Do equation of state parametrizations of dark energy faithfully capture the dynamics of the late universe?

Abstract

We investigate how strongly late-time inferences about DE dynamics depend on the functional prior used to represent the expansion history. Using identical late-time combinations of CC, DESI BAO measurements, the Pantheon+ SN1a sample, and the H0DN prior, we compare a node-based reconstruction of the reduced Hubble function $E(z)$ with a representative family of smooth low-dimensional DE EoS parametrizations, including CPL. Over the redshift range constrained by the data, both approaches yield consistent $H(z)$, and, in the absence of H0DN, compatible values of $H_0$. However, a clear method dependence emerges at intermediate redshift ($z\sim 1.7$): the reconstruction favors stronger deceleration, $q_{\mathrm{Rec}}(1.7)\simeq 0.56-0.61$, whereas the smooth parametrizations cluster at $q(1.7)\simeq 0.32-0.40$, implying a persistent $\sim 2-3\sigma$ discrepancy across dataset combinations and parametrizations. For the EoS-based parametrizations, whose effective DE densities remain positive by construction, the preferred $w_{\mathrm{DE}}(1.7)<-1$ values correspond to NECB-violating (phantom-like) behaviour, but this is a less robust discriminator as $w_{\mathrm{DE}}$ becomes ill-conditioned as ${\rho }_{\mathrm{DE}}\to 0$. In the effective-fluid mapping, the reconstruction accommodates the same late-time kinematical preference through a rapid descent of ${\rho }_{\mathrm{DE}}(z)$ toward very small values and a sign change, whereas the EoS-based parametrizations absorb it through smoother, and in several cases NECB-violating, evolution over $z\sim 1-2$. Although the reconstruction improves the best-fit likelihood, especially with H0DN, Bayesian evidence continues to favor the simpler parametric descriptions. Our results isolate $z\sim 1.5-2$ as the key window in which EoS-based DE parametrizations can compress localized kinematic structure and associated features of DE that are still permitted by current late-time data.

20 pages, 7 figures, 3 tables