By measuring the leftover electromagnetic radiation from the big bang, and knowing the amount of ordinary matter around, one may calculate there are about a billion photons per baryon (proton or neutron).
This is a really tiny number. In the early universe, when the temperature was high enough to create baryon antibaryon pairs, they were created and anihillated back into photons freely, such that, in equillibrium there would be about the same number of baryons antibaryons and photons.
As the Universe expands and the temperature falls, photons no longer have enough energy to create new pairs, and the baryons and antibaryons anihillate. If their numbers were exactly equal, all that would be left today would be radiation, and that is what is meant dramatically by "shouldn't exist".
So there must have been a tiny primordial excess, of one more baryon per billion antibaryons. Long ago Sakharov identified what is needed for this to happen, these are the Sakharov conditions:
1) The conservation of baryon number (ammount of baryons) must be violated. This is a given, since you're trying to create an excess of baryons (antibaryons count as negative baryon number) . In the standard model, there are nonperturbative processes that operate at high enough temperature that can do this.
2) The symmetry between particle and antiparticle (CP symmetry) must be violated. Again this is necessary otherwise no net ammount of baryons over antibaryons would be created in excess. The weak interactions have a tiny ammount of CP violation in the quark sector, but it is not enough, so extra violation is needed. This is what this experiment was looking for. One place where CP breaking is expected to occur is in the lepton sector, but it could not be measured yet. It is expected to happen soon, however, and maybe it will be enough.
3) The reaction must happen out of thermal equillibrium, or else it can be readily undone. Here at lesst two options come to mind. One is the decay of heavy neutrinos (yet undiscovered) in the early universe. Another is that when the Universe cooled and the Higgs field froze in its current value, giving particles mass, a phase transition happened, much like the freezing of water, where ice crystals form, it is possible that bubbles formed in the early universe. Inside the bubble particles have mass, outside they don't. These bubbles expanded at light speed and collided with each other, and these collisions with the surrounding plasma may also create out of equillibrium conditions. The collisions generate gravitational waves, which maybe detected by the LISA space interferometer to be launched in the 2030s.
This baryon assymetry is one of the few indications of needing physics beyond the standard model of particle physics, so it is a really exciting field. Stay tunned!
