GRAVITATIONAL THEORY WITHOUT THE COSMOLOGICAL CONSTANT PROBLEM, SYMMETRIES OF SPACE-FILLING BRANES, AND HIGHER DIMENSIONS

We show that the principle of nongravitating vacuum energy, when formu lated in the first order formalism, solves the cosmological constant p roblem. The most appealing formulation of the theory displays a local symmetry associated with the arbitrariness of the measure of integrati on. This can be motivated by thinking of this theory as a direct coupl ing of physical degrees of freedom with a ''space-filling brane'' and in this case such local symmetry is related to space-filling brane gau ge invariance. The model is formulated in the first order formalism us ing the metric G(AB) and the connection Gamma(BC)(A) as independent dy namical variables. An additional symmetry (Einstein-Kaufman symmetry) allows one to eliminate the torsion which appears due to the introduct ion of the new measure of integration. The most successful model that implements these ideas is realized in a six-or higher-dimensional spac e-time. The compactification of extra dimensions into a sphere gives t he possibility of generating scalar masses and potentials, gauge field s, and fermionic masses. It turns out that remaining four-dimensional space-time must have an effective zero cosmological constant.