We initiate a study of cosmological implications of sphaleron-mediated $CP$-violation arising from the electroweak vacuum angle under the reasonable assumption that the semiclassical suppression is lifted at finite temperature. In this article, we explore the implications for existing scenarios of baryogenesis. Many compelling models of baryogenesis rely on electroweak sphalerons to relax a $(B+L)$ charge asymmetry. Depending on the sign of the $CP$-violating parameter, it is shown that the erasure of positive $(B+L)$ will proceed more or less quickly than the relaxation of negative $(B+L)$. This is a higher order effect in the kinetic equation for baryon number, which we derive here through order $n_{B+L}^2$. Its impact on known baryogenesis models therefore seems minor, since phenomenologically $n_{B+L}$ is much smaller than the entropy density. However, there remains an intriguing unexplored possibility that baryogenesis could be achieved with the vacuum angle alone providing the required $CP$-violation.

• Received 13 July 2015

DOI:https://doi.org/10.1103/PhysRevD.92.043513