Testing non-conservative Conformal Killing Gravity with cosmological observations

In this paper we test Non-Conservative Conformal Killing Gravity (NC-CKG), a geometric extension of general relativity in which the cosmological constant arises as a constant of integration and the energy-momentum tensor is allowed to deviate from covariant conservation through an effective coupling parameter, τ . We constrain the model with a Bayesian MCMC analysis combining Cosmic Chronometers, DESI DR2 baryon acoustic oscillations, and three Type Ia supernova compilations (Pantheon+, Union3, and DES-Dovekie). Across all dataset combinations, τ remains consistent with zero, with only a mild tendency toward negative values. A negative τ corresponds to a faster dilution of the pressureless matter density than the standard a − 3 scaling, while the current data do not provide statistically significant evidence for a departure from matter conservation. The conformal-Killing density parameter Ω D is negative in all dataset combinations, while the resulting expansion history gives transition redshifts in the range z t ≈ 0.68–0.74. When the SH0ES local distance-ladder calibration is included, the model gives H 0 = 72.85 ± 0.98 km s − 1 Mpc − 1 . This high value is not driven by the additional freedom in τ , since flat ΛCDM and conservative CKG give comparable constraints under the same calibration. Model selection via AIC and BIC generally favours the conservative limit ( τ = 0 ) or ΛCDM over the full non-conservative model. Overall, NC-CKG remains a geometrically motivated alternative to dark energy, although current background-expansion data do not require non-conservation. Future observations will provide stronger tests of the model.