Antiproton evolution in little bangs and in the Big Bang

The abundances of antiprotons and protons are considered within momentum-integrated Boltzmann equations describing Little Bangs, i.e., fireballs created in relativistic heavy-ion collisions. Despite a large antiproton annihilation cross section we find a small drop of the ratio of antiprotons to protons from 170 MeV (chemical freeze-out temperature) to 100 MeV (kinetic freeze-out temperature) for CERN-SPS and BNL-RHIC energies thus corroborating the solution of the previously exposed 'antiproton puzzle'. In contrast, the Big Bang evolves so slowly that the antibaryons are kept for a long time in equilibrium resulting in an exceedingly small fraction. The adiabatic path of cosmic matter in the phase diagram of strongly interacting matter is mapped out.