Arnorian Battle Armor?

I don't believe I've researched that one yet, but it sounds like it would increase your soldiering for when you invade, rather than being an armor for ships. I could be wrong?

There's a couple techs like that that don't do anything.
There's a telepathic missile defense tech as well.
Check in the info screen about the tech to make sure it adds a new improvement, or ship component or ... before you research it. If the window is empty, it does nothing.

My best guess is that these techs fit in with the campaign somehow and shouldn't be in the sandbox galxy mode, but I haven't played the campaign yet to confirm that.
Cheers.

I have a feeling that like the Temple of Neutrality, these aren't in the game yet.

Yeah I've not gotten far enough along in a game either campaign or sandbox.. usually crap hits the fan long before you can get that much research done.

Soooo...

some time passed and I wondered if anybody discovered the hidden meaning of those strange tech branches?

The techs they were supposed to have were added to the game quite a while ago. So now they are actually useful. Pretty effective too. I had one large ship with the subspace rebounders laugh off a fleet of a dozen Drengin ships in my last game. Well, maybe not laugh off, but at least emerge victorious.

Both should be there and working if you are a good civilization (as well as two shield techs). Arnorian Battle Armor is pretty nice, and the tech itself gives ships with or without the armor +5 hp. The armor itself is a pretty good buy, though it is a bit big (as are all armor techs at that point, still a steal for 5 defense).

Telepathic Defense, or rather Telepathetic Defense isn't worth researching. Save the time getting it and go after PD combo (about 3 missile techs away). The first PD combo is exactly the same (both have only 3 defense) and these techs research fast. Thereafter all missile protection techs are far superior to telepathic defense. This is a big deal since missiles scale up rapidly in terms of the damage they do.

They are a result of your ethical choice in Xeno Ethics, I've used the battle armour before, personal favorite is teh psycic blaster.