  We showed that the principle of nongravitating vacuum energy, when formulated
in the first order formalism, solves the cosmological constant problem. The
most appealing formulation of the theory displays a local symmetry associated
with the arbitrariness of the measure of integration. This can be motivated by
thinking of this theory as a direct coupling of physical degrees of freedom
with a "space - filling brane" and in this case such local symmetry is related
to space-filling brane gauge invariance. The model is formulated in the first
order formalism using the metric and the connection as independent dynamical
variables. An additional symmetry (Einstein - Kaufman symmetry) allows to
eliminate the torsion which appears due to the introduction of the new measure
of integration. The most successful model that implements these ideas is
realized in a six or higher dimensional space-time. The compactification of
extra dimensions into a sphere gives the possibility of generating scalar
masses and potentials, gauge fields and fermionic masses. It turns out that
remaining four dimensional space-time must have effective zero cosmological
constant.
