Dynamical analysis of anisotropic scalar-field cosmologies for a wide range of potentials

Abstract: We perform a detailed dynamical analysis of anisotropic scalar-field cosmologies, and in particular of the most significant Kantowski-Sachs, Locally Rotationally Symmetric (LRS) Bianchi I and LRS Bianchi III cases. We follow the new and powerful method of $f$-devisers, which allows us to perform the whole analysis for a wide range of potentials. Thus, one can just substitute the specific potential form in the final results and obtain the corresponding behavior, without the need of new calculations. We find a very rich behavior, and amongst others the universe can result in isotropized solutions with observables in agreement with observations, such as de Sitter, quintessence-like, or stiff-dark energy solutions. In particular, all expanding, accelerating, stable attractors are isotropic. Additionally, we prove that as long as matter obeys the null energy condition, bounce behavior is impossible. Finally, applying the general results to the well-studied exponential and power-law potentials, we find that some of the general stable solutions disappear. This feature may be an indication that such simple potentials might restrict the dynamics in scalar-field cosmology, opening the way to the introduction of more complicated ones.