  The origin of the matter-antimatter asymmetry in the Universe is a
fundamental question of physics. Electroweak baryogenesis is a compelling
scenario for explaining it but it requires beyond the Standard Model sources of
the CP symmetry violation. The simplest possibility is CP violation in the
third generation fermion Higgs couplings, widely investigated theoretically and
searched for experimentally. It has been found that the experimental bounds on
the CP violation in the quark Yukawa couplings exclude their significant role
in the electroweak baryogenesis, but it can be still played by the $\tau$
lepton Yukawa coupling. It is shown in this paper that, within the context of
the Standard Model Effective Field Theory and assuming an underlying flavour
symmetry of the Wilson coefficients, the electron dipole moment bound on the
$\tau$ lepton Yukawa coupling is two orders of magnitude stronger than
previously reported. This sheds strong doubts on its role in the electroweak
baryogenesis, further stimulates the interest in its experimental verification
and makes electroweak baryogenesis even more difficult to explain.
