  There is no known fundamental reason to demand as a cosmological initial
condition that the bulk possess an SO(3,1) isometry. On the contrary, one
expects bulk curvature terms that violate the SO(3,1) isometry at early epochs,
leading to a violation of Lorentz invariance on our brane. Demanding that the
Lorentz noninvariant terms are small leads to a new ``flatness'' problem, not
solved by the usual formulation of inflation. Furthermore, unlike in four
dimensions, the Lorentz violations induced from the bulk curvature cannot
always be removed as the infrared cutoff is taken arbitrarily large. This means
that the equivalence principle in higher dimensions does not guarantee the
equivalence principle in dimensionally reduced theories. Near-future
experiments are expected to severely constrain these Lorentz-violating
``signatures'' of extra dimensions.
