What is the connection between dark energy and the elusive force of antigravity?

[kurious]

A proton and an electron in a hydrogen atom experience electric and
gravitational forces on them.If a photon is absorbed the electric and
gravitational forces decrease.But suppose the sum of all forces in a
region of space-time stays constant:if the electric and gravitational
force decreased
then perhaps another force- a new force, so far unknown to science -
increases, so the sum of all forces is the same as it was before the
electric and gravitational forces decreased.
This means that the electric and gravitational force carriers would
have to communicate with the force carriers of the new force field.And
the same would apply to the colour force and weak force.But the new
force would have to have no effect on the trajectories of electrons,
protons etc. or else forces would not be observed to change with
distance -forces would be constant. So how would the new force
influence the physical world?
If we consider the momenta of force carriers as representing a force,
then
as the momenta of the electric force,for example, get smaller as the
electric force weakens with distance,the momenta of the new force
carriers would get larger.The electric force carriers would transfer
energy to the new force carriers.
The new force carriers must be exerting their effects not on protons
and electrons and other leptons and hadrons but on space itself!
Just as electric force carriers push electric charges apart, the new
force carriers could push regions of space apart.In other words, the
new force which keeps the sum of all forces in a region of space
constant, is dark energy.

 

[Antonio Lao]

then perhaps another force- a new force, so far unknown to science

The new force I am looking for is the repulsive force of antigravity. Brian Greene, in his new book "The Fabric of the Cosmos" talk about how forces are dependent on the spacetime dimensions. The discussions starting from page 394 to page 400 do make sense. These could possibly solidify what I have already thought all along that for 1-space and 1-time spacetime the two force terms in $r_i \times F_i \cdot r_j \times F_j$ are constant forces and therefore conservative due to the high level of symmetry in the topology.

There should be only two basic topologies regardless of the many permutations in the cross and dot product of vectors. One topology is gravity and one is antigravity. The mystery is why antigravity cannot be easily detected by our current technologies. If we can utilize this force of antigravity then future space travel is more than just a pipe dream of science fiction writers.