Well it looks like their is a testing scheme that will be conducted at CERN in the near future called AEGIS intending to do just this. It seems to consist of firing a beam of anti-hydrogen and seeing if it’s deflected up rather then down. http://aegis.web.cern.ch/aegis/experiment.html My point was that the experiment is JUST a matter of instrument sensitivity in a controlled lab environment which is something researchers are very good at doing. The ‘energetic’ part (making Anti-hydrogen) which is what’s expensive has already been done.