Developments of the Relativistic Bohm-Poisson Equation and Dark Energy

The nonlinear and novel Bohm-Poisson-Schrödinger equation proposed by us is studied further. It has solutions leading to repulsive gravitational behavior. An exact analytical expression for the observed vacuum energy density is obtained. Further results are provided which include two possible extensions of the Bohm-Poisson equation to the full relativistic regime. Two specific solutions to the novel Relativistic Bohm-Poisson equation (associated to a real scalar field) are provided encoding the repulsive nature of dark energy. One solution leads to an exact cancellation of the cosmological constant, but an expanding decelerating cosmos; while the other solution leads to an exponential accelerated cosmos consistent with a de Sitter phase, and whose extremely small cosmological constant is Λ = 3 R2 H , consistent with current observations. We conclude with some final remarks about Weyl’s geometry.