Present and future evidence for evolving dark energy

We compute the Bayesian evidences for one- and two-parameter models of evolving dark energy, and compare them to the evidence for a cosmological constant, using current data from Type Ia supernova, baryon acoustic oscillations, and the cosmic microwave background. We use only distance information, ignoring dark energy perturbations. We find that, under various priors on the dark energy parameters, $\Lambda \mathrm{CDM}$ is currently favored as compared to the dark energy models. We consider the parameter constraints that arise under Bayesian model averaging, and discuss the implication of our results for future dark energy projects seeking to detect dark energy evolution. The model selection approach complements and extends the figure-of-merit approach of the Dark Energy Task Force in assessing future experiments, and suggests a significantly-modified interpretation of that statistic.

Figure 1

68% and 95% confidence constraints on $w_0$ and $w_a$ for model IV (left plot) and model V (right plot). Note the axis ranges are different, to show the full prior ranges in each case. Model IV corresponds to a flat prior on the parameters over the range plotted, and Model V corresponds to a quintessence prior which amounts to a flat prior within the region shown by dotted lines (the contours go just a little out of that region due to the effect of binning the likelihoods of the obtained samples on a grid). The solid contours are for $\mathrm{WMAP}+\mathrm{SDSS}(\mathrm{BAO})+\mathrm{\text{Astier}}05$, and dot-dashed contours are for $\mathrm{WMAP}+\mathrm{SDSS}(\mathrm{BAO})+\mathrm{\text{Riess}}04$.

Figure 2

Marginalized posterior parameter distributions in Models II, III, IV, and V, using the $\mathrm{WMAP}+\mathrm{SDSS}(\mathrm{BAO})+\mathrm{\text{Astier}}05$ data combination.

Figure 3

Posterior parameter distributions obtained using the $\mathrm{WMAP}+\mathrm{SDSS}(\mathrm{BAO})+\mathrm{\text{Astier}}05$ data combination from Bayesian model averaging (BMA). The left set of four panels averages over all the five models under consideration, and the right over the quintessence-type models (I, II and V) alone. Some smoothing of the delta-functions has been carried out by binning.