Torsion, Chern–simons Term and Diffeomorphism Invariance

Abstract

In the torsion⊗curvature approach of gravity Chern-Simons modification has been considered here. It has been found that Chern-Simons contribution to the bianchi identity has become cancelled from that of the scalar field part. But "homogeneity and isotropy" consideration of present day cosmology is a consequence of the "strong equivalence principle" and vice-versa.1 It is to be noted here that in the presence of spinorial matter only the axial vector part of the torsion couples to the spinor field [8,9].

Dirac spinors in Bianchi-I f(R)-cosmology with torsion

“…In the present paper we started from gravitational theories of the f (R) type in which the Ricci scalar R contains torsion as well as the metric field, considering them in the case in which the spacetime is filled with Dirac matter fields; we have employed these models to study anisotropic cosmological models BI: with respect to Einstein gravity, additional gravitational effects arise as a consequence of the non-linearity of the f (R) function and the natural torsion-spin coupling, known to induce centrifugal barriers [22]. These non-linear and repulsive centrifugal effects may enforce one another, especially in the case anisotropies are considered; the relationship between torsion and anisotropies of the spacetime has been widely investigated in the literature, and recent accounts are for example those in [23,24]). An important issue that must be highlighted is the fact that, despite the anisotropic background, the Einstein tensor is diagonal, while, because of the intrinsic features of the spinor field, the energy tensor is not diagonal: in this circumstance the nondiagonal part of the gravitational field equations results into the constraints (3.10) characterizing the structure of the spacetime or the helicity of the spinor field or both; in our understanding, the only physically meaningful situation is the one in which two axes are equal and one spatial component of the axial vector torsion does not vanish, giving rise to a universe that is spatially shaped as an ellipsoid of rotation revolving about the only axis along which the spin density is not equal to zero.…”

Axial Current, Killing Vector and Newtonian Gravity

“…In multiplicative torsion approach of gravity [7][8][9][10][11][12][13] one gets axial vector current 1-form for spinor field Ψ, J 5 = Ψγ 5 γΨ, to be an exact 1-form, given by the equation…”