Constraining Antimatter Domains in the Early Universe with Big Bang Nucleosynthesis

We consider the effect of a small-scale matter-antimatter domain structure on big bang nucleosynthesis and place upper limits on the amount of antimatter in the early universe. For small domains, which annihilate before nucleosynthesis, this limit comes from underproduction of ${}^4\mathrm{He}$. For larger domains, the limit comes from ${}^3\mathrm{He}$ overproduction. Since most of the ${}^3\mathrm{He}$ from $\overline{p}{}^4\mathrm{He}$ annihilation are themselves annihilated, the main source of primordial ${}^3\mathrm{He}$ is the photodisintegration of ${}^4\mathrm{He}$ by the electromagnetic cascades initiated by the annihilation.