Anisotropic cosmological exact solutions of Petrov type D of a mixture of dark energy and an attractive Bose-Einstein condensate

Abstract

Two exact solutions to Einstein equations were obtained; whose difference is the kind of initial expansion (greater on an axis or on a plane) in an anisotropic and homogeneous symmetry of Petrov type D. In these solutions, a mixture of dark energy and a ”standard” attractive Bose-Einstein Condensate (BEC) were considered. The initial singularity problem was studied and is only present in one of these models. Also, the study of temperature allowed to determine that it is null at the start of the universe and as time increases asymptotically, it tends to a constant value, hence a BEC is essential in the first expansion phase and, for this work, with 8 / 9 parts of the total early universe energy. Hubble and deceleration parameters were studied as well and it was determined that the Hubble parameter initially gets indefinite in t = 0, but tends to a constant value when time increases; for the deceleration parameter, it was stated that the universe initially expands in a decelerated form, but from a certain value, it starts continuously to expand fast towards a constant value. As time increases asymptotically, models tend to a one of FRWL flat type of dark energy.