Background dynamics and observational constraints of flat and non-flat $Λ(t)$CDM models from $H(z)$ and DESI DR2 BAO measurements

Abstract

In this work, we present comprehensive observational constraints on the time-varying vacuum $Λ(t)$CDM cosmology using the latest baryon acoustic oscillation (BAO) data from Dark Energy Spectroscopic Instrument (DESI) Data Release 2 measurements in combination with cosmic chronometer $H(z)$ data. We explicitly quantify the impact of vacuum dynamics on the expansion history, the total effective equation of state parameter of the unified cosmic fluid, the effective dark energy equation of state parameter, and the deceleration parameter in the spatially flat $Λ(t)$CDM model. We perform a full Markov Chain Monte Carlo (MCMC) analysis and statistical model comparison, providing a consistent assessment of the $Λ(t)$CDM model relative to the standard $Λ$CDM framework. Our results demonstrate that $H(z)$ and BAO observations strongly constrain deviations from the $Λ$CDM model, driving the vacuum dynamics parameter toward $α\simeq 0$, while significantly reducing parameter degeneracies and alleviating the Hubble tension.

Figures (7)

• Figure 1: Three-dimensional representation of the Hubble parameter $H(a)$ in the spatially flat $\Lambda(t)$CDM model, shown in the $\alpha-a$ phase space, for $\Omega_{m0}=0.3038$ and $H_0=68.91~{\rm km~s^{-1}Mpc^{-1}}$DESI:2025hao.
• Figure 2: Normalized Hubble expansion rate in the spatially flat $\Lambda(t)$CDM model as a function of the scale factor for different values of the vacuum dynamics parameter $\alpha$.
• Figure 3: Total effective EoS parameter of the unified cosmic fluid (solid lines) and the effective DE EoS parameter (dashed lines) as functions of the scale factor for different values of the vacuum dynamics parameter $\alpha$ in the spatially flat $\Lambda(t)$CDM model.
• Figure 4: Evolution of the deceleration parameter as a function of the scale factor for different values of the vacuum dynamics parameter $\alpha$ in the spatially flat $\Lambda(t)$CDM model.
• Figure 5: One-dimensional likelihoods and 1$\sigma$, 2$\sigma$ and 3$\sigma$ confidence levels contours constraints on the parameters of the $\Lambda(t)$CDM model from $H(z)$ measurements: for the flat space (left panel) and the non-flat space (right panel).