Exploring $$\phi $$CDM model dynamics

Abstract In this paper, we introduce the $$\phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math> CDM model, and we compare to the concordance model. We provide their epoch evolution, we perform a dynamical analysis to each model, and a comparative analysis between the two models. We revitalise these two models, since we study them in systems with higher number of variables. Furthermore, the $$\phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math> CDM model is more complete than the one that we found in the literature, since we take into account all the so far discovered epochs, radiation, matter, and dark energy epochs. In contrast in the literature there is no study including the radiation epoch for this model. We find that both models 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 $$\phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math> CDM model has the following exotic transition from a dominant radiation energy density ratio epoch and a low dominant matter energy density ratio and high dominant radiation energy density ratio epoch, towards a dominant scalar potential energy density ratio epoch, in the matter-potential-scalar plane.