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 limits on the time variation of the four dimensional Newton's 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.