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Also, neutrinos can turn into other things in flight. For instance, an electron neutrino can briefly turn into an electron and a W^+ (well, in the same sense that a photon can "turn into" and electron and a positron, which isn't really quite a correct description, anyway). The thing is, because the mass of the W is so high, this sort of fluctuation is much rarer and lasts for a much shorter time. (This is where the statement about the weak force making these oscillations less relevant comes in.)
But, the problem with evidence for deviation from the speed of light is that, to not be an effect too small to measure, we would need to be looking at extremely low energy neutrinos. But, we don't actually have any ways to detect neutrinos with such small energies.
All that said, I actually have some issues with the idea presented. I haven't gone through the paper in detail; but, it seems like it's probably generating a violation of relativity by not actually working in a fully relativistic framework in the first place. It looks like the treatment of gravity may be too classical; but, that's just from a cursory look.
2) Even if population growth stops, energy growth doesn't necessarily. Per capita energy use has been increasing for pretty much all of human history. And, there's no reason to think that we aren't going to keep inventing new technologies that need ever more energy. (And, I should note here that most improvements in energy efficiency work by reducing the amount of energy that goes to waste heat, not by reducing the amount of energy required for the purpose for which we're expending energy. CFLs and LED light bulbs put out the same amount of energy in light as do incandescents; but, they give off less heat, for example.) If this continues, we'll still have a problem.
3) Expanding into the galaxy still has a non-exponential limit on our growth. In that case, at best we increase the available space and energy resources quadratically, since our outward expansion is limited by the speed of light.
4) Human ingenuity does not trump physics. If there are no new energy resources to tap, no amount of cleverness will allow growth in energy use to continue. And, please note, zero point energy is not a magical reservoir of unlimited energy waiting to be tapped.
5) I don't have to believe that today's conception of physics is 100% correct (and, in fact, I can tell you with 100% certainty that our current understanding of physics is, at best, incomplete) to be extremely confident that there aren't major unknown sources of available energy that can supersede the output of the sun. I can conclude this because the only phenomena that are not fully explained by known physics are things that couple only extremely weakly to the ordinary matter we are able to exert direct control over. So, any major untapped sources of energy either don't exist or are not accessible in any practical way.
6) Even ignoring the point that cold fusion is total nonsense (fusion in general is not; but, cold fusion has been shown, time and again, to be totally unsupported by the evidence), any energy source reliant on materials present on Earth will be, at best, a temporary solution. Eventually, solar will be the only source practically available.
7) Finally, TFA doesn't need to consider "a lot more obvious possibilities" when they can all be dismissed as having far less total energy available than the sun. Maybe other technologies can allow us to use energy faster than the sun outputs for a time; but, ultimately, that's just putting off the inevitable limitations for a finite (and, frankly, surprisingly short) time, unless we learn to stem our energy use.