Solving the Conundrum of Dark Matter and Dark Energy in Galaxy Clusters

This paper develops the Dark Matter by Quantum Gravitation theory, DMbQG theory hereafter, in clusters of galaxies in the cosmologic model ΛCDM of the Universe. Originally this theory was developed by the author for galaxies, especially using MW and M31 rotation curves. An important result got by the DMbQG theory is that the total mass associated to a galactic halo depend on the square root of radius, being its dominion unbounded. Apparently, this result would be absurd because of divergence of the total mass. As the DE is negligible at galactic scale, it is needed to extend the theory to clusters in order to study the capacity of DE to counterbalance to DM. Thanks this property, the DMbQG theory finds unexpected theoretical results. In this work, it is defined, the total mass as baryonic matter plus DM and the gravitating mass as the addition of the total mass plus the negative mass associated to dark energy. In clusters it is defined the zero gravity radius (R_ZG hereafter) as the radius needed by the dark energy to counterbalance the total mass. It has been found that the ratio R_ZG/R_VIRIAL ≈ 7.3 and its Total mass associated at R_ZG is ≈2.7 M_VIRIAL. In addition, it has been calculated that the sphere with the extended halo radius R_E = 1.85 R_ZG has a ratio DM density versus DE density equal to 3/7 and its total mass associated at R_E is ≈3.6 M_VIRIAL. This works postulates that the factor 3.6 may equilibrate perfectly the strong imbalance between the Local mater density parameter (0.08) versus the current Global matter density one (0.3). Currently, this fact is a big conundrum in cosmology, see chapter 7. Also it has been found that the zero velocity radius, R_ZV hereafter, i.e. the cluster border because of the Hubble flow, is ≈0.6 R_ZG and its gravitating mass is ≈ 1.5 M_VIR. By derivation of gravitating mass function, it is calculated that at 0.49 R_ZG, this function reaches its maximum whose value is ≈1.57 M_VIR. Throughout the paper, some of these results have been validated with recent data published for the Virgo cluster. As Virgo is the nearest big cluster, it is the perfect benchmark to validate any new theory about DM and DE. These new theoretical findings