In this paper, we investigate the running vacuum energy (RVE) model within the framework of
gravity (
-RVE). In this context, the modified Friedmann equation can be used to establish a formal analogy with the
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In this paper, we investigate the running vacuum energy (RVE) model within the framework of
gravity (
-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
and
. We consider two cases of
-RVE, denoted as Model I (parametrized by
) and Model II (parametrized by
and
), corresponding to the first and second derivatives of
H, respectively. The models are constrained using recent DESI BAO data in combination with
, cosmic chronometer (CC), and CMB observations. Our analysis shows a deviation of
from zero at a significance level of ∼
for Model I, while in Model II,
and
deviate from zero at
and
, respectively, relative to
CDM. Furthermore, the statistical comparison based on the Akaike, Bayesian, and Deviance Information Criteria (AIC, BIC, DIC) indicates that Model I remains competitive with
CDM, while Model II is penalized due to its higher complexity and the sensitivity associated with the additional parameter
.
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