Physical Consequences of a Theory with Dynamical Volume Element

Abstract

We survey motivation, basic ideas and physical consequences of a theory where the underlying action involves terms both with the usual volume element $\sqrt{-g}{d}^{4}x$ and with the new one $\Phi d^{4}x=4!d{\phi }_1\wedge d{\phi }_2\wedge d{\phi }_3\wedge d{\phi }_4$. The latter may be interpreted as the 4-form determined on the 4-D space-time manifold (not necessary Riemannian). Regarding the scalar fields ${\phi }_a(a=1,...4)$ as new dynamical variables and proceeding in the first order formalism we realize the so-called Two Measures Theory which possesses a number of attractive features. We discuss new physical effects which arise from this theory and in particular strong gravity effect in high energy physics experiments.

23 pages, 7 figures, plenary talk given at the Workshop Geometry, Topology, QFT and Cosmology, Paris, 28-30 May 2008