## Gravitational Field Equations and Theory of Dark Matter and Dark Energy    [PDF]

Tian Ma, Shouhong Wang
The main objective of this article is to derive a new set of gravitational field equations and to establish a new unified theory for dark energy and dark matter. The new gravitational field equations with scalar potential are derived using the Einstein-Hilbert functional, and the scalar potential is a natural outcome of the divergence-free constraint of the variational elements. Associated with this scalar potential is the scalar potential energy density $\Phi$, which represents a new type of energy caused by the non-uniform distribution of matter in the universe. The negative part of this potential energy density $\Phi$ represents the dark matter, which produces attraction, and the positive part represents the dark energy, which drives the acceleration of expanding galaxies. In addition, this potential energy density $\Phi$ is conserved with mean zero: $\int_M \Phi dM=0$. Furthermore, the new field equations resolve a few difficulties encountered by the classical Einstein field equations.
View original: http://arxiv.org/abs/1206.5078