Motion of test particles for Weyl-interaction modified gravity

Abstract

Since LHC has still given no signal of Supersymmetry, though the energy at which the signal was expected has been passed, one is left short of any good candidate for dark matter. We had proposed [A. Qadir, H. W. Lee and K. Y. Kim, Int. J. Mod. Phys. D 26 (2017) 1741001, 10 pp.] a modification of the Einstein–Hilbert action to explicitly display a term of matter and gravity interaction, [Formula: see text]. The hope had been that this would also resolve the problem of Quantum Gravity. However, the argument given for the purpose of quantum gravity, would more naturally lead one to expect the contraction, [Formula: see text], of the Weyl tensor with two copies of the stress–energy tensor rather than the product of the Ricci scalar and the trace of the stress–energy tensor. Here, the attempt is made to see if this prescription will provide a satisfactory explanation of the dark matter at all scales. One would then try to see if the problem of quantum gravity is resolved by the same prescription.