Anisotropic cosmological models with spinor and scalar fields and viscous fluid in presence of a Λ term: Qualitative solutions J. Math. Phys. 49, 112502 (2008) We consider the Riemann-Cartan geometry as a basis for the Einstein-Sciama-Kibble theory coupled to spinor fields: we focus on f(R) and conformal gravities, regarding the flag-dipole spinor fields, type-(4) spinor fields under the Lounesto classification. We study such theories in specific cases given, for instance, by cosmological scenarios: we find that in such background the Dirac equation admits solutions that are not Dirac spinor fields, but in fact the aforementioned flag-dipoles ones. These solutions are important from a theoretical perspective, as they evince that spinor fields are not necessarily determined by their dynamics, but also a discussion on their structural (algebraic) properties must be carried off. Furthermore, the phenomenological point of view is shown to be also relevant, since for isotropic Universes they circumvent the question whether spinor fields do undergo the Cosmological Principle. C 2013 AIP Publishing LLC. [http://dx

We consider generally-relativistic gauge transformations for the spinorial fields finding two mutually exclusive but together exhaustive classes in which fermions are placed adding supplementary information to the results obtained by Lounesto, and identifying quantities analogous to the momentum vector and the Pauli-Lubanski axial vector we discuss how our results are similar to those obtained by Wigner; by taking into account the system of Dirac field equations we will investigate the consequences for the dynamics: and in particular we shall address the problem of getting the non-relativistic approximation in a consistent way. We are going to comment on extensions.

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.

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We study Dirac spinors in Bianchi type-I cosmological models, within the framework of torsional $f(R)$-gravity. We find four types of results: the resulting dynamic behavior of the universe depends on the particular choice of function $f(R)$; some $f(R)$ models do not isotropize and have no Einstein limit, so that they have no physical significance, whereas for other $f(R)$ models isotropization and Einsteinization occur, and so they are physically acceptable, suggesting that phenomenological arguments may select $f(R)$ models that are physically meaningful; the singularity problem can be avoided, due to the presence of torsion; the general conservation laws holding for $f(R)$-gravity with torsion ensure the preservation of the Hamiltonian constraint, so proving that the initial value problem is well-formulated for these models.Comment: 25 pages, 1 figur

Not long ago, the definition of eigenspinors of charge-conjugation belonging to a special Wigner class has lead to the unexpected theoretical discovery of a form of matter with spin 1 2 and mass dimension 1, called ELKO matter field; ELKO matter fields defined in flat spacetimes have been later extended to curved and twisted spacetimes, in order to include in their dynamics the coupling to gravitational fields possessing both metric and torsional degrees of freedom: the inclusion of non-commuting spinorial covariant derivatives allows for the introduction of more general dynamical terms influencing the behaviour of ELKO matter fields. In this paper, we shall solve the theoretical problem of finding the most general dynamics for ELKO matter, and we will face the phenomenological issue concerning how the new dynamical terms may affect the behaviour of ELKO matter; we will see that new effects will arise for which the very existence of ELKO matter will be endangered, due to the fact that ELKOs will turn incompatible with the cosmological principle. Thus we have that anisotropic universes must be taken into account if ELKOs are to be considered in their most general form.

We consider the most general torsional completion of gravitation together with electrodynamics for the Dirac spinorial material fields, and we show that consistency arguments constrain torsion to be completely antisymmetric and the dynamics to be parity-invariant and described by actions that are either least-order derivative or renormalizable.

In this article we will take into account the most complete back-ground with torsion and curvature, providing the most exhaustive coupling for the Dirac field: we will discuss the integrability of the interaction of the matter field and the reduction of the matter field equations.