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

Abstract

The time evolution of the baryon asymmetry ($\frac{k{n}_{B}}{s}$) due to the interactions of a superheavy gauge boson (mass ${M}_{X}\ensuremath{\sim}{10}^{15}$ GeV, coupling strength $\ensuremath{\alpha}\ensuremath{\sim}\frac{1}{45}$) is obtained by numerically integrating the Boltzmann equations. Particle interactions in the very early universe ($t\ensuremath{\lesssim}{10}^{\ensuremath{-}35}$ sec) are assumed to be described by the SU(5) grand unification theory. To a good approximation the results depend upon one parameter, $K\ensuremath{\equiv}2.9\ifmmode\times\else\texttimes\fi{}{10}^{17} \ensuremath{\alpha} \frac{\mathrm{GeV}}{{M}_{X}}$. 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 $\ensuremath{\cong}\mathrm{exp}(\ensuremath{-}5.5K)$. If both $C$ and $\mathrm{CP}$ are violated then an initially symmetrical universe evolves a baryon asymmetry which today corresponds to $\frac{k{n}_{B}}{s}\ensuremath{\cong}7.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\frac{\ensuremath{\epsilon}}{[1+{(16K)}^{1.3}]}$, where $\frac{\ensuremath{\epsilon}}{2}$ is the baryon excess produced when an $X\ensuremath{-}\overline{X}$ pair decays. Decays and inverse decays of superheavy bosons are primarily responsible for these results (as Weinberg and Wilczek suggested); however for $K\ensuremath{\gg}1$ baryon production falls off much less rapidly than they had expected. A gauge boson of mass 3\ifmmode\times\else\texttimes\fi{}${10}^{14}$ GeV could have generated the observed asymmetry $\frac{k{n}_{B}}{s}\ensuremath{\cong}{10}^{\ensuremath{-}9.8\ifmmode\pm\else\textpm\fi{}1.6}$ if $\ensuremath{\epsilon}\ensuremath{\cong}{10}^{\ensuremath{-}4.3\ifmmode\pm\else\textpm\fi{}1.6}$. In a companion paper the role of Higgs bosons is considered.

Keywords

Affiliated Institutions

• University of Chicago US

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