  We study electroweak baryogenesis within the framework of the littlest Higgs
model with T parity. This model has shown characteristics of a strong
first-order electroweak phase transition, which is conducive to baryogenesis in
the early Universe. In the T parity symmetric theory, there are two gauge
sectors, viz., the T-even and the T-odd ones. We observe that the effect of the
T-parity symmetric interactions between the T-odd and the T-even gauge bosons
on gauge-higgs energy functional is quite small, so that these two sectors can
be taken to be independent. The T-even gauge bosons behave like the Standard
Model gauge bosons, whereas the T-odd ones are instrumental in stabilizing the
Higgs mass. For the T-odd gauge bosons in the symmetric and asymmetric phases
and for the T-even gauge bosons in the asymmetric phase, we obtain, using the
formalism of Arnold and McLerran, very small values of the ratio, (Baryon
number violation rate/Universe expansion rate). We observe that this result, in
conjunction with the scenario of inverse phase transition in the present work
and the value of the ratio obtained from the lattice result of sphaleron
transition rate in the symmetric phase, can provide us with a plausible
baryogenesis scenario.
