Nonparametric Dark Energy Reconstruction from Supernova Data

Understanding the origin of the accelerated expansion of the Universe poses one of the greatest challenges in physics today. Lacking a compelling fundamental theory to test, observational efforts are targeted at a better characterization of the underlying cause. If a new form of mass-energy, dark energy, is driving the acceleration, the redshift evolution of the equation of state parameter $w(z)$ will hold essential clues as to its origin. To best exploit data from observations it is necessary to develop a robust and accurate reconstruction approach, with controlled errors, for $w(z)$. We introduce a new, nonparametric method for solving the associated statistical inverse problem based on Gaussian process modeling and Markov chain Monte Carlo sampling. Applying this method to recent supernova measurements, we reconstruct the continuous history of $w$ out to redshift $z=1.5$.

Figure 1

Priors (red lines) and posteriors (black lines) for the GP hyperparameters $\rho$ and ${\kappa }^2$. The lower left panel shows the distribution of the GP mean. The lower right panel shows the results for ${\Delta }_{\mu }$. The posteriors for different $\alpha$ choices are very similar, and we show only the results for $\alpha \simeq 2$ here.

Figure 2

Nonparametric reconstruction of $w(z)$ based on GP modeling combined with MCMC. The upper panel uses a Gaussian covariance function, the bottom panel, an exponential covariance function. Both results are very close and in agreement with a cosmological constant (black dashed line). The dark blue shaded region indicates the 68% confidence level, while the light blue region extends it to 95%.