Theoretical Physics

TP
>
Volume 4, Number 1, March 2019

Developments of the Relativistic Bohm-Poisson Equation and Dark Energy
DOI:

10.22606/tp.2019.41003
**Author(s)**
Carlos Castro Perelman

**Affiliation(s)**
Center for Theoretical Studies of Physical Systems, Clark Atlanta University, Atlanta, GA, 30314, United States

**Abstract**
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 = 3
R2H
, consistent with current observations. We conclude with some
final remarks about Weyl’s geometry.

**Keywords**
Bohm’s Potential, Cosmology, Dark Energy.

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