Dark Energy as an Inverse Problem

TL;DR

This paper develops a model--independent inverse problem approach to reconstruct dark energy's equation of state w(z) from current and future cosmic distance data, highlighting limitations and potential improvements.

Contribution

It introduces a non-parametric inverse problem method for reconstructing w(z) and assesses its effectiveness with current and simulated future data sets.

Findings

Current data lack sufficient information to determine w(z) at z > 0.6.

A slight preference for w_{0} < -1 and w'(z) > 0 at z ~ 0.2--0.3.

Synthetic data from future surveys improve resolution of w(z).

Abstract

A model--independent approach to dark energy is here developed by considering the determination of its equation of state as an inverse problem. The reconstruction of w(z) as a non--parametric function using the current SNe Ia data is explored. It is investigated as well how results would improve when considering other samples of cosmic distance indicators at higher redshift. This approach reveals the lack of information in the present samples to conclude on the behavior of w(z) at z > 0.6. At low level of significance a preference is found for w_{0} < -1 and w'(z) > 0 at z ~ 0.2--0.3. The solution of w(z) along redshift never departs more than 1.95\sigma from the cosmological constant w(z)=-1, and this only occurs when using various cosmic distance indicators. The determination of w(z) as a function is readdressed considering samples of large number of SNe Ia as those to be provided by SNAP. It is found an improvement in the resolution of w(z) when using those synthetic samples, which is favored by adding data at very high z. Though the set of degenerate solutions compatible with the data can be retrieved through this method, these degeneracies in the solution will difficult the physical interpretation of the results. Through this approach, we have explored as well the gain in information in w(z) and the quality of the inversion achieved using different data sets of cosmic distance indicators.