A regularized free-form estimator for dark energy

We construct a simple, regularized estimator for the dark energy equation of state by using the recently introduced linear response approximation. We show that even a simple regularization substantially improves the performance of the free-form fitting approach. The use of the linear response approximation allows an analytical construction of the maximum likelihood estimator, in a convenient and easy to use matrix form. We show that, in principle, such regularized free-form fitting can give us an unbiased estimate of the functional form of the equation of state of dark energy. We show the efficacy of this approach on simulated SuperNova Acceleration Probe class data, but it is easy to generalize this method to include other cosmological tests. We provide a possible explanation for the sweet spots seen in other reconstruction methods.