摘要：Research on the accelerated expansion of our Universe captures a lot of attention. The dark energy (DE) is a way to explain it. In this paper we will consider scalar field quintessence DE with EoS, where the dynamics of the DE models related to the dynamics of the scalar field. We are interested in the study of the behavior of the Universe in the presence of interacting quintessence DE models in Lyra manifold with a varying . In a considered framework we also would like to propose a new form for . We found that the models correspond to the transit Universe, which will enter the accelerated expansion phase and will remain there with a constant deceleration parameter . We found also that the is a decreasing function which takes a small positive value with and dominating in the old Universe. Observational constraints are applied and causality issue via is discussed as a possible way to either reject or accept the models.
