Friedmann cosmology with decaying vacuum density in Brans–Dicke theory

In this paper, we study Friedmann cosmology with time-varying vacuum energy density in the context of Brans-Dicke theory. We consider an isotropic and homogeneous flat space, filled a matter-dominated perfect fluid dynamical cosmological term $\Lambda(t) $, obeying equation state vacuum. As exact nature possible is yet to be found, explore $\Lambda(t)$ given by phenomenological law $\Lambda(t)=\lambda+\sigma H$, where $\lambda$ $\sigma$ are positive constants. solve model then focus on two different cases $\Lambda_{H1}$ $\Lambda_{H2}$ assuming $\Lambda=\lambda$ $\Lambda=\sigma respectively. Notice that analog standard $\Lambda$CDM, but within cosmology. find analytical solution main functions such as Hubble parameter, scale factor, deceleration parameters for these models. order test viability scenarios, perform sets joint observational analyses recent Type Ia supernova data (Pantheon), measurements parameter data, Baryon acoustic oscillation/Cosmic microwave background Local constant each model. For sake comparison, same analysis performed $\Lambda$CDM Each shows transition from decelerated phase accelerated can viewed effective quintessence behavior. Using selection criteria AIC BIC distinguish existing dark models, $\Lambda$-cosmology (i.e. our $\Lambda_{H1}$) performs at level comparable whereas less favoured.