Antineutron repelled by gravity? I was reading an old post, Can gravity be shielded, like electromagnetism?. One of the responses had this comment. 

There are some experiments trying to measure whether antiprotons (
  antimatter) is repelled by gravity.

There seem to be good reasons to doubt it - see the same comment or Anti-matter repelled by gravity - is it a serious hypothesis? [duplicate]. But apparently not everyone is convinced. 
My question is about these experiments. 
I can see difficulties in trying to measure the weight of an anitproton or an antihydrogen atom. It sounds much easier to see if antineutrons are repelled or attracted by gravity. After all, it is easy to show that ultracold neutrons are attracted. For example, see this. 
It should be an obvious step for somebody to try it with antineutrons. But a quick Google didn't turn up anything. So


*

*Has it been tried?

*Would it tell us anything about antiprotons or antihydrogen? My naive thinking is that $n \rightarrow p + e + \bar{\nu}_e + \gamma$, so that the effect of gravity on $n$ might be much like $p$ or $p + e$.
 A: It's probably easier to measure gravitational masses for anti-hydrogen or anti-ions, because those particles can be cooled and trapped using only electromagnetic fields. 
The problem is that antiparticles are generally "hot" when they are created. The processes that create antiparticles have an energy threshold beneath which they don't work at all (this is of course the rest energy $mc^2$ of any new particles created). However pair-creation processes aren't very efficient at the energy threshold. As a sort of order-of-magnitude estimate, pair creation won't really compete with other processes until the reaction energy is above the threshold by a factor of two or more above the threshold. 
This means that antiparticles tend to be born relativistic and must be cooled before you make precision measurements with them.
Cooling and trapping antihydrogen is a hard problem with an interesting literature.
The neutron is not accelerated or decelerated by electric fields, and its magnetic moment of $50\,\rm neV/T$ is too feeble to use laboratory fields to accelerate it by much.  Matter neutrons from fission or spallation, with mega-eV energies, are cooled to milli- or nano-eV energies by interactions with the nuclei of matter atoms. I don't know whether there's a record for "coldest antineutron," but I can tell you that the literature on neutron gravitational experiments doesn't discuss antineutron gravitation. It would be a hard problem.
