  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.
