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.