Running vacuum model versus $Λ$CDM -- a Bayesian analysis

Abstract: We study the running vacuum model in which the vaccum energy density depends on square of Hubble parameter in comparison with the $\Lambda$CDM model. In this work, the Bayesian inference method is employed to test against the standard $\Lambda$CDM model to appraise the relative significance of our model, using the combined data sets, Pantheon+CMB+BAO and Pantheon+CMB+BAO+Hubble data. The model parameters and the corresponding errors are estimated from the marginal likelihood function of the model parameters. Marginalizing over all model parameters with suitable prior, we have obtained the Bayes factor as the ratio of Bayesian evidence of our model and the $\Lambda$CDM model. The analysis based on Jeffrey's scale of bayesian inference shows that the evidence of our model against the $\Lambda$CDM model is weak for both data combinations. Even though the running vacuum model gives a good account of the evolution of the universe, it is not superior to the $\Lambda$CDM model.