# On the universality of MOG weak field approximation at galaxy cluster scale

## TL;DR

This paper tests the universality of Yukawa-corrected gravity parameters at galaxy cluster scales using Sunyaev-Zeldovich data, finding that the parameters are not universal but the modified gravity model can still fit cluster profiles with scale-dependent parameters.

## Contribution

It demonstrates that the universal Yukawa correction parameters are inconsistent at galaxy cluster scales, but a scale-dependent approach can successfully model cluster observations.

## Key findings

- Universal Yukawa parameters are ruled out at >3.5σ for galaxy clusters.
- Modified gravity can fit cluster profiles with scale-dependent parameters.
- The theory remains viable when the scale dependence of the potential is considered.

## Abstract

In its weak field limit, Scalar-tensor-vector gravity theory introduces a Yukawa-correction to the gravitational potential. Such a correction depends on the two parameters, $\alpha$ which accounts for the modification of the gravitational constant, and $\mu^{*-1}$ which represents the scale length on which the scalar field propagates. These parameters were found to be universal when the modified gravitational potential was used to fit the galaxy rotation curves and the mass profiles of galaxy clusters, both without Dark Matter. We test the universality of these parameters using the the temperature anisotropies due to the thermal Sunyaev-Zeldovich effect. In our model the intra-cluster gas is in hydrostatic equilibrium within the modified gravitational potential well and it is described by a polytropic equation of state. We predict the thermal Sunyaev-Zeldovich temperature anisotropies produced by Coma cluster, and we compare them with those obtained using the Planck 2013 Nominal maps. In our analysis, we find $\alpha$ and the scale length, respectively, to be consistent and to depart from their universal values. Our analysis points out that the assumption of the universality of the Yukawa-correction to the gravitational potential is ruled out at more than $3.5\sigma$ at galaxy clusters scale, while demonstrating that such a theory of gravity is capable to fit the cluster profile if the scale dependence of the gravitational potential is restored.