Dynamical Volume Element in Scale-Invariant and Supergravity Theories

The use in the action integral of a volume element of the form $\Phi d^{D}x$, where $\Phi$ is a metric-independent measure density, can yield new interesting results in all types of known generally coordinate-invariant theories: (1) 4-D theories of gravity plus matter fields; (2) reparametrization invariant theories of extended objects (strings and branes); (3) supergravity theories. In case (1) we obtain interesting insights concerning the cosmological constant problem, inflation and quintessence without the fifth force problem. In case (2) the above formalism leads to dynamically induced tension and to string models of non-abelian confinement. In case (3), we show that the modified-measure supergravity generates an arbitrary dynamically induced cosmological constant, i.e., a new mechanism of dynamical supersymmetry breaking.