The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Examining the observational evidence for dynamical dark energy

We examine the ability of the $Lambda$CDM model to simultaneously fit different types of cosmological observations and apply a recently proposed test, based on the Kullback-Leibler divergence, to quantify the tension between different subsets of data. We find a tension between the distance indicators derived from a $Lambda$CDM model using a combined dataset, and the recent $H_0$ measurements, as well as the high redshift Baryon Acoustic Oscillations (BAO) obtained from the Lyman-$alpha$ forest spectra. We then allow for a dynamical dark energy (DE) and perform a Bayesian non-parametric reconstruction of the DE equation of state as a function of redshift. We find that the tension with $H_0$ and Lyman-$alpha$ forest BAO is effectively relieved by a dynamical DE. Although a comparison of the Bayesian evidence for dynamical DE with that of $Lambda$CDM shows that the tension between the datasets is not sufficiently strong to support a model with more degrees of freedom, we find that an evolving DE is preferred at a $3.5sigma$ significance level based solely on the improvement in the fit. We also perform a forecast for the upcoming DESI survey and demonstrate that, if the current best fit DE happens to be the true model, it will be decisively supported by the Bayesian evidence.