ANTI-MATTER IN THE UNIVERSE ON VERY LARGE SCALES

It is well known that there cannot be symmetry between matter and anti-matter on scales up to and including that of clusters of galaxies. It is often stated, however, that there could be such symmetry at the ultimate grouping scale - that of superclusters (SCs). In such a situation there would be equal masses of material in superclusters and in anti-superclusters in the Universe, but the overlap regions would be sufficiently weak that the ensuing annihilation gamma-rays would have a flux below that observed. A number of situations are examined here, including the SC, SCBAR hypothesis, and it is shown that even this last-mentioned situation is not allowed. There is thus apparently no geometry that would allow the matter, anti-matter symmetry hypothesis to be retained. It is pointed out that if protons are unstable, and if the lifetime of the Universe is much longer than the proton lifetime, then matter, anti-matter symmetry is in fact restored eventually - at least for nucleons and electrons.