Weyl-Cartan-Weitzenböck gravity through Lagrange multiplier

Abstract

We consider an extension of the Weyl-Cartan-Weitzenböck (WCW) and teleparallel gravity, in which the Weitzenböck condition of the exact cancellation of curvature and torsion in a Weyl-Cartan geometry is inserted into the gravitational action via a Lagrange multiplier. In the standard metric formulation of the WCW model, the flatness of the space-time is removed by imposing the Weitzenböck condition in the Weyl-Cartan geometry, where the dynamical variables are the spacetime metric, the Weyl vector and the torsion tensor, respectively. However, once the Weitzenböck condition is imposed on the Weyl-Cartan space-time, the metric is not dynamical, and the gravitational dynamics and evolution is completely determined by the torsion tensor. We show how to resolve this difficulty, and generalize the WCW model, by imposing the Weitzenböck condition on the action of the gravitational field through a Lagrange multiplier. The gravitational field equations are obtained from the variational principle, and they explicitly depend on the Lagrange multiplier. As a particular model we consider the case of the Riemann-Cartan space-times with zero non-metricity, which mimics the teleparallel theory of gravity. The Newtonian limit of the model is investigated, and a generalized Poisson equation is obtained, with the weak field gravitational potential explicitly depending on the Lagrange multiplier and on the Weyl vector. The cosmological implications of the theory are also studied, and three classes of exact cosmological models are considered.

f(T,𝒯) gravity and cosmology

“…Additionally, note that if one starts from TEGR, but instead of the f (R) is inspired by higher-curvature modifications of General Relativity, one can construct higher-order torsion gravity, such as the f (T, T G ) paradigm [56,57], which also presents interesting cosmological behavior. Finally, another modification of TEGR is to extend it inserting the Weitzenböck condition in a Weyl-Cartan geometry via a Lagrange multiplier, with interesting cosmological implications [58,59].…”

Stellar evolution of compact stars in curvature–matter-coupling gravity

“…This is the simplest functional form which describes the relation between geometry and matter only through the strong coupling between the Ricci and stress tensors. This model is first suggested by Haghani et al [8] and has widely been used to study different cosmological issues. Haghani et al [8] examined the evolution as well as dynamics of the universe corresponding to this model and found that for δ > 0, this model well describes the expanding and collapsing phases of cosmos.…”

“…It may provide a matter based deviation from the equation of motion and also assists to analyze dark source effects as well as late-time acceleration. Motivated by this argument, a more complicated and extended theory having strong non-minimal curvature-matter combination is developed called f (R, T, Q) gravity [8,9].…”

Cosmology with higher-derivative matter fields

“…Thus, the modification of the Universe content [1] is materialized, in general, by the addition of extra dynamical scalar fields, for instance canonical (quintessence) [2][3][4][5][6][7], phantom [8][9][10][11][12], their combination [13][14][15], K-essence [16,17], Galileon [18], etc. On the other hand, one can modify the gravitational sector [19], for instance constructing f (R) gravity [20][21][22][23][24][25][26][27][28][29], f (T ) gravity [30][31][32][33], Weyl-Cartan-Weitzenböck gravity [34,35], Gauss-Bonnet gravity [36][37][38], Hořava-Lifshitz gravity [39][40][41][42][43], nonlinear massive gravity [44][45][46][47], etc, which apart from ...…”