Cosmological exact solutions of Petrov type D. A mixture of three fluids: quintessence, dust and radiation

Abstract

In this paper, two exact solutions to the Einstein’s equations are obteined for an anisotropic and homogeneous symmetry of Petrov Type D, where the difference between the solutions is if the expansion is presented, initially, in a greater way on an axis or if it is presented in a greater way on a plane. In the solutions, it is considered a mixture with minimal interaction of three fluids, quintessence (P = −μ/3), dust (P = 0) and radiation (P = μ/3); besides the general case of the three fluids, the particular cases when the mixture contains two of them are analyzed, the singularities and the role that each one of the fluids have on them are studied; the Hubble parameters, the deceleration parameter and the role that the fluids represent on them are determined and analyzed, and the temperature of those fluids and the role that these fluids play on that magnitude in different time periods is determined.