  If spacetime contains large compact extra dimensions, the fundamental mass
scale of nature, $Lambda$, may be close to the weak scale, allowing
gravitational physics to significantly modify electroweak symmetry breaking.
Operators of the form $(1/Lambda^2) |phi^* D phi|^2$ and $(1/Lambda^2) phi^* W
B phi$, where $W$ and $B$ are the SU(2) and U(1) field strengths and $phi$ is
the Higgs field, remove the precision electroweak bound on the Higgs boson mass
for values of $Lambda$ in a wide range: $4 TeV < Lambda < 11 TeV$. Within this
framework, there is no preference between a light Higgs boson, a heavy Higgs
boson, or a non-linearly realized SU(2)xU(1) symmetry beneath $Lambda$. If
there is a Higgs doublet, then operators of the form $(1/Lambda^2) phi^* phi
(G^2, F^2)$, where $G$ and $F$ are the QCD and electromagnetic field strengths,
modify the production of the Higgs boson by gluon-gluon fusion, and the decay
of the Higgs boson to 2 photons, respectively. At Run II of the Tevatron
collider, a 2-photon signal for extra dimensions will be discovered if $Lambda$
is below 2.5 (1) TeV for a Higgs boson of mass 100 (300) GeV. Furthermore, such
a signal would point to gravitational physics, rather than to new conventional
gauge theories at $Lambda$. The discovery potential of the LHC depends
sensitively on whether the gravitational amplitudes interfere constructively or
destructively with the standard model amplitudes, and ranges from $Lambda$ = 3
- 10 (2 - 4) TeV for a light (heavy) Higgs boson.
