Testing the running vacuum model in light of DESI-DR2 Measurements

Abstract

Motivated by the fact that quantum effects leave an imprint on the vacuum equation of state, making it depart from the standard cosmological constant relation, $P_{\rm vac}=-ρ_{\rm vac}$, this work investigates generalized running vacuum models (RVMs) by considering a dynamical vacuum equation of state in which the vacuum energy density, $ρ_{\text{vac}}$, evolves as a function of the Hubble parameter, $H$, and its time derivative, $\dot{H}$. This formulation extends previous running vacuum approaches by incorporating a dependence of the vacuum energy density on both, $H^2$ and $\dot{H}$. The corresponding Friedmann equations are derived and analyzed to study their impact on cosmic expansion. The model parameters are constrained through a joint statistical analysis combining the cosmic microwave background shift parameters, DESI-DR2 observations, PantheonPlus type Ia supernovae compilation, and Hubble rate $H(z)$ measurements. Model comparison is performed using information criteria, the Akaike Information Criterion (AIC) and Deviance Information Criterion (DIC), in order to assess the statistical performance of the RVMs relative to the standard $Λ$CDM scenario. The results show that the generalized RVMs provide a good fit to current observations and represent a statistically competitive alternative to the standard $Λ$CDM model. Notably, all three running vacuum formulations yield lower AIC and DIC values than $Λ$CDM, indicating that dynamical running vacuum energy remains a viable cosmological scenario.