The KdV in Cosmology: a useful tool or a distraction?

TL;DR

This paper critically examines the use of the Schwarzian derivative technique in cosmology, revealing it as a consequence of linearizability of cosmological equations and linking it to Schrödinger equations.

Contribution

It clarifies the mathematical foundations of the Schwarzian derivative method in cosmology and connects it to linear differential equations and Schrödinger equations.

Findings

Schwarzian derivative technique arises from linearizability of cosmological equations.

The linearized form of the equations is equivalent to a Schrödinger equation.

The paper questions the utility of the Schwarzian method in cosmological analysis.

Abstract

The letter is a response to the recent article by J. Lidsey. We demonstrate that the Schwarzian derivative technique developed therein is but a consequence of linearizabiliy of the original cosmological equations. Furthermore, we show the required linearized equation to be nothing else but a Schr\"odinger equation.