Lost in the Log-Polynomial Expansion: Comment on arXiv:2101.08278

TL;DR

This paper critiques a recent method using orthogonalized logarithmic polynomials for approximating flat dm, arguing it does not resolve fundamental issues with previous polynomial expansions and may still lead to misleading conclusions.

Contribution

It provides a critical analysis showing that the new orthogonalized logarithmic polynomial technique does not fix earlier identified problems in dm approximations.

Findings

The new method does not address the core issues of polynomial approximation.

The original criticisms about log polynomial expansions remain valid.

The recent technique may still lead to misleading inferences.

Abstract

In [1] we highlighted the fact that the log polynomial expansion employed in Nature Astron. 3, no.3, 272-277 (2019) [2] is a poor approximation to flat $\Lambda$CDM, so using it to infer deviations from flat $\Lambda$CDM is not well-motivated. The "orthogonalized logarithmic polynomials" recently presented in arXiv:2101.08278 [3] are an attempt to respond to the earlier criticism [1]. Here we demonstrate that this new technique [3] - interesting though it may be - fails to address the fundamental problem raised in [1]. Unfortunately, the claim made in [2] may still be lost in the expansion.