Title: On the universality of MOG weak field approximation at galaxy cluster scale,
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.