Problems with time-varying extra dimensions or “Cardassian expansion” as alternatives to dark energy

It has recently been proposed that the Universe might be accelerating as a consequence of extra dimensions with time-varying size. We show that, although these scenarios can lead to acceleration, they run into serious difficulty when taking into account the limits on the time variation of the four-dimensional Newton constant. On the other hand, models of ``Cardassian'' expansion based on extra dimensions which have been constructed so far violate the weak energy condition for the bulk stress energy, for parameters that give an accelerating Universe.