GRAVITATIONAL THEORY WITHOUT THE COSMOLOGICAL CONSTANT PROBLEM

We develop a gravitational theory where the measure of integration in the action principle is not necessarily root-G but it is determined dy namically through additional degrees of freedom. This theory is based on the demand that such measure respects the principle of ''non-gravit ating vacuum energy'' which states that the Lagrangian density L can b e changed to L + const. without affecting the dynamics. Formulating th e theory in the first-order formalism we get as a consequence of the v ariational principle a constraint that enforces the vanishing of the c osmological constant. The most realistic model that implements these i deas is realized in a six or higher dimensional space-time. The compac tification of extra dimensions into a sphere gives the possibility of generating scalar masses and potentials, gauge fields and fermionic ma sses. It turns out that the remaining four-dimensional space-time must have effective zero cosmological constant.