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2T-gravity in d+2 dimensions predicts 1T General Relativity (GR) in ddimensions, augmented with a local scale symmetry known as the Weyl symmetry in1T field theory. The emerging GR comes with a number of constraints,particularly on scalar fields and their interactions in 1T field theory. Theseconstraints, detailed in this paper, are footprints of 2T-gravity and could bea basis for testing 2T-physics. Some of the conceptually interestingconsequences of the "accidental" Weyl symmetry include that the gravitationalconstant emerges from vacuum values of the dilaton and other Higgs-type scalarsand that it changes after every cosmic phase transition (inflation, grandunification, electroweak phase transition, etc.). We show that thisconsequential Weyl symmetry in d dimensions originates from coordinatereparametrization, not from scale transformations, in the d+2 spacetime of2T-gravity. To recognize this structure we develop in detail the geometricalstructures, curvatures, symmetries, etc. of the d+2 spacetime which isrestricted by a homothety condition derived from the action of 2T-gravity.Observers that live in d dimensions perceive GR and all degrees of freedom asshadows of their counterparts in d+2 dimensions. Kaluza-Klein (KK) type modesare removed by gauge symmetries and constraints that follow from the 2T-gravityaction. However some analogs to KK modes, which we call "prolongations" of theshadows into the higher dimensions, remain but they are completely determined,up to gauge freedom, by the shadows in d dimensions.

Geometry and Symmetry Structures in 2T Gravity