The gravitational analog of Maxwell's equations: A solution to the vacuum-energy and dark-energy problems.

If a reasonable estimate of the vacuum energy of quantum fields is included in the source term of Einstein's equation, that equation makes predictions wich are vastly at variance with observation. This is the ``vacuum-energy problem." In order to obtain reasonable results from Einstein's equation, one must ignore the vacuum energy of quantum fields; a practiice so common it is usually not even stated. This talk points out that there is a set of equations for the curvature tensor, the ``curvature equations," which are (1) formally analogous to Maxwell's equations, (2) are true and valid equations in conventional general relativity, and (3) do not suffer from the vacuum-energy problem. It is suggested that the curvature equations might be a better choice for the field equations of general relativity than the Einstein equation. This bold suggestion is supported by the fact that, according to the curvature equations, the vacuum energy of quantum fields makes no contribution to the curvature of spacetime, the Einstein equation emerges as a first integral of the curvature equations, and the cosmological constant is found to be an integration constant unrelated to the vacuum energy of quantum fields, and so its small observed value is not inconsistent with estimates of the vacuum energy of quantum fields.