Cosmological constraints on two vacuum decay models

We constrain two vacuum decay models ($\Lambda(t)$CDM, proposed by the authors of~\cite{Brito:2024bhh}) utilizing the baryon acoustic oscillations (BAO) data released by the Dark Energy Spectroscopic Instrument (DESI), distance prior from the cosmic microwave background (CMB) observed by the Planck satellite, Hubble rate data obtained via the cosmic chronometers (CC) method and type Ia supernova (SNIa) data. The interaction terms between dark matter and dark energy are defined as $Q=3\varepsilon H\rho_{\Lambda}$ for model I and $3\varepsilon aH\rho_{\Lambda}$ for model II. We find that the decay parameter is constrained to be $\varepsilon=0.0094^{+0.0037}_{-0.0033}$ for model I and $\varepsilon=0.0119\pm{0.0045}$ for model II, respectively, indicating a potential interaction between dark matter and dark energy at the $2\sigma$ confidence level. The current Hubble parameter values are estimated to be $H_{0}=70.30\pm{0.67}$ for model I and $H_{0}=70.28\pm{0.64}$ for model II. These values of $H_0$ fall between those derived from the Planck and SH0ES data, suggesting that these two vacuum decay models could provide a potential solution to alleviate the Hubble tension problem.