Is cosmography a useful tool for testing cosmology?

TL;DR

Cosmography, a model-independent approach based on the universe's large-scale homogeneity and isotropy, faces significant limitations and biases, making it unreliable for testing cosmological models like ΛCDM or ruling out alternatives.

Contribution

This paper critically evaluates the cosmographic approach, revealing its shortcomings and biases, and argues it is currently ineffective for testing cosmological theories.

Findings

Cosmography results depend heavily on the choice of auxiliary variables.

The method cannot effectively rule out models with higher-order derivatives.

Cosmography is unable to reliably reconstruct complex cosmological theories.

Abstract

Model-independent methods in cosmology has become an essential tool in order to deal with an increasing number of theoretical alternatives for explaining the late-time acceleration of the Universe. In principle, this provides a way of testing the Cosmological Concordance (or $\Lambda$CDM) model under different assumptions and ruling out whole classes of competing theories. One such model-independent method is the so-called cosmographic approach, which relies only on the homogeneity and isotropy of the Universe on large scales. We show that this method suffers from many shortcomings, providing biased results depending on the auxiliary variable used in the series expansion and is unable to rule out models or adequately reconstruct theories with higher-order derivatives in either the gravitational or matter sector. Consequently, in its present form, this method seems unable to provide reliable or useful results for cosmological applications.