fractal on very large scales?

Matt Kleban (NYU) and I discussed the fractal Universe today, in the context of my polemic. He questioned a number of things, including whether the fractal dimension could be less than three but only very slightly, and what would that mean? Also, if you believe some forms of inflation, the Universe sort-of has to be a fractal on super-super-horizon scales; is that an issue? Of course I don't think either of those issues is so important, because neither conflicts with CDM (the theory I would love to be wrong), but he brought up some very relevant points. One of these is whether the fact that there are always order-unity density fluctuations possible on all scales means that it might be hard to define or understand the mean density in any single realization. But it remains true that there are no GR calculations of any observables in any expanding Universe with a distribution of matter with fractal dimension significantly different from three on large scales. That lack is a substantial hindrance to the success of any model that is fractal in that sense (for the reasons I try to give in the polemic).

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