Response to a critique of "Cotton Gravity"

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.