  We demonstrate that a model with extra dimensions formulated in Csaki et al.
(Phys Rev D 62, 045015), which fatefully reproduces Friedmann-Robertson-Walker
(FRW) equations on the brane, allows for an apparent superluminal propagation
of massless signals. Namely, a massive brane curves the spacetime and affects
the trajectory of a signal in a way that allows a signal sent from the brane
through the bulk to arrive (upon returning) to a distant point on the brane
faster than the light can propagate along the brane. In particular, the signal
sent along the brane suffers a greater gravitational time delay than the bulk
signal due to the presence of matter on the brane. While the bulk signal never
moves with the speed greater than the speed of light in its own locality, this
effect still enables one to send signals faster than light from the brane
observer's perspective. For example, this effect might be used to resolve the
cosmological horizon problem. In addition, one of the striking observational
signatures would be arrival of the same gravitational wave signal at two
different times, where the first signals arrives before its electromagnetic
counterpart. We used GW170104 gravitational wave event to impose a strong limit
on the model with extra dimensions in question.
