Model building with a dynamical volume element in gravity, particle theory and theories of extended object

Full Text:The Volume Element of Space Time can be considered as a geometrical object which can be independent of the metric. The use in the action of a volume element which is metric independent leads to the appearance of a measure of integration which is metric independent. This can be applied to all known generally coordinate invariant theories, we will discuss three very important cases: 1. 4-D theories describing gravity and matter fields, 2. Parametrization invariant theories of extended objects and 3. Higher dimensional theories including gravity and matter fields. In case 1, a large number of new effects appear: (i) spontaneous breaking of scale invariance associated to integration of degrees of freedom related to the measure, (ii) under normal particle physics laboratory conditions fermions split into three families, but when matter is highly diluted, neutrinos increase their mass and become suitable candidates for dark matter, (iii) cosmic coincidence between dark energy and dark matter is natural, (iv) quintessence scenarios with automatic decoupling of the quintessence scalar to ordinary matter, but not dark matter are obtained (2) For theories or extended objects, the use of a measure of integration independent of the metric leads to (i) dynamical tension, (ii) string models of non abelian confinement (iii) The possibility of new Weyl invariant light-like branes (WTT.L branes). These Will branes dynamically adjust themselves to sit at black hole horizons and in the context of higher dimensional theories can provide examples of massless 4-D particles with nontrivial Kaluza Klein quantum numbers, (3) In Bronx and Kaluza Klein scenarios, the use of a measure independent of the metric makes it possible to construct naturally models where only the extra dimensions get curved and the 4-D observable space-time remain flat