Reconstructing the evolution of deceleration parameter with the non-parametric Bayesian method

In order to answer the question of whether the current acceleration of the cosmic expansion is slowing down or not, in this paper we use a non-parametric Bayesian method to reconstruct the evolution of the deceleration parameter $q\left(z\right)$ from the latest observations including the type Ia supernova data, the baryon acoustic oscillation data, the Planck cosmic microwave background data, the Hubble data as well as the local value of Hubble constant. We find that all the data support a currently increasing cosmic acceleration, a spatially flat universe is favored and the effects of the spatial curvature on the reconstructed result are negligible. Moreover, the evolution of $q\left(z\right)$ displays an oscillatory behavior, which is preferred by observations at the $3.2\sigma$ confidence level as compared with that in the $\Lambda$CDM. But, the reconstructed $q\left(z\right)$ is punished by the Bayesian information criteria due to more many model parameters.