completely anti-symmetric $4$th order tensor in the formulation is shown to incorporate a dynamical geometric torsion correction and is argued to be identified with a non-perturbative correction. The four-form turns out to be $U(1)$ gauge invariant underlying an onshell NS form. We show that an emergent gravity theory may elegantly be described with an axionic scalar presumably signifying a quintessence coupling to the Riemann type geometries. The curvatures are appropriately worked out to obtain a $d$$=$$12$ emergent {\it form} theory. Investigation reveals that a pair of $(M{\bar M})_{10}$-brane is created across an event horizon. We show that an emergent $M$ theory in a decoupling limit identifies with the bosonic sector of $N$$=$$1$ Supergravity in $d$$=$$11$.
In the framework of teleparallel equivalent of general relativity, we study a gravity theory where a scalar field beyond its minimal coupling, is also coupled with the vector torsion through a non-minimal derivative coupling. After a suitable choice of auxiliary variables that allows us to perform the phase-space analysis of the model we obtain the critical points and their stability. While there is no scaling attractor in non-interacting scenario, by considering an interaction between dark energy and dark matter, we find scaling attractors in which the fractional densities of dark energy and …
A non-minimal photon-torsion axial coupling in the quantum electrodynamics (QED) framework is considered. The geometrical optics in Riemann-Cartan spacetime is considering and a plane wave expansion of the electromagnetic vector potential is considered leading to a set of the equations for the ray congruence. Since we are interested mainly on the torsion effects in this first report we just consider the Riemann-flat case composed of the Minkowskian spacetime with torsion. It is also shown that in torsionic de Sitter background the vacuum polarisation does alter the propagation of individual ph…
In this paper, we provide a vacuum solution with torsion in quadratic Riemann-curvature gravity. Physically, the solution means that vacuum can have a nonzero vacuum field with large torsion. We show that the Einstein-Hilbert action can be derived if we expand the quadratic curvature of the Lagrangian in a torsion-free Riemannian space-time around a nonzero vacuum field. We also show that the cosmological constant caused by a nonzero vacuum field is equal to zero.
The issues of quintessence and cosmic acceleration can be discussed in the framework of $F(R, {\cal G})$ theories of gravity where $R$ is the Ricci curvature scalar and ${\cal G}$ is the Gauss-Bonnet topological invariant. It is possible to show that such an approach exhausts all the curvature content related to the Riemann tensor giving rise to a fully geometric approach to dark energy.
Starting with topological field theories we investigate the Ray-Singer analytic torsion in three dimensions. For the lens Spaces L(p;q) an explicit analytic continuation of the appropriate zeta functions is contructed and implemented. Among the results obtained are closed formulae for the individual determinants involved, the large $p$ behaviour of the determinants and the torsion, as well as an infinite set of distinct formulae for zeta(3): the ordinary Riemann zeta function evaluated at s=3. The torsion turns out to be trivial for the cases L(6,1), L((10,3) and L(12,5) and is, in general, gr…
We obtain explicit expressions for the determinants of the Laplacians on zero and one forms for an infinite class of three dimensional lens spaces $L(p,q)$. These expressions can be combined to obtain the Ray-Singer torsion of these lens spaces. As a consequence we obtain an infinite class of formulae for the Riemann zeta function $ζ(3)$. The value of these determinants (and the torsion) grows as the size of the fundamental group of the lens space increases and this is also computed. The triviality of the torsion for just the three lens spaces $L(6,1)$, $L(10,3)$ and $L(12,5)$ is also noted. (…
Dynamo action is shown to be induced from homogeneous non-minimal photon-torsion axial coupling in the quantum electrodynamics (QED) framework in Riemann flat spacetime contortion decays. The geometrical optics in Riemann-Cartan spacetime is considering and a plane wave expansion of the electromagnetic vector potential is considered leading to a set of the equations for the ray congruence. Since we are interested mainly on the torsion effects in this first report we just consider the Riemann-flat case composed of the Minkowskian spacetime with torsion. It is also shown that in torsionic de Sit…
We revisit an effective space-time torsion curvature in a second order formalism, underlying the non-linear $U(1)$ gauge dynamics, of a two form on a $D_4$-brane in type IIA superstring theory. The formalism incorporates the significance of a global NS two form into the theory via its perturbative coupling to a dynamical two form. In particular, we explore the non-linear gauge dynamics on a $D_4$-brane in presence of a non-trivial background metric. The fact that the global modes of a NS two form in an open string theory sources the background metric on a $D_4$-brane may hint at the existence …
Connections with (skew-symmetric) torsion on non-symmetric Riemannian manifold satisfying the Einstein metricity condition (NGT with torsion) are considered. It is shown that an almost Hermitian manifold is an NGT with torsion if and only if it is a Nearly Kähler manifold. In the case of an almost contact metric manifold the NGT with torsion spaces are characterized and a possibly new class of almost contact metric manifolds is extracted. Similar considerations lead to a definition of a particular classes of almost para-Hermitian and almost paracontact metric manifolds. The conditions are give…
We study Spin(9)-structures on 16-dimensional Riemannian manifolds and characterize the geometric types admitting a connection with totally skew-symmetric torsion.
In Riemann-Cartan spacetimes with torsion only its axial covector piece $A$ couples to massive Dirac fields. Using renormalization group arguments, we show that besides the familiar Riemannian term only the Pontrjagin type four-form $dA\wedge dA$ does arise additionally in the chiral anomaly, but not the Nieh-Yan term $d^\star A$, as has been claimed in a recent paper [PRD 55, 7580 (1997)].
The dual Komar mass generalizes the concept of the NUT parameter and is akin to the magnetic charge in electrodynamics. In asymptotically flat spacetimes it coincides with the dual supertranslation charge. The dual mass vanishes identically on Riemannian manifolds in General Relativity unless conical singularities corresponding to Misner strings are introduced. In this paper we propose an alternative way to source the dual mass locally. We show that this can be done by enlarging the phase space of the theory to allow for a violation of the algebraic Bianchi identity using local fields. A minim…
Regularization of Gauss-Bonnet Gravity in Riemann-Cartan Geometry
School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（基础物理与数学科学学院，杭州高等研究院，UCAS）；University of Chinese Academy of Sciences（中国科学院大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University（湖南师范大学物理与量子效应及应用协同创新中心）
We present the coupling of the torsion scalar $T$ and the trace of energy-momentum tensor $\mathcal{T}$, which produces new modified $f(T,\mathcal{T})$ gravity. Moreover, we consider the functional form $f(T,\mathcal{T}) =α\mathcal{T}+βT^2$ where $α$ and $β$ are free parameters. As an alternative to a cosmological constant, the $f(T,\mathcal{T})$ theory may offer a theoretical explanation of the late-time acceleration. The recent observational data to the considered model especially the bounds on model parameters is applied in detail. Furthermore, we analyze the cosmological behavior of the de…
In this work, we investigate the effects of the torsion-fermionic interaction on the energy levels of fermions within a Riemann-Cartan geometry using a model-independent approach. We consider the case of fermions minimally coupled to the background torsion as well as non-minimal extensions via additional couplings with the vector and axial fermionic currents which include parity-breaking interactions. In the limit of zero-curvature, and for the cases of constant and spherically symmetric torsion, we find a Zeeman-like effect on the energy levels of fermions and anti-fermions depending on wheth…
We use the conservation law of the stress-energy and spin tensors to study the motion of massive brane-like objects in Riemann-Cartan geometry. The world-sheet equations and boundary conditions are obtained in a manifestly covariant form. In the particle case, the resultant world-line equations turn out to exhibit a novel spin-curvature coupling. In particular, the spin of a zero-size particle does not couple to the background curvature. In the string case, the world-sheet dynamics is studied for some special choices of spin and torsion. As a result, the known coupling to the Kalb-Ramond antis…
We describe a new type of generalized gravity-matter models where $f(R)=R+R^2$ gravity couples in a non-conventional way to a scalar "inflaton" field, to a second scalar "darkon" field responsible for dark energy/dark matter unification, as well as to a non-standard nonlinear gauge field system, which is responsible for a charge confining/deconfinfing mechanism. The essential non-conventional feature of our models is employing the formalism of non-Riemannian volume forms, i.e. metric-independent non-Riemannian volume elements on the spacetime manifold, defined in terms of auxiliary antisymmetr…
We analyze the projected effective Einstein equation in a 4-dimensional arbitrary manifold embedded in a 5-dimensional Riemann-Cartan manifold. The Israel-Darmois matching conditions are investigated, in the context where the torsion discontinuity is orthogonal to the brane. Unexpectedly, the presence of torsion terms in the connection does not modify such conditions whatsoever, despite of the modification in the extrinsic curvature and in the connection. Then, by imposing the Z_2-symmetry, the Einstein equation obtained via Gauss-Codazzi formalism is extended, in order to now encompass the to…
We derive an interacting quintessence model on the framework of a recently introduced new class of geometrical scalar-tensor theories of gravity formulated on a Weyl-Integrable geometry, where the gravitational sector is described by both a scalar and a tensor metric field. By using a Palatini variational principle we construct a scalar-tensor action invariant under the Weyl symmetry group of the background geometry, which in the Einstein-Riemann frame leads to a gravitoelectromagnetic theory. We use the gauge freedom of the theory and the fact that the Weyl scalar field couples with matter fi…
We construct $F(T,\left(\nabla{T}\right)^2,\Box {T})$ gravitational modifications, which are novel classes of modified theories arising from higher-derivative torsional terms in the action, and are different than their curvature analogue. Applying them in a cosmological framework we obtain an effective dark energy sector that comprises of the novel torsional contributions. We perform a detailed dynamical analysis for two specific examples, extracting the stable late-time solutions and calculating the corresponding observables. We show that the thermal history of the universe can be reproduced,…
We show that on every Spin(7) manifold there always exists a unique linear connection with totally skew-symmetric torsion preserving a nontrivial spinor and the Spin(7) structure. We express its torsion and the Riemannian scalar curvature in terms of the fundamental 4-form. We present an explicit formula for the Riemannian covariant derivative of the fundamental 4-form in terms of its exterior differential. We show the vanishing of the (\hat)-A genus and obtain a linear relation between Betti numbers of a compact Spin(7) manifolds which are locally but not globally conformally equivalent to a …
Recently, the {\it spacelike} part of the $SU(2)$ Yang--Mills equations has been identified with geometrical objects of a three--dimensional space of constant Riemann--Cartan curvature. We give a concise derivation of this Ashtekar type (``inverse Kaluza--Klein") {\it mapping} by employing a $(3+1)$--decomposition of {\it Clifford algebra}--valued torsion and curvature two--forms. In the subcase of a mapping to purely axial 3D torsion, the corresponding Lagrangian consists of the translational and Lorentz {\it Chern--Simons term} plus cosmological term and is therefore of purely topological or…
We construct an extension of f(T) gravity with the inclusion of a non-minimal torsion-matter coupling in the action. The resulting theory is a novel gravitational modification, since it is different from both f(T) gravity, as well as from the non-minimal curvature-matter-coupled theory. The cosmological application of this new theory proves to be very interesting. In particular, we obtain an effective dark energy sector whose equation-of-state parameter can be quintessence or phantom-like, or exhibit the phantom-divide crossing, while for a large range of the model parameters the Universe resu…
The role of torsion in quantum three-dimensional gravity is investigated by studying the partition function of the Euclidean theory in Riemann-Cartan spacetime. The entropy of the black hole with torsion is found to differ from the standard Bekenstein-Hawking result, but its form is in complete agreement with the first law of black hole thermodynamics.
We consider a model belonging to the class of gravities with dynamical torsion. The model is free of ghosts and gradient instabilities about Minkowski and torsionless Einstein backgrounds. We find that at zero cosmological constant, the model admits a self-accelerating solution with non-Riemannian connection. Small value of the effective cosmological constant is obtained at the expense of the hierarchy between the dimensionless couplings.
We consider a non-standard generalized model of gravity coupled to a neutral scalar "inflaton" as well as to the fields of the electroweak bosonic sector. The essential new ingredient is employing two alternative non-Riemannian space-time volume-forms (non-Riemannian volume elements, or covariant integration measure densitities) independent of the space-time metric. The latter are defined in terms of auxiliary antisymmentric tensor gauge fields, which although not introducing any additional propagating degrees of freedom, trigger a series of important features such as: (i) appearance of two in…
Torsions, curvatures, structure equations and Bianchi identities for locally anisotropic superspaces (containing as particular cases different supersymmetric extensions and prolongations of Riemann, Finsler, Lagrange and Kaluza--Klein spaces) are investigated.
Recently, gravitational gauge theories with torsion have been discussed by an increasing number of authors from a classical as well as from a quantum field theoretical point of view. The Einstein-Cartan(-Sciama-Kibble) Lagrangian has been enriched by the parity odd pseudoscalar curvature (Hojman, Mukku, and Sayed) and by torsion square and curvature square pieces, likewise of even and odd parity. (i) We show that the inverse of the so-called Barbero-Immirzi parameter multiplying the pseudoscalar curvature, because of the topological Nieh-Yan form, can only be appropriately discussed if torsion…
We investigate a bounce inflation model with a graceful exit into the Friedmann-Robertson-Walker (FRW) decelerated Universe within $f(T)$ gravity framework, where $T$ is the torsion scalar in the teleparallelism. We study the cosmic thermal evolution, the model predicts a supercold Universe during the precontraction phase, which is consistent with the requirements of the slow-roll models, while it performs a reheating period by the end of the contraction with a maximum temperature just below the grand unified theory (GUT) temperature. However, it matches the radiation temperature of the hot bi…
