Tales from Wonderland

Abstract

Knowing that the Universe is quite isotropic, one may, as already discussed in Chapter 1, wonder how likely such a Universe is. We take the following research question. Question 1. Is the asymptotic future of a cosmology filled with a perfect fluid alongside j-form matter isotropic? Take a cosmological model (M, g, u). Then the research question stated above will be addressed under the following assumptions. Assumption 5.1 (Philosophy). We assume the weak cosmological principle (WCP). Id est; we assume that the manifold M of the model is homogeneous on spatial sections, meanwhile simultaneously allowing for anisotropies in the metric g. Assumption 5.2 (Matter). We take as matter content a perfect fluid with barotropic, non-phantom (a) equation of state with which the fundamental observer u will be aligned and a j-form fluid. We also investigate the effects of adding a cosmological constant. Assumption 5.3 (Theory). General Relativity is assumed to be the correct theory of gravity. Finally, in repetition: the ruthless swiftness of time has forced us to leave the Kantowski-Sachs model out and concentrate on the Bianchi models. (a) With ‘barotropic’ we mean that the fluid is a function of pressure only. ‘Nonphantom’ means that the equation-of-state parameter Knowing that the Universe is quite isotropic, one may, as already discussed in Chapter 1, wonder how likely such a Universe is. We take the following research question. Question 1. Is the asymptotic future of a cosmology filled with a perfect fluid alongside j-form matter isotropic? Take a cosmological model (M, g, u). Then the research question stated above will be addressed under the following assumptions. Assumption 5.1 (Philosophy). We assume the weak cosmological principle (WCP). Id est; we assume that the manifold M of the model is homogeneous on spatial sections, meanwhile simultaneously allowing for anisotropies in the metric g. Assumption 5.2 (Matter). We take as matter content a perfect fluid with barotropic, non-phantom (a) equation of state with which the fundamental observer u will be aligned and a j-form fluid. We also investigate the effects of adding a cosmological constant. Assumption 5.3 (Theory). General Relativity is assumed to be the correct theory of gravity. Finally, in repetition: the ruthless swiftness of time has forced us to leave the Kantowski-Sachs model out and concentrate on the Bianchi models. (a) With ‘barotropic’ we mean that the fluid is a function of pressure only. ‘Nonphantom’ means that the equation-of-state parameter y is not allowed to be negative.