Confronting dark energy in Harada's Conformal Killing Gravity with observational data

Based on a comprehensive analysis of recent observational data-a combination of DESI DR1, Planck CMB, and Pantheon+ SN Ia-this study critically evaluates the two dark energy (DE) proposals within Harada's Conformal Killing Gravity (CKG) model. The model in question predicts either a dominant phantom-type effective DE component with EoS $\omega = -5/3$ or a hybrid scenario combining a cosmological constant ($\omega = -1$) with a subdominant $\omega = -5/3$ fluid (around $5\%$) to address the Hubble tension (HT) and late-time acceleration. An analysis based on the Trans-Planckian Censorship Conjecture (TCC) demonstrates that the pure CKG fluid scenario $\omega = -5/3$ is excluded, whereas the hybrid model remains only marginally compatible. Our Markov Chain Monte Carlo (MCMC) analysis constrains the effective DE density parameter to $\Omega_{\text{eff}} = 0.009^{+0.006}_{-0.007}$ ($68\%$ CL), consistent with zero and ruling out the around $5\%$ contribution required by Harada's CKG. The resulting Hubble expansion history $H(z)$ and effective EoS $\omega_{\text{eff}}(z)$ are indistinguishable from those of $\Lambda$CDM. Bayesian model comparison via the Akaike Information Criterion (AIC) shows no statistical preference for CKG over $\Lambda$CDM ($\Delta \text{AIC} = +2.6$), disfavoring the additional complexity of the CKG model. The key output of this study is that both DE proposals in Harada's CKG are ruled out by current cosmological data, and HT remains unresolved.