Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-04-09
Phys.Rev.D77:125027,2008
Physics
High Energy Physics
High Energy Physics - Theory
24 pages, revision includes minor corrections and additional clarifying material
Scientific paper
10.1103/PhysRevD.77.125027
The field theoretic action for gravitational interactions in d+2 dimensions is constructed in the formalism of 2T-physics. General Relativity in d dimensions emerges as a shadow of this theory with one less time and one less space dimensions. The gravitational constant turns out to be a shadow of a dilaton field in d+2 dimensions that appears as a constant to observers stuck in d dimensions. If elementary scalar fields play a role in the fundamental theory (such as Higgs fields in the Standard Model coupled to gravity), then their shadows in d dimensions must necessarily be conformal scalars. This has the physical consequence that the gravitational constant changes at each phase transition (inflation, grand unification, electro-weak, etc.), implying interesting new scenarios in cosmological applications. The fundamental action for pure gravity, which includes the spacetime metric, the dilaton and an additional auxiliary scalar field all in d+2 dimensions with two times, has a mix of gauge symmetries to produce appropriate constraints that remove all ghosts or redundant degrees of freedom. The action produces on-shell classical field equations of motion in d+2 dimensions, with enough constraints for the theory to be in agreement with classical General Relativity in d dimensions. Therefore this action describes the correct classical gravitational physics directly in d+2 dimensions. Taken together with previous similar work on the Standard Model of particles and forces, the present paper shows that 2T-physics is a general consistent framework for a physical theory.
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