Evolution of cosmological baryon asymmetries. I. The role of gauge bosons

The time evolution of the baryon asymmetry ($\frac{k{n}_B}{s}$) due to the interactions of a superheavy gauge boson (mass $M_X\sim {10}^{15}$ GeV, coupling strength $\alpha \sim \frac{1}{45}$) is obtained by numerically integrating the Boltzmann equations. Particle interactions in the very early universe ($t\lesssim {10}^{-35\mathrm{}}$ sec) are assumed to be described by the SU(5) grand unification theory. To a good approximation the results depend upon one parameter, $K\equiv 2.9\times {10}^{17} \alpha \frac{\mathrm{GeV}}{M_X}$. If $C$ and $\mathrm{CP}$ are not violated in the decays of the superheavy boson no asymmetry develops, and any initial baryon asymmetry is reduced by a factor of $\cong \exp \mathrm{}(-5.5K)\mathrm{}$. If both $C$ and $\mathrm{CP}$ are violated then an initially symmetrical universe evolves a baryon asymmetry which today corresponds to $\frac{k{n}_B}{s}\cong 7.8\times {10}^{-3\mathrm{}}\frac{\epsilon }{[1+{\mathrm{}\left(16K\right)\mathrm{}}^{1.3}]}$, where $\frac{\epsilon }{2}$ is the baryon excess produced when an $X-\overline{X}$ pair decays. Decays and inverse decays of superheavy bosons are primarily responsible for these results (as Weinberg and Wilczek suggested); however for $K\gg 1$ baryon production falls off much less rapidly than they had expected. A gauge boson of mass 3×${10}^{14}$ GeV could have generated the observed asymmetry $\frac{k{n}_B}{s}\cong {10}^{-9.8\mathrm{}\pm 1.6}$ if $\epsilon \cong {10}^{-4.3\mathrm{}\pm 1.6}$. In a companion paper the role of Higgs bosons is considered.