V. S. Leonov
It is shown that the four-dimensional space-time convenient to characterize the four-dimensional gravitational action potential C2. Then dC2 may be a new invariant in addition to the known invariant ds2. In this case, the speed of light С can be expressed by a complex number. The square modulus of the speed of light C defines the gravitational potentials balance inside of the four-dimensional space time perturbed by gravity. The gravitational potentials balance describes the state of an elementary particle inside the gravitational well. Newton's classical gravitational potential φ indicates the depth of the gravitational well. The action potential C2 indicates the depth of the four-dimensional space-time. The introduction of the potentials of С2 and does not change of Newton's law of universal gravitation for force gravity which is directed at the "bottom" of the gravitational well. There is shown that dark energy and dark matter is a manifestation of the deformation (curvature) of four-dimensional space time. Our four-dimensional Universe is homogeneous and is not flat but has a curvature thereby determining the effect of gravity and antigravity.
PACS numbers: 04.20.-q; 03.30.+p