Reconstructing the history of dark energy using maximum entropy

Abstract

We present a Bayesian technique based on a maximum entropy method to reconstruct the dark energy equation of state $w(z)$ in a non--parametric way. This 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 Ia supernovae measurement from the HST/GOODS program and the first year Supernovae Legacy Survey (SNLS), complemented by cosmic microwave background and baryonic acoustic oscillations data. We find that the SNLS data are compatible with $w(z) = -1$ at all redshifts $0 \leq z \lsim 1100$, with errorbars of order 20% for the most constraining choice of priors. The HST/GOODS data exhibit a slight (about $1σ$ significance) preference for $w>-1$ at $z\sim 0.5$ 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 equation of state 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 equation of state, that can potentially miss or underestimate real structure in the data.