What do we know about cosmography

TL;DR

This paper uses bias-variance trade-off to evaluate cosmography's effectiveness in describing supernova data and constrains dark energy properties, highlighting the potential of future measurements to improve cosmographic analysis.

Contribution

It introduces a bias-variance based approach to assess cosmography, identifies the optimal order for approximation, and explores its implications for dark energy modeling.

Findings

Cosmography up to second order best describes supernova data.

Future measurements can significantly improve cosmographic constraints.

Supernova cosmography cannot reliably estimate dark energy parameters.

Abstract

In the present paper, we investigate the cosmographic problem using the bias-variance trade-off. We find that both the z-redshift and the $y=z/(1+z)$-redshift can present a small bias estimation. It means that the cosmography can describe the supernova data more accurately. Minimizing risk, it suggests that cosmography up to the second order is the best approximation. Forecasting the constraint from future measurements, we find that future supernova and redshift drift can significantly improve the constraint, thus having the potential to solve the cosmographic problem. We also exploit the values of cosmography on the deceleration parameter and equation of state of dark energy $w(z)$. We find that supernova cosmography cannot give stable estimations on them. However, much useful information was obtained, such as that the cosmography favors a complicated dark energy with varying $w(z)$, and the derivative $dw/dz<0$ for low redshift. The cosmography is helpful to model the dark energy.