Quadratic Torsion Term Research Articles

Torsional dark energy

Dark energy from kinetic torsion is discussed. The torsion incorporated in the Einstein–Cartan (EC) Lagrangian is assumed to be totally anti-symmetric, represented by a timelike axial vector [Formula: see text]. The dynamics of torsion is invoked by a novel kinetic term that gives rise to dark energy, while the massive quadratic torsion term, emanating from the EC part, represents a stiff fluid that leads to a bouncing term.

Spherically symmetric vacuum solutions and horizons in covariant f(T) gravity theory

In this paper we study properties that the vacuum must possess in the minimal extension to the teleparallel equivalent of general relativity (TEGR) where the action is supplemented with a quadratic torsion term. No assumption is made about the weakness of the quadratic term although in the weak-field regime the validity of our previously derived perturbative solution is confirmed. Regarding the exact nature of the vacuum, it is found that if the center of symmetry is to be regular, the mathematical conditions on the tetrad at the isotropy point mimic those of general relativity. With respect to horizons it is found that, under very mild assumptions, a smooth horizon cannot exist unless the quadratic torsion coupling, $\alpha$, vanishes, which is the TEGR limit (with the Schwarzschild tetrad as its solution). This analysis is then supplemented with computational work utilizing asymptotically Schwarzschild boundary data. It is verified that in no case studied does a smooth horizon form. For $\alpha > 0$ naked singularities occur which break down the equations of motion before a horizon can form. For $\alpha < 0$ there is a limited range of $\alpha$ where a vacuum horizon might exist but, if present, the horizon is singular. Therefore physically acceptable black hole horizons are problematic in the studied theory at least within the realm of vacuum static spherical symmetry. These results also imply that static spherical matter distributions generally must have extra restrictions on their spatial extent and stress-energy bounds so as to render the vacuum solution invalid in the singular region and make the solutions finite.

The dark side of the torsion: dark energy from propagating torsion

An extension to the Einstein–Cartan (EC) action is discussed in terms of cosmological solutions. The torsion incorporated in the EC Lagrangian is assumed to be totally anti-symmetric, represented by a time-like axial vector S^mu . The dynamics of torsion is invoked by a novel kinetic term. Here we show that this kinetic term gives rise to dark energy, while the quadratic torsion term, emanating from the EC part, represents a stiff fluid that leads to a bouncing cosmology solution. A constraint on the bouncing solution is calculated using cosmological data from different epochs.

Torsion-induced gravitational theta term and gravitoelectromagnetism

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 theta term in gravitoelectromagnetism. This is distinct from the common gravitational theta 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 theta 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-induced theta parameter can lead to excess mass density at the interface of regions where theta varies and consequently it generates a correction to Newton’s law of gravity. We discuss also an analogue of the Witten effect for gravitational dyons.

Non-minimal coupling of torsion–matter satisfying null energy condition for wormhole solutions

We explore wormhole solutions in a non-minimal torsion-matter coupled gravity by taking an explicit non-minimal coupling between the matter Lagrangian density and an arbitrary function of torsion scalar. This coupling depicts the transfer of energy and momentum between matter and torsion scalar terms. The violation of null energy condition occurred through effective energy-momentum tensor incorporating the torsion-matter non-minimal coupling while normal matter is responsible for supporting the respective wormhole geometries. We consider energy density in the form of non-monotonically decreasing function along with two types of models. First model is analogous to curvature-matter coupling scenario, that is, torsion scalar with $T$-matter coupling while the second one involves a quadratic torsion term. In both cases, we obtain wormhole solutions satisfying null energy condition. Also, we find that the increasing value of coupling constant minimizes or vanishes the violation of null energy condition through matter.

Formula omitted] theories of gravity without big-bang singularity

The R+S2 theories of gravity, where S2 denotes the quadratic torsion terms, are analyzed under three cases. In the first two cases, the matter fields are described by two different spin fluids which are not homogeneous and isotropic. In the third case, a homogeneous and isotropic torsion field is used. It is found that under all the three cases, the R+S2 theories may avert the big-bang singularity of the Robertson–Walker universe, with three corresponding constraints on the parameters.

Connection dynamics of a gauge theory of gravity coupled with matter

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 (PGT) 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(2)-connection dynamical formalism of the theory can be obtained. Hence, the techniques of loop quantum gravity (LQG) can be employed to quantize this PGT with non-zero torsion. Moreover, the Barbero–Immirzi parameter in LQG acquires its physical meaning as the coupling parameter between the Hilbert–Palatini term and the quadratic torsion term in this gauge theory of gravity.

Projective Invariance in Cosmological Models and Dark Energy

We study theories of gravitation that are based on the Einstein – Hilbert action that are not projectively invariant and can therefore completely determine their connections. We are thus lead to the conclusion that the geometry is necessarily Riemann – Cartan and at least the trace part of a torsion field must be present. We examine the consequence of including these torsion fields in cosmological models. Our results differ from those obtained earlier in the Einstein – Cartan – Sciama – Kibble theory. We also consider a model that includes a series of quadratic torsion terms. This series leads to a potential function that has the effect of “turning on” the cosmological constant. This potential function then acts like dark energy. This model also shows that the torsion field can produce an inflationary period.

Asymptotic flatness, reflection symmetry, and Birkhoff's theorem forR+R2actions containing quadratic torsion terms

The proof of the Birkhoff-type theorem: For asymptotically flat 0(3) spherically symmetric spacetime the unique solution of the vacuum field equations is the Schwarzschild solution with vanishing torsion, is extended to R+R/sup 2/ actions containing a quadratic torsion term. The simplifying power of the assumption of asymptotic flatness is severely degraded when reflection symmetry is not assumed, further underscoring the sensitivity of Riemann-Cartan theories to reflection symmetry, and inhibiting the proof of a similar theorem for SO(3) spherical symmetry.