Dynamical Oscillations in Dark Energy: Joint Constraints on the $w_{sin}$CDM Model from DESI, OHD, and Supernova Samples

In this study, we investigate the oscillatory dark energy model $w_{\sin}\mathrm{CDM}$ based on the DESI BAO data together with OHD, Pantheon Plus, and SH0ES measurements. We examine how the DESI data influence the dark energy equation-of-state plane $(w_0, w_a)$ within cosmological models that are free from Hubble tension and employ a Monte Carlo Markov Chain (MCMC) approach. Our findings indicate that although the parameter space still favors $w_a < 0$ and $w_0 > -1$ , the cosmological constant remains consistent with the DESI+OHD+PP combination at the $2\sigma$ level. We also observe that the best-fit Hubble constant $H_0$ is higher for the DESI+OHD+PP+SH0ES data combination, leading to a residual Hubble tension of less than $1\sigma$ to remain consistent with the SH0ES measurement. These results suggest that attempts to address the Hubble tension tend to reduce indication of DESI for the oscillatory dark energy model. Therefore, claims that the cosmological constant should be approached with greater caution, considering both the latest observational datasets and the existing cosmological tensions. We also obtained the present deceleration parameter and the effective equation-of-state value as $q_0 = -0.36$ and $w_{\mathrm{eff}} = -0.57$, respectively, for the DESI+OHD+PP+SH0ES dataset combination. Further analysis indicated a strong departure of $w_0$ from $w=-1$ at the $4\sigma$ level for the DR2+OHD+DES-5yr data combination. The inferred $\Omega_{m}$ tended to shift toward higher values when supernova samples were included, indicating a systematic preference for larger $\Omega_{m}$ in combinations involving supernova data.