Interactive spinorial and scalar fields congruent to the Chaplygin's gas. Exact cosmologic solutions in a space-time of Petrov D

Abstract

This study obtained two exact cosmologic solutions to the Einstein equations considering the interactive, non-lineal, and self-consistent spinorial and scalar fields, congruent to the gas model of Chaplin in a homogeneous anisotropic symmetry of Petrov D. The function of the scalar field, the components of the spinorial field, and the interaction among them were analyzed, and it was determined that the phase of the components of the spinorial field is related to the scalar field, so that for great values of the time, the phase of the components of the spinorial field is proportional to the function of the scalar field. It is established that the lagrangian of non-lineal interaction for great values of time behaves similar to a combination of the models of dark energy and Soler; for great and small time values, it behaves similar to a free spinorial field, but with diverse changes in the effective masses of the spinorial field in the lagrangian.

Cosmologic exact solutions of isobaric interactive scalar and spinorial fields in an anisotropic space-time of Petrov D

“…These and other aspects has been discussed in [3]. The importance of the study of scalar fields and interactive self-consistent cosmologic spinorials has been approached in [4].It was obtained that a determined self-consistent interaction between them leads to a cosmologic model equivalent to the Chapligyn gas; for said fields, the phase of the components of the spinorial field is related to the function of the scalar field, so that for great times, the phase of the components of the spinorial field is proportional to the function of the scalar field. It is established that for great times the non-lineal lagrangian of interaction behaves similar to the model of Soler; and for small periods, it behaves similar to a free spinorial field, but with some variation in the massive term of the lagrangian.…”

Cosmologic solution of scalar and spinorial interactive fields with the dark energy pattern and a magnetic primordial not perturbed field in an anisotropic space-time of Petrov D

“…Some of the exact solutions that have been studied are primordial not-perturbed magnetic fields with fluids like the dark energy, the Hard Universe and the Ekpyrotic in an anisotropic space-time of the Petrov D. In [2], it is determined that for a group of fluids, if P = λµ, for λ ∈]1/3, 1[, there is no solution in ; the same happens for a Zeldovich fluid (λ = 1), and for a magnetic field with no fluid. On the other hand, the importance of studying spinorial fields and interactive scalars as possible matter sources has been discussed in [4], where it has been obtained that the phase of the spinor tends to be proportional to the function of the scalar field for great periods. This triggered the interest of studying the possibilities of interaction between said fields, such as the spinorial, scalar, and the primordial magnetic in an anisotropic space-time of Petrov D; this allows to evaluate the influence of one in another, including the gravitational field.…”