Running vacuum model versus ΛCDM – a Bayesian analysis

Abstract

ABSTRACT We study the significance of the running vacuum model in which the vacuum energy density depends on the square of Hubble parameter, in comparison with the ΛCDM model. The Bayesian inference method is employed to appraise the relative significance of the running vacuum model, using the combined data sets, SN1a+CMB+BAO and SN1a+CMB+BAO+OHD. The model parameters and the corresponding errors are estimated from the marginal probability density function of the model parameters. The parameter that distinguish the running vacuum model from the ΛCDM model is ν. With the SN1a+CMB+BAO data set, we have found that the parameter ν is different from zero at ∼2.7σ. With the second data set, SN1a+CMB+BAO+OHD, the significance improved considerably to 3.4σ. 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 ΛCDM model. The analysis based on Jeffrey’s scale of bayesian inference shows that the evidence of our model against the ΛCDM model is weak for the data set SN1a+CMB+BAO. We have obtained a definite evidence of running vacuum model for SN1a+CMB+BAO + OHD data set. This indicates that the dark energy could be dynamical.