Response to a critique of "Cotton Gravity"

TL;DR

This paper defends Cotton Gravity against recent criticism, clarifying misconceptions and demonstrating that the critique's claims about the theory's predictiveness and physical validity are unfounded.

Contribution

It provides a detailed rebuttal to the critique, correcting misunderstandings and reaffirming the theoretical consistency of Cotton Gravity.

Findings

The critique's claim of non-predictiveness is incorrect.

Cotton Gravity remains a consistent and predictive theory.

The geometric constraints do not render the theory undetermined.

Abstract

We address in this article the criticism in a recently submitted article by Clement and Noiucer (arXiv:2312.17662 [gr-qc]) on "Cotton Gravity" (CG), a gravity theory alternative to General Relativity. These authors claim that CG is "not predictive" for producing "too many" spherically symmetric vacuum solutions, while taking the Bianchi I vacuum as test case they argue that geometric constraint on the Cotton tensor lead to an undetermined problem, concluding in the end that CG "is not a physical theory". We provide arguments showing that this critique is incorrect and misrepresents the theory.