$w_{dm}$-$w_{de}$ cosmological model with new data samples of cosmological observations

Abstract: We revisit a cosmological model where dark matter (DM) and dark energy (DE) follow barotropic equations of state, allowing deviations from the standard $\Lambda$CDM framework (i.e. $w_{dm} \neq 0$, $w_{de} \neq -1$) considering both, flat and non-flat curvature. Using a dynamical system approach, we identify equilibrium states that govern stability, expansion, and contraction. Expansion occurs when $H>0$, while contraction is linked to $H < 0$. Accelerated expansion arises from DE dominance, whereas radiation- and matter-dominated phases lead to deceleration. Some solutions are unphysical, because of density constraints, but viable cases offer insights into cosmic transitions, including the Einstein static universe, which allows shifts between accelerating and decelerating phases. We perform a Bayesian analysis with updated datasets, including observational Hubble data, Pantheon+ Type Ia supernovae, strong lensing systems, and baryon acoustic oscillations, to constrain the parameters $w_{dm}$ and $w_{de}$. Our results from the data joint analysis show consistency with $\Lambda$CDM within $3\sigma$, but none of the cases reproduce $w_{dm} = 0$ and $w_{de} = -1$. Nevertheless, the comparison with the standard model using the Akaike and Bayesian information criteria indicates that only the non-flat scenario has the potential to be competitive. This suggests that a non-dust-like DM may impact structure formation, while DE could shift toward quintessence fluid. While $\Lambda$CDM remains a strong model, our findings indicate that alternative dark sector models with non-standard EoS could be viable and offer new insights into cosmic evolution.