Superluminal propagation along the brane in space with extra dimensions

We demonstrate that a model with extra dimensions formulated in Csaki et al. (Phys Rev D 62:045015, 2000), 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.