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

Dynamical vacuum models provide a minimal phenomenological extension of the standard Λ cold dark matter (ΛCDM) model in which the vacuum energy density evolves with cosmic time, potentially affecting late-time expansion. We investigated the background evolution of spatially flat and non-flat Λ (t) CDM cosmologies, parametrised by a dimensionless vacuum parameter, α, through their effective equation of state (EoS) and deceleration parameter, as well as their expansion dynamics. We aim to constrain their parameters using observational data and to assess their performance relative to spatially flat and non-flat ΛCDM models. We derived analytical expressions for the total effective and dark energy EoS parameters, as well as the deceleration parameter. We performed parameter estimation using Markov chain Monte Carlo (MCMC) analysis with 32 cosmic chronometer H (z) measurements and 13 DESI DR2 baryon acoustic oscillation (BAO) data points. Model comparison was carried out using ̧hi²_ Akaike, corrected Akaike, Bayesian, and deviance information criteria, and Akaike weights. The Λ (t) CDM model reproduces the standard matter-dominated evolution at early times and approaches a de Sitter phase at late times. The vacuum parameter, α, modifies the expansion history, shifting the transition from matter domination to dark energy domination, and altering the timing of the acceleration transition. Constraints from H (z) data alone are weak and exhibit parameter degeneracies, particularly in the spatially non-flat case. The inclusion of DESI DR2 BAO data significantly tightens constraints and yields α consistent with zero within 1σ in both spatially flat and non-flat scenarios. The spatial curvature is constrained to values consistent with flatness. The inclusion of BAO data also reduces the Hubble tension with early Universe measurements to below the 1σ level, while a residual ∼ 2. 6–3. 2σ tension with late-time determinations remains. Information criteria favour the spatially flat ΛCDM model. Current expansion data show no statistically significant evidence of vacuum dynamics. The Λ (t) CDM model is observationally viable but is not preferred to the standard spatially flat ΛCDM cosmology.