This is pretty close to the premise of the Isaac Asimov novel The Gods Themselves. In that story, humans create an infinite source of energy by trading material with a parallel universe in which the nuclear strong force is slightly stronger than ours. (Or is it infinite...)
No mention was made specifically of how to rule out spontaneous pair production, although I'm guessing it would be the same answer as how they rule out cosmic sources? Would spontaneous pair production be dependent on anything external at all?
Getting rid of cosmic ray neutrons is a ridiculously hard problem that they are going to deal with mostly by looking at how the neutron detection rate varies as they change the distance between the detector and the reactor core.
The most pernicious source for experiments like this are "fireball neutrons" that are generated from a high-energy muon producing an event that blows up a nucleus in the surrounding rock (via an intermediate pion shower IIRC). This gives you a source of neutrons with energies well up into the 100's of MeV, which will merrily pass through metres of shielding, and a few of them are bound to thermalize in the detector, although most will pass right through.
They've obviously run the numbers on all this (these are very well-known problems for detector design) and decided they can discriminate against backgrounds of this type sufficiently well to make the experiment worthwhile, which all else being equal it certainly is: the possibility of putting brane-world theories to the test is simply too delightful to pass up.
Also, this:
"So any change in this gravitational field should influence the rate at which the neutrons leak in and out of our brane."
How can this happen in a unverse that obeys both the relativisc principle and the gravity acceleration equivalence? Will different observers see a different number of particles written at the detector display?
Quantum tunneling can only happen over a very short range, on the order of the de Broglie wavelength for the particle, which will be a subatomic distance for interesting neutron energies. They are measuring neutrons that pass through/around metres of material, so tunneling is unimportant.
I always find it funny how news articles are able to take the most basic (but interesting) type of work in physics and turn into the craziest headlines.
I don't really fancy their usage of "universe" though, since it's normally defined to be all that exists.
"universe" may be as shortsighted as our ancestors calling our favorite space-faring rock "uniearth". Such a sibylline definition falls on its head as soon as one tries to define "existence" and finds it ultimately bound to lowly concepts of space or time. What to say of a "uni"-verse that is a constant collapse of probabilistic functions, where every possible permutation simultaneously exists until observed? Let's be humble, and cut some slack at putting words on what we're looking at, because we're really not quite so sure.
There are actually multiple definitions that have arisen as our understanding of the cosmos has grown [1]. The word has always been a filler for "all the stuff there is" but as science has evolved it's become useful to make a distinction based on "all the stuff there is in <whatever>".
The context of this article makes it pretty clear that a brane-constrained definition is being used.
I think the meaning of the word has shifted to mean "bound to our brane", so hypothetical effects that transcend branes are referred to as potentially extra-universal.
