  We present a qualitatively new mechanism for dynamical spontaneous breakdown
of supersymmetry in supergravity. Specifically, we construct a modified
formulation of standard minimal N=1 supergravity as well as of anti-de Sitter
supergravity in terms of a non-Riemannian spacetime volume-form (generally
covariant integration measure density). The new supergravity formalism
naturally triggers the appearance of a dynamically generated cosmological
constant as an arbitrary integration constant which signifies spontaneous
(dynamical) breaking of supersymmetry. Applying the new formalism to anti-de
Sitter supergravity allows us to appropriately choose the above mentioned
arbitrary integration constant so as to obtain simultaneously a very small
effective observable cosmological constant as well as a large physical
gravitino mass as required by modern cosmological scenarios for slowly
expanding universe of the present epoch.
