Fables of reconstruction: controlling bias in the dark energy equation of state

TL;DR

This paper introduces a Bayesian non-parametric method with a carefully chosen prior for reconstructing the dark energy equation of state w(z) from observational data, achieving high accuracy and minimal bias.

Contribution

It presents a novel, efficient approach using correlated priors and principal component analysis to improve reconstruction of w(z) while reducing bias and variance.

Findings

Reconstruction accuracy is typically under 10% up to redshift z=1.5.

The method effectively minimizes bias in the mean behavior of w(z).

Performance depends on the assumed smoothness of w(z).

Abstract

We develop an efficient, non-parametric Bayesian method for reconstructing the time evolution of the dark energy equation of state w(z) from observational data. Of particular importance is the choice of prior, which must be chosen carefully to minimise variance and bias in the reconstruction. Using a principal component analysis, we show how a correlated prior can be used to create a smooth reconstruction and also avoid bias in the mean behaviour of w(z). We test our method using Wiener reconstructions based on Fisher matrix projections, and also against more realistic MCMC analyses of simulated data sets for Planck and a future space-based dark energy mission. While the accuracy of our reconstruction depends on the smoothness of the assumed w(z), the relative error for typical dark energy models is <10% out to redshift z=1.5.