  We propose a variant of electroweak-scale baryogenesis characterized by the
spontaneous breaking of the charge-parity (CP) symmetry in the early Universe
driven by the vacuum expectation value of a CP-odd scalar. This CP breaking
period in the early Universe would be ended by the electroweak phase
transition, with CP being (approximately) conserved at present, thus avoiding
the stringent electric dipole moment experimental constraints on
beyond-the-Standard-Model sources of CP violation. We study an explicit
realization via a non-minimal Higgs sector consisting of two Higgs doublets and
a singlet pseudoscalar (2HDM + $a$). We analyze the region of the 2HDM + $a$
parameter space where such an early Universe period of CP violation occurs, and
show that the required thermal history and successful baryogenesis lead to a
predictive scenario, testable by a combination of LHC searches and low-energy
flavour measurements.
