The DM by Quantum Gravitation theory (DMbQG hereafter), is a novel theory developed in the two main papers [1] and [2] Abarca,M.(2024). In the present work, in the framework of DMbQG theory it will derived the formula for the mass associated to the turnaround radius depending on the turnaround radius and it will be shown that the new expression has a deeper physical meaning regarding the same formula in the current LCDM paradigm. The DMbQG theory states a direct relation between the virial radius and the turnaround radius as well as the virial mass and the mass associated to the turnaround radius.The most important contribution of this work is placed in the chapter 2 where it has been demonstrated that the formula for the mass associated to the turnaround radius, using the DMbQG theory, is the same that the one in the current LCDM paradigm. However the new formula has a deeper physical meaning because its dimensionless factor is simpler regarding the one in the current LCDM paradigm. It is remarkable the fact that the both dimensionless factors depend on exclusively from the Universal omega parameters for the mass or for the DE and the both ones differ only a 5%. The fact that in the framework of DMbQG theory has been found a better formula for the mass associated to the turnaround radius is a strong support for the DMbQG theory whose hypothesis about the origin of DM is exclusively the gravitational field. The chapters 3, 4 and 5 are devoted to test the DMbQG theory in the clusters, Virgo, Coma and the Local Group of galaxies using recent data published about these clusters. The tests are mainly focused on the turnaround radius and its mass associated and all of them have been a complete success by the DMbQG theory.