Dirac fields in f ( R )-gravity with torsion

Abstract

We study f (R)-gravity with torsion in presence of Dirac massive fields. Using the Bianchi identities, we formulate the conservation laws of the theory and we check the consistency with the matter field equations. Further, we decompose the field equations in torsionless and torsional terms: we show that the nonlinearity of the gravitational Lagrangian reduces to the presence of a scalar field that depends on the spinor field; this additional scalar field gives rise to an effective stress-energy tensor and plays the role of a scale factor modifying the normalization of Dirac fields. Problems for fermions regarding the positivity of energy and the particle-antiparticle duality are discussed.

The most general ELKO matter in torsional f(R)‐theories

“…Further general-ization giving us an ECSK-like theory is the one for which the gravitational Lagrangian is non-linear in the Ricci scalar R: then, Einstein theory is in relationship with the ECSK theory in the same way in which the metric f (R)theory is in relationship with the metric-torsional f (R)theory [3][4][5][6]. Although in this last case torsion is present even without spin, nonetheless the matter fields that best exploit the coupling between torsion and spin density tensor are those having spin, that is the spinor fields; the simplest case is the spin- 1 2 field, which in the case of Dirac fields it has been studied in [7].…”

Cosmological solutions in F(T) gravity with the presence of spinor fields

“…On the other hand, the possibility of reproducing dark energy by means of spinor fields has been also considered in the literature [19]. In this sense, any cosmological solution can be reconstructed by the appropriate self-interacting term of the spinor field in the framework of GR and even within higher-order theories of gravity as F (R) gravity [20], so that the cosmological history might be explained by sources of Dirac fields. Furthermore, some inflationary models with the presence of spinor fields have been proposed [21], where emergent solutions and loop corrections during the inflationary phase have been studied [22].…”

Stiff Fluid in Accelerated Universes with Torsion

“…From some time past, the interest to ECT has grown in connection with the fact that torsion arises naturally in the supergravity [33][34][35], Kaluza-Klein [36][37][38], and syperstring [39][40][41] theories. ( ) gravity with torsion has been developed [42][43][44][45] as one of the simplest extensions of the ECT. In [43] it has been demonstrated that, in ( ) gravity, torsion can be a geometric source for the accelerated expansion.…”