Constraining the time-varying vacuum energy models in Brans-Dicke theory

Abstract

In this work, we constrain the time-varying vacuum energy models in Brans-Dicke theory within the framework of a flat Friedmann-Lamaître-Robertson-Walker space-time by using the latest observational data. In the first step, the analytical solution of field equations are found by considering the two functional forms of cosmological constant, viz. power-series form: $\Lambda =n_{1} H+n_{2} H^{2}$ and power-law form: $\Lambda \propto a^{-n}$, where $n_{1}$, $n_{2}$ and $n$ are all constants, and $H$ and $a$ are the Hubble parameter and scale factor, respectively. Then, to test the viability of the models, the latest data sample such as Hubble $H(z)$ data, Type Ia supernovae and baryon acoustic oscillations are used to constrain the model parameters. We apply the Markov Chain Monte Carlo (MCMC) method to find the best-fit values of the space parameters of both the models. The cosmological implications of the models are discussed by using the best-fit values of parameters. It is found that both the models are in good agreement with the datasets and are consistent with the analytical solutions. We use jerk parameter and selection criteria (AIC and BIC) to find the consistency of the proposed models with the observation as compared to $\Lambda$CDM model. Both the models explain the late-time acceleration of the Universe.