Electroweak Phase Transition in Scale Invariant Standard Model

In an extension to the scale invariant standard model by two real singlet scalars $s$ and $s'$ in addition to the Higgs field, we investigate the strong first-order electroweak phase transition as a requirement for baryogenesis. This is the minimal extension to the scale invariant standard model with two extra degrees of freedom that possesses the physical Higgs mass of $125$ GeV. The scalar $s'$ being stable because of the $\mathbb Z_2$ discrete symmetry is taken as the dark matter candidate. We then show that the electroweak phase transition is strongly first-order, the dark matter relic density takes the desired value $\Omega_{\text{DM}}h^2 \sim 0.11$, and the constraints from direct detection experiments are respected only if $m_{s'}\equiv m_{\text{DM}} \gtrsim 4.5$ TeV. The model also puts a lower bound on the scalon mass, $m_s \gtrsim 200$ GeV.