Testing Running Vacuum Energy in f(Q) Gravity with DESI Data

In this paper, we investigate the running vacuum energy (RVE) model within the framework of f(Q) gravity (f(Q)–RVE). In this context, the modified Friedmann equation can be used to establish a formal analogy with the structure of the RVE. A key feature is that the vacuum equation of state is no longer fixed but receives a dynamical correction proportional to H˙ and H¨/H. We consider two cases of f(Q)–RVE, denoted as Model I (parametrized by ν) and Model II (parametrized by ν and α), corresponding to the first and second derivatives of H, respectively. The models are constrained using recent DESI BAO data in combination with Pantheon+, cosmic chronometer (CC), and CMB observations. Our analysis shows a deviation of ν from zero at a significance level of ∼1.4σ for Model I, while in Model II, ν and α deviate from zero at 0.7σ and 1.3σ, respectively, relative to ΛCDM. Furthermore, the statistical comparison based on the Akaike, Bayesian, and Deviance Information Criteria (AIC, BIC, DIC) indicates that Model I remains competitive with ΛCDM, while Model II is penalized due to its higher complexity and the sensitivity associated with the additional parameter α.