Classical Spinors on Curved Spacetime: applications to Cosmology and Astrophysics

Abstract

We focus our attention on the spinor model proposed in an article by J. Magueijo et al. and we analyze it from the point of view of the cosmological background. We show that this model, under some conditions, can well-describe the background behavior of DM and, under other conditions, the behavior of DE. Furthermore, we show that the SET of the spinorial fluid, in the context of the cosmological background, can be recast in the form of that of a Perfect Fluid whose four-velocity is given by the normalized vector current density. Successively, we concentrate on the analysis of the scalar cosmological perturbations of this model, following the usual SVT Decomposition approach. We show that the treatment of cosmological perturbations is very difficult and cannot be done directly. Due to this fact, we tackle the problem with another method: the (1+3)-decomposition. We prove that we can further decompose the SET of a spinorial fluid, thanks to the presence of the axial current density. Employing the results found in an article by L. Fabbri et al. and the polar form of spinors, we show how the thermodynamical quantities that characterize the spinorial fluid can be written in terms of the four-velocity, the normalized axial current density, the chiral angle, and the projector on the hyperplane orthogonal to the first two. Moreover, in the context of scalar perturbations, we obtain an expression for the adiabatic speed of sound of the pressure perturbation in terms of the parameters that characterize the spinorial field written in polar form. In the end, we tackle the problem of spherically symmetric halos surrounding galaxies by analyzing the behavior of the SET of the spinorial fluid in a spherically symmetric space-time. We prove that, in general, none of its components vanish, giving rise to the problem of the suitability of the model for the description of spherically symmetric objects.