Modified Equations of State for Dark Energy and Observational Limitations

Cosmological models with variable and modified equations of state for dark energy are confronted with observational data, including Type Ia supernovae, Hubble parameter data $H(z)$ from different sources, and observational manifestations of cosmic microwave background radiation (CMB). We consider scenarios generalizing the $\Lambda$CDM, $w$CDM, and Chevallier--Polarski--Linder (CPL) models with nonzero curvature and compare their predictions. The most successful model with the dark energy equation of state $w= w_0+ w_1(1-a^2)/2$ was studied in detail. These models are interesting in possibly alleviating the Hubble constant $H_0$ tension, but they achieved a modest success in this direction with the considered observational data.