Cosmological exact solutions set of a perfect fluid in an anisotropic space-time in Petrov type D

Abstract

In this document a set of exact solutions is obtained by using the model of a perfect fluid on an homogeneous and anisotropic space-time that belongs to (Local Rotational Symmetry) Petrov's type D. This solutions represent the possible scenarios of a Universe for which the pressure P and the energetic density µ of a fluid are proportional (P = λµ), where λ can have any value. Hence, the aforementioned solution has importance for the fluid models with standard matter (λ ∈ [0, 1/3]), and also for other models, like quintessence, dark energy, phantom, ekpyrotic etc. It is established that for any state of the fluid, there are two possible solutions that depend on the matter expanding faster on a perpendicular coordinate on a plane, rather tan the plane itself, or if the situation is the opposite. Possible singularities are studied, and cases where the solutions are not singular in t = 0 are established; moreover, to the possibility for the solutions, depending of the t values, to become isotropic, pointing out that going from a model that was anisotropic at the beginning to an isotropic one with the augmentation of t, depends on whether the pressure P of the fluid is lower or not than the density of the energy µ.

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

“…The found solutions represent non-lineal interactive and consistent scalar and spinorial fields, similar to the mixture of the dust and the dark energy fluids. These two particular cases are possible when σ = 0 y C 1 + 2 mC 0 = 0, (the "dust case"), and when σ = 0 and C 1 +2 mC 0 = 0, (the "dark energy case"), as a result of what was obtained in [3]. The analysis of said solutions is analogous to the one done in [6], in terms of the singularities, the dependence on the sign on (24), and the relation to the Hubble parameters and the deceleration.…”

“…For all these cases, it was obtained that the function of the scalar field(ϕ) increases with time; this makes that the phase of the components of the spinorial field (of the spinor) becomes proportional to said function. For these times, the metric tends to behave as its equivalent of the dark energy [3], which is reflected in the function of the scalar field through the supremacy of the constant σ, whose sense is similar to the cosmologic constant Λ. On the other hand, for small values of time, the model of isobaric fluid tends to behave as its analogous of the dust type (P = 0), which is also reflected in ϕ and the phase of the spinorial field through the supremacy of the constant C 1 .…”

“…Thanks to data obtained by the COBE, WMAP, and PLANCK satellites, and the discovering of the acceleration of the Universe [1,2], the study of possible cosmologic scenarios has extended. 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.…”

“…The present work studied and obtained two exact solutions for the interactive and self-consistent scalar and spinorial fields in an anisotropic symmetry of Petrov D, whose metric behavior is equivalent to the solution of a isobaric scalar field [6]. The symmetry that will be used in this work is the homogeneous and anisotropic of the Petrov D, which follows the pattern [3]…”

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

“…Thanks to data of the background radiation obtained by the satellites COBE, WMAP, and PLANCK, and the discovering of the acceleration of the universe [1], [2], cosmology has become more dynamic; these and other aspects have been already discussed in [3]. The study of the physic fields in cosmology, such as the scalar, the spinorial, and the electromagnetic, in combinations of ideal fluids, isolated, or in their interactions, have relevance because of the possibility of investigating the different states of the matter for which the Universe could pass through, its influence over the possible singularities, and the changes for which the anisotropic space-time configuration could pass through.…”