Simple $\phi\Lambda$ CDM dynamics

In this paper, we introduce the $\phi\Lambda$CDM model and compare it to the concordance model. We present their respective epoch evolutions, perform a detailed dynamical analysis for each model, and conduct a comparative analysis between the two. This study revitalizes these models by considering systems with a higher number of variables. Additionally, the $\phi\Lambda$CDM model we present is both more comprehensive and simpler than those found in the literature, as it accounts for all known epochs, including the radiation, matter, and dark energy phases. Notably, existing studies on this model often omit the radiation epoch and focus on simpler dynamics. We find that both models, the $\phi\Lambda$CDM and the $\Lambda$CDM, can describe the generally accepted scenario of cosmic evolution, and current observations. Both models, describe qualitative and quantitative current observations about the epoch behaviour of the species of the universe. We find the $\phi\Lambda$CDM model has the following exotic transition from a \textit{dominant radiation energy density ratio} epoch, or a \textit{low scalar kinetic term energy density ratio} epoch, towards a \textit{dominant cosmological constant energy density ratio} epoch. This renders the $\phi\Lambda$CDM a richer phenomenologically model than the concordance cosmological model. The software of the study is publicly available online.