Expectations and sensitivity of the scalar field Dark Energy reconstruction from the SNe Ia data

TL;DR

This paper investigates a model-independent method for reconstructing the scalar field potential of Dark Energy from SNe Ia data, highlighting its limitations with current data precision and the challenges in obtaining reliable reconstructions.

Contribution

The paper introduces a no-Ansatz reconstruction method for Dark Energy scalar fields and assesses its stability and limitations using synthetic and real SNe Ia datasets.

Findings

Reconstruction is perfect with synthetic data but unreliable with real data.

Errors in potential and kinetic term reconstructions are large and often unphysical.

Current data precision limits the effectiveness of the model-independent approach.

Abstract

The current paper is addressing the possibility of the Dark Energy scalar field potential reconstruction from the SNe Ia data and the problems arising during the process. We describe the method and test its limits, stability of the reconstruction with respect to the $\Omega_m$ and $H_0$ parameters, as well as several issues connected to the errors propagation, with use of synthetic data. After that, we test the method with real Union2.1 and JLA, as well as recent PANTHEON SNe Ia datasets. It worths mentioning that in our approach we assume no {\it Ans\"atzen} on the dynamical variables (e.g., $H(z)$), which makes our method free of any degeneracies and biases which arise if one assume one or another way to parameterize $H(z)$, or the equation of state, or some other variable. On the other hand, the price we pay for this freedom is immense -- although the scheme demonstrates perfect reconstruction in the case of synthetic data, the reconstruction from the real data seems almost impossible, at least on the current data precision level. The errors of the resulting potential and of the kinetic term are huge; for the Hubble parameter they are smaller but still severalfold larger than those obtained with parameterization. Finally, we test the method with non-SNe $H(z)$ datasets, and the results are also disappointing -- similar to the SNe case, the reconstruction is not possible as the reconstructed kinetic term enters the negative values. This could be treated as a manifestation of the insufficient data precision, or as the overestimation of $(H_0, \Omega_m)$ values -- we discuss both possibilities.