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.