ELKO and Dirac Spinors seen from Torsion

In this paper, the recently-introduced ELKO and the well-known Dirac spinor fields will be compared; however, instead of comparing them under the point of view of their algebraic properties or their dynamical features, we will proceed by investigating the analogies and similarities in terms of their geometrical character viewed from the perspective of torsion. The paper will be concluded by sketching some consequences for the application to cosmology and particle physics.Comment: 11 page

Newton-Euler, Lagrange and Kirchhoff formulations of rigid body dynamics: a unified approach

A unified formulation of rigid body dynamics based on Gauss principle is proposed. The Lagrange, Kirchhoff and Newton-Euler equations are seen to arise from different choices of the quasicoordinates in the velocity space. The group-theoretical aspects of the method are discussed.Comment: 5 page

Exact solutions for Weyl fermions with gravity

We consider the single-handed spinor field in interaction with its own gravitational field described by the set of field equations given by Weyl field equations written in terms of derivatives that are covariant with respect to the gravitational connection plus Einstein field equations soured with the energy tensor of the spinor: for the Weyl spinor and the ensuing spacetime of Weyl-Lewis-Papapetrou structure, we will find all exact solutions. The obtained solution for the metric tensor is that of a PP-wave spacetime while the spinor field is a flag-dipole.Comment: 12 page

Weak Forces and Neutrino Oscillations under the standards of Hybrid Gravity with Torsion

We present a unifying approach where weak forces and neutrino oscillations are interpreted under the same standards of torsional hybrid gravity. This gravitational theory mixes metric and metric-affine formalism in presence of torsion and allows to derive an effective scalar field which gives rise to a running coupling for Dirac matter fields. In this picture, two phenomena occurring at different energy scales can be encompassed under the dynamics of such a single scalar field, which represents the further torsional and curvature degrees of freedom.Comment: 13 page

Reconstructing exact scalar-tensor cosmologies via conformal transformations

We propose a new reconstruction method for scalar--tensor gravity based on the use of conformal transformations. The new method allows the derivation of a set of interesting exact cosmological solutions in brans Dicke gravity as well as other extensions of General Relativity.Comment: 8 pages, 2 figure

Critical exact solutions for self-gravitating Dirac fields

We consider the Einstein-Dirac field equations describing a self-gravitating massive neutrino, looking for axially-symmetric exact solutions; in the search of general solutions, we find some that are specific and which have critical features, such as the fact that the space-time curvature turns out to be flat and the spinor field gives rise to a vanishing bi-linear scalar $\overline{\psi}\psi=0$ with non-vanishing bi-linear pseudo-scalar $i\overline{\psi}\gamma^5\psi\not=0$: because in quantum field theory general computational methods are built on plane-wave solutions, for which bi-linear pseudo-scalar vanishes while the bi-linear scalar does not vanish, then the solutions we found cannot be treated with the usual machinery of quantum field theory. This means that for the Einstein-Dirac system there exist admissible solutions which nevertheless cannot be quantized with the common prescriptions; we regard this situation as yet another issue of tension between Einstein gravity and quantum principles. Possible ways to quench this tension can be seen either in enlarging the validity of quantum field theory or by restricting the space of the solutions of the Einstein-Dirac system of field equations.Comment: 12 page

On the well formulation of the Initial Value Problem of metric--affine f(R)f(R)-gravity

We study the well formulation of the initial value problem of f(R)-gravity in the metric-affine formalism. The problem is discussed in vacuo and in presence of perfect-fluid matter, Klein-Gordon and Yang-Mills fields. Adopting Gaussian normal coordinates, it can be shown that the problem is always well-formulated. Our results refute some criticisms to the viability of f(R)-gravity recently appeared in literature.Comment: 11 page

Integrability of Dirac equations in static spherical space-times

We consider the Dirac equations in static spherically-symmetric space-times, and we present a type of spinor field whose structure allows the separation of elevation angle and radial coordinate in very general situations. We demonstrate that after such a separation of variables the Dirac equations reduce to two equations that can always be integrated, at least in principle. To prove that ours is a fully-working method, we find an explicit exact solution in the special case of the de Sitter universe.Comment: 10 page

The dynamics of Bianchi I universes in RnR^n cosmologies with torsion

We analyze the phase space of Bianchi I cosmologies filled by a spin fluid in the framework of $f(R)$-gravity with torsion using a combination of the dynamical systems approach and the 1+3 covariant formalism. In the simple case of $f(R)=R^n$ our results allow a quantification of the role of torsion and the spin of the cosmic fluid in the evolution of the cosmology. While torsion is able to modify the cosmological dynamics with respect to the purely metric case, the spin has little influence on the cosmology. We argue that this is due to the different symmetries of the tensor characterizing the anisotropies and the spin tensor. The cosmological model we analyzed presents isotropization for a wide set of initial conditions and values of the parameters and allows for two types of exotic bounce solutions.Comment: 22 page, 6 figures, submitted to Classical and Quantum Gravit

Renormalizability of the Dirac Equation in Torsion-Gravity with Non-Minimal Coupling

We will consider the torsional completion of gravity for a background filled with Dirac matter fields, studying what happens when fermionic non-minimal coupling is taken into account: we will show that, although non-minimal couplings are usually disregarded because of their ill-defined behaviour in ultraviolet regimes, this is due to the fact that torsion is commonly neglected, whereas when torsion is not left aside, even non-minimal couplings behave properly. In detail, we will see that non-minimal coupling allows to renormalize the Dirac equation even when torsion is taken into consideration and that in some type of non-minimally coupled models parity-oddness might be present even in the gravitational sector. In addition, we will show that in the presence of the considered non-minimal coupling, torsion is able to evade cosmological singularities as it can happen in the minimal coupling case and in some other non--minimally coupled theory. In the course of the paper, we shall consider a specific interaction as prototype to study this fermionic non-minimal coupling, but we will try to present results that do not depend on the actual structure of the non-minimal couplings by investigating alternative types of interaction.Comment: 19 page