In the frame of conformal Killing gravity cosmology, we performed a Bayesian analysis on two different datasets of baryon acoustic oscillations (DESI and SDSS DR16), two datasets of SNeIa ($\mathrm{Pantheon}+\text{and}\mathrm{Union}3$), and using the cosmic microwave background (CMB) Planck likelihood. The results for $H_0$ and ${\mathrm{\Omega }}_M$ in a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) background are consistent with the $\mathrm{\Lambda }$ cold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$) scenario. We obtain a non-negligible negative value for the novel density of dark sector, ${\mathrm{\Omega }}_D$, and its relevance in the evolution of the cosmological observables, thus finding quantitatively what its contribution is on real data to match the standard scenario. The results confirm the dynamical character of dark energy. We also calculate the deceleration parameter $q_0$ and the present time dark energy equation of state parameter $w_0$: the latter belongs to the quintessence regime. The evaluation of the first acoustic peak of CMB places it near to the best value provided by the Planck Collaboration. In this scenario, we can conclude that late time and early time data can be successfully matched under the same standard.

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• Alternative gravity theories
• Cosmological parameters
• Cosmology
• Dark energy
• Dark matter