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

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 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 a 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. (C) 2017 The Author(s). Published by Elsevier B.V.We warmly acknowledge John Moffat for fruitful discussion and his valuable comments. I.D.M acknowledge financial supports from University of the Basque Country UPV/EHU under the program "Convocatoria de contratacion para la especializacion de personal investigador doctor en la UPV/EHU 2015", from the Spanish Ministerio de Economia y Competitividad through the research project FIS2010-15492, and from the Basque Government through the research project IT-956-16. M.D.L. is supported by the ERC Synergy Grant "BlackHoleCam" - Imaging the Event Horizon of Black Holes (Grant No. 610058). M.D.L. acknowledge INFN Sez. di Napoli (Iniziative Specifiche QGSKY and TEONGRAV). This article is based upon work from COST Action CA1511 Cosmology and Astrophysics Network for Theoretical Advances and Training Actions (CANTATA), supported by COST (European Cooperation in Science and Technology)