Conformal Killing Gravity: New Constraints from DESI DR2 BAO datasets
We investigate a geometric approach referred to as the Conformal Killing Gravity (CKG), in which the dark energy sector emerges naturally from the conformal Killing symmetry of the Robertson--Walker space-time. Within this framework, the divergence-free conformal Killing tensor behaves as an effective perfect fluid, giving rise to a dynamical dark-energy component whose density, pressure, and equation of state are uniquely determined by the underlying geometry, without introducing any empirical dark-energy parametrization. The resulting CKG model extends the standard $\Lambda$CDM cosmology through a single additional parameter while recovering the $\Lambda$CDM limit in the absence of the geometric contribution. We constrain the model using Planck PR4 (NPIPE) CMB temperature, polarization, and lensing observations, ACT DR6 CMB lensing, DESI DR2 baryon acoustic oscillation measurements, and the Pantheon$+$, DES-Dovekie, and Union3 Type Ia supernova compilations. The analysis shows that the CKG favors a quintessence-like dark-energy evolution with no evidence for phantom crossing, while the reconstructed equation of state rapidly approaches the cosmological constant at earlier cosmic times. Furthermore, the model predicts a future critical redshift in the range $-0.8 \lesssim z_c \lesssim -0.7$, indicating that the present cosmic expansion eventually reaches a turning point before the formal singular limit at $z=-1$. Since the geometric contribution modifies only the post-recombination expansion history, the sound horizon remains essentially unchanged and the model does not provide a complete solution to the $H_0$ tension. Our results demonstrate that the CKG provides a simple, physically motivated, and observationally favored framework for describing the late-time accelerated expansion of the Universe.