Testing Cotton gravity as dark matter substitute with weak lensing

TL;DR

This study tests Cotton gravity, a modified gravity theory proposed as a dark matter substitute, using galaxy-galaxy weak lensing data, and finds it cannot fully replace dark matter based on observational evidence.

Contribution

The paper provides the first observational test of Cotton gravity with galaxy-galaxy lensing data, constraining its viability as a dark matter alternative.

Findings

Cotton gravity significantly deviates from observed lensing signals.

It cannot independently replace dark matter in explaining galaxy rotation and lensing.

Constraints on the combination of dark matter and Cotton gravity are established.

Abstract

Harada proposed a modified theory of gravity called Cotton gravity, and argued that it successfully explains the rotation curves of $84$ galaxies without the need of dark matter. In this work we use galaxy-galaxy lensing technique to test whether the modification effect of Cotton gravity can indeed be a viable substitute for dark matter. Using the spherically symmetric solution of Cotton gravity, we obtain the deflection angle via Gauss-Bonnet theorem and the weak lensing shear. We use five galaxy catalogs divided in 5 stellar mass bins from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7), each of which is further divided into blue star forming galaxy and red passive galaxy sub-catalogs. We find that Cotton gravity on its own has significant deviation from the measured galaxy-galaxy lensing signals, thus it cannot replace the role of dark matter. If we consider the combination of dark matter and Cotton gravity, the modification is tightly constrained. Our analysis also applies to other modified gravity theories whose an additional linear term appears in the Schwarzschild solution.