modify the doublets couplings to the fermions, and since the lightest Higgs contains a singlet amount, its mass could be (much) smaller than SM bound $\sim $114 GeV. One remarks from Fig. \[Mhn\] (right), that the EWPT could be strongly first-order for small values of the lightest neutralino masses; $m_{\chi _{1}}<15$ GeV. Such a light mass of neutralino with a spin-independent cross section of order $%
10^{-5}$pb could be a possible interpretation of the recent observations of CoGeNT and DAMA/LIBRA [@LDM]. In particular, the lightest neutralino can have a non negligible component of the superpartner of the $U(1)^{\prime }$ gauge boson [@next].

The critical temperature is, in general, higher when comparing with minimal SM ($\sim $100 $GeV$), the generic value is larger than $300-600$ $GeV$. This is a consequence of the interaction of the doublets with the singlet that has, in general, a very large vev. However for the benchmarks, giving a strong first-order EWPT, $T_{c}$ is relatively smaller than the generic value. In fact, for points **(1)** as $T_{c}$ is smaller than about $180
$ GeV, the stronger the EWPT becomes.

In order to understand this point, we take a benchmark from Fig. \[Mhn\], and study the dependence of 