So when you crank the engine, the trunk opens?
Here is what you can do:
Take the FOB off your keychain, set it on a table or something where no one will touch it and it won’t move or shake. Start the car several times and see if the trunk will open on its own. If it does, it is the wireless control module and I think on the Cobalt it is built into the BCM.
If the problem does not persist, the FOB in question is the problem. It is hypersensitive on one or several buttons or simply the way your key touches the fob is causing a trigger.
Always try to isolate the problem when working on anything to eliminate possibilities until you are left with the only possible answer.