Roldao da Rocha, Luca Fabbri, J. M. Hoff da Silva, R. T. Cavalcanti, J. A. Silva-Neto
The Dirac equation in a f(R) Riemann-Cartan cosmological scenario admits solutions, that are shown here not to be Dirac spinor fields, which seems to play a fundamental role on the matter fields properties in such cosmological framework, as: a) spinor fields in torsional f(R) or conformal gravity, that satisfy the Dirac equation, correspond to non-standard, flagpole, spinor fields (in both Lounesto and Wigner classification); b) the field equations imply a constraint among the bilinear covariants associated to the spinor field. Some constraints imposed on the metric and/or on the spinor field imply that an isotropic universe with matter fields circumvent the question that Dirac fields do not undergo the cosmological principle. Remarkably, if the spinor fields are assumed to satisfy the Dirac equation, they are shown not to be legitimate Dirac spinor fields, under Lounesto spinor field classification, but indeed flag-dipole singular spinor fields. Such type of spinor fields can still be led to flagpole spinor fields, which encompass Elko, a prime candidate to the dark matter problem, and Majorana spinor fields. This case is evinced when the spin direction associated to the spinor field vanishes, providing an anisotropic universe without fermionic torsional interactions.
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http://arxiv.org/abs/1302.2262
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