We present updated observational constraints on the simple-gDE model, characterized by a constant inertial mass density (IMD) $\rho_{ \rm DE}+p_{ \rm DE}$,which belongs to the broader graduated dark energy family, and compare its cosmological implications with those of the $w$CDM and the $\Lambda$CDM models. This parametrization provides a physically motivated, one-parameter extension of $\Lambda$CDM, perspective on DE dynamics beyond the usual equation-of-state approach. We use the newly released DESI DR2 BAO data in combination with either CMB measurements from Planck 2018 or late-time probes, CC and the Pantheon+ SNe Ia sample, considered both with and without SH0ES calibration in this analysis. The data favor a small positive IMD, and Bayesian evidence indicates that the models remain statistically indistinguishable within spatially flat scenarios. Consequently, none of these models exhibits a sign transition in the DE energy density, and no improvement in $H_0$ tension. Allowing spatial curvature qualitatively enlarges the phenomenology of the dark sector. In particular, the interplay between spatial curvature and a nonzero IMD permits sign transitions in both the effective dark-energy density and the IMD during cosmic evolution. For the BAO+CC+SN+SH0ES dataset, the $o$Simple-gDE model yields a transition redshift $z^\dagger = 1.51^{ +0.68}_{ -0.34}$, while the crossing of the Null Energy Condition boundary (NECB), defined by $\rho_{ \rm DE}+p_{ \rm DE}=0$, occurs at $z_{ \rm NECB}=2.36^{ +1.48}_{ -1.48}$. The model is statistically favored over $o\Lambda$CDM and $ow$CDM. These results highlight the potential role of IMD as a fundamental parameter in DE phenomenology and demonstrate that geometric effects, such as spatial curvature, can reveal dynamical features of the dark sector that remain hidden within the spatially flat $\Lambda$CDM framework.
Categories: astro-ph.CO gr-qc