Reconstructing the history of dark energy using maximum entropy

We present a Bayesian technique based on a maximum-entropy method to reconstruct the dark energy equation of state (EOS) w(z) in a non-parametric way. This Maximum Entropy (MaxEnt) technique allows to incorporate relevant prior information while adjusting the degree of smoothing of the reconstruction in response to the structure present in the data. After demonstrating the method on synthetic data, we apply it to current cosmological data, separately analysing Type la supernova measurement from the HSTIGOODS programme and the first-year Supernovae Legacy Survey (SNLS), complemented by cosmic microwave background and baryonic acoustic oscillation data. We find that the SNLS data are compatible with w (z) = -1 at all redshifts 0 <= less than or similar to 1100, with error bars of the order of 20 per cent for the most-constraining choice of priors. The HSTIGOODS data exhibit a slight (about I a significance) preference for w > - 1 at z similar to 0.5 and a drift towards w > -1 at larger redshifts which, however, is not robust with respect to changes in our prior specifications. We employ both a constant EOS prior model and a slowly varying w(z) and find that our conclusions are only mildly dependent on this choice at high redshifts. Our method highlights the danger of employing parametric fits for the unknown EOS, that can potentially miss or underestimate real structure in the data.