  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.
