Torsion, Dirac Field, Dark Matter and Dark Radiation

Abstract

The role of torsion and a scalar field φ in gravitation, especially, in the presence of a Dirac field in the background of a particular class of the Riemann-Cartan geometry is considered here. Recently, a Lagrangian density with Lagrange multipliers has been proposed by the author which has been obtained by picking some particular terms from the SO(4, 1) Pontryagin density, where the scalar field φ causes the de Sitter connection to have the proper dimension of a gauge field. In this article the scalar field has been linked to the dimension of the Dirac field. Here we get the field equations for the Dirac field and the scalar field in such a way that both of them appear to be mutually non-interacting. In this scenario the scalar field appears to be a natural candidate for the dark matter and the dark radiation.

Torsion, Chern–simons Term and Diffeomorphism Invariance

“…So this conclusion remains valid even in the presence of CS modified extended GR. When we consider other form of cosmic energy density, may be in the early universe, we have to adopt a non-FRW geometry where we may have to forgo the isotropy and homogeneity of the universe [15], then the above result shows that conservation of energy-momentum tensor of baryonic matter is violated but the total energy-momentum tensor of both baryonic and dark matter/radiation is always conserved.…”

“…If we consider axial vector torsion together with a scalar field φ connected to a local scale factor [14], then the Euler-Lagrange equations also link, in laboratory scale, the mass of the scalar field with the Nieh-Yan density and, in cosmic scale of FRW-cosmology, they predict only three kinds of the phenomenological energy density representing mass, radiation and cosmological constant. In a recent paper [15], it has been shown that this scalar field may also be interpreted to be linked with the dark matter and dark radiation. Recently it has been shown that [16], using field equations of all fields except the frame field, the starting Lagrangian reduces to a generic f (R) gravity Lagrangian which, for FRW metric, gives standard FRW cosmology.…”

Some Mathematical Aspects of f(R)-Gravity with Torsion: Cauchy Problem and Junction Conditions

“…Cartan was the first to introduce torsion in the geometrical background; after him, Sciama and Kibble embodied it within the framework of Einstein gravity implementing the idea that spin can be source of torsion as energy does for curvature [11][12][13]. The resulting theory, known as Einstein-Cartan-Sciama-Kibble (ECSK) theory, has been the first generalization of GR trying to take the spin of elementary fields into account, and it still remains one of the most serious attempts in this direction [14][15][16].…”

de Sitter spacetimes with torsion in the model of de Sitter gauge theory of gravity

“…The problem of matching the exterior solution with an interior solution has been studied in[12] 3. The same connection with different gravitational dynamics has also been studied (See, e.g [19][20][21][22][23][24][25][26][27]…”