Kinematic and Dynamic Parameters of Anisotropic Models with Inflaton, Without A Priori Relation Between the Scale Factors and with A Posteriori Isotropization
In this work, we present a detailed review of the calculations concerning homogeneous and anisotropic cosmological models, with particular emphasis on the Kantowski-Sachs cosmological model. As an innovative contribution, we derive an exact solution for the field equations, expressed in terms of a general form for the material content of the universe. We obtain the expressions for the energy density in this general case, as well as investigate the specific scenario involving the presence of a scalar field. We examine the evolutionary dynamics of the model that encompasses Hubble, density, and deceleration parameters. Additionally, we calculate the kinematic parameters associated with the model, namely: the scalar expansion Θ, the shear scalar σ, the rotation parameter ω, and the parameter Rα\b{eta}UαU\b{eta}, also known as the Raychaudhuri scalar or convergence condition, all of these parameters expressed within the framework of the Raychaudhuri equation. Instead of employing a preestablished relation between the scale factors of the model, we allow them to evolve freely, without a priori conditions. Thus, we can verify that the isotropic nature of the studied scenario manifests itself rapidly, leading to the traditional isotropic model.