7.6. THEORY OF DARK MATTER AND DARK ENERGY 489
Now we consider the constantk 1 in (7.6.63). Due to the astronomical fact that no gravi-
tational force between clusters of galaxies, we have
F(r) = 0 , r=the average distance between galactic clusters.By (7.6.71), we take
(7.6.73) r=
√
2
5
× 1020 km.Then we deduce from (7.6.63) that
k 1 r−k 0
r−
1
r^2= 0 ,
which, by (7.6.70) and (7.6.73), leads to
(7.6.74) k 1 = 10 −^57 km−^3.
In summary, we conclude that the dark matter and dark energy are essentially gravitational
effect generated by the gravitational potential fieldgμ ν, its dual fieldΦμand their nonlinear
interactions. They can be regarded as the gravitational field energy caused bygμ νandΦμ.