Is Dark Energy Increasing or Decreasing in the Late Universe?

The concordance cosmological model $\Lambda$CDM assumes dark energy to be a constant, consistent with early-time observations, evidenced by Planck-$\Lambda$CDM analyses. However, in the face of late-time tensions, the nature of dark energy remains a central open problem. Modern precision cosmology offers a potential new window in the $w(a){\rm CDM}$ framework, which provides a model-independent prescription for its unknown equation of state $w(a)$. A confrontation of $w(a){\rm CDM}$ with data generally constitutes a nonlinear inference problem. We find that $w_0w_a$ estimates posterior to a fully non-linear $w(a)$ analysis are stabilized by the {\it Baryon Acoustic Oscillation} (BAO) constraint on $c_M=\Omega_{m,0}h^2$, inherited for instance from Planck-$\Lambda$CDM analysis of the CMB. It produces $w_0w_a$ estimates that are invariant under constraint-preserving variations in $\Omega_{m,0}$. In contrast, the early-linearization $w_0w_a$CDM shows pronounced correlation with $\Omega_{m,0}$ even when preserving $c_M$. We quantify this correlation resulting from the non-commutativity of $w_0w_a$ estimation and linearization in $w(a)$CDM. This discrepancy is demonstrated in controlled mock-data experiments. Applied to cosmic chronometer data, $w_0w_a$ estimates from correlation-free late linearization of $w(a)$CDM analysis favor $w_0<-1$, whereas $w_0w_a$CDM favors $w_0>-1$. If the correlation between $w_0$ and $\Omega_{m,0}$ in $w_0w_a$CDM is interpreted as arising from linearization effects rather than a physical origin, application to DESI DR2 may shift $w_0$ downward, potentially extending to $w_0 < -1$, corresponding to increasing dark energy at the present epoch. Alternatively, if the correlation is of hitherto unseen physical origin, the $w_0w_a$CDM parametrization is self-consistent and no such correction to the DESI inference may be required.