GRAVITATIONAL THEORY WITHOUT THE COSMOLOGICAL CONSTANT PROBLEM

We develop the principle of nongravitating vacuum energy, which is imp lemented by changing the measure of integration in the action from roo t-gd(D)x to an integration in an internal space of D scalar fields phi (a). As a consequence of such a choice of the measure, the matter Lagr angian L-m can be changed by adding a constant while no cosmological t erm is induced. Here we develop this idea to build a new theory which is formulated through the first order formalism, for example, when usi ng vielbein e(a)(mu) and spin connection omega(mu)(ab) (a,b=1,2,...,D) as independent variables. The equations obtained from the variation o f e(a)(mu) and the fields phi(a) imply the existence of a nontrivial c onstraint. This approach can be made consistent with invariance under arbitrary diffeomorphisms in the internal space of scalar fields phi(a ) (as well as in ordinary space-time), provided that the matter model is chosen so as to satisfy the above-mentioned constraint. If the matt er model is not chosen so as to satisfy automatically this constraint, the diffeomorphism invariance in the internal space is broken. In thi s case the constraint is dynamically implemented by the degrees of fre edom that become physical because of the breaking of the internal diff eomorphism invariance. However, this constraint always dictates the va nishing of the cosmological constant term and the gravitational equati ons in the vacuum coincide with vacuum Einstein's equations with zero cosmological constant. The requirement that the internal diffeomorphis ms be a symmetry of the theory points towards the unification of force s in nature such as in the Kaluza-Klein scheme.