Finite-Temperature Stability from a Doublet Inflation Field with Right-Handed Neutrinos

Abstract We study the augmentation of the Standard Model (SM) with another $SU(2)$ Higgs doublet and right-handed neutrinos. The second Higgs doublet ($\Phi _2$) is defined as odd under the $Z_2$ symmetry, and hence the lightest stable neutral particle from the additional doublet becomes the cold dark matter candidate. The right-handed neutrino field coupled to the Higgs field provides nonzero mass for the neutrinos. The inert doublet field coupled nonminimally to gravity as $\zeta _2 \Phi _2^\dagger \Phi _2 R$ also acts as an inflaton field. The inflationary bounds restrict the interaction couplings as $\lambda _2/\zeta _2^2 \approx 4\times 10^{-10}$. After inflation ends, the scalar bosonic degrees of freedom from the inert doublet can contribute to the electroweak phase transition. The strongly first-order phase transition bound, i.e. $\frac{\phi _{+}(T_c)}{T_c} \ge 1.0$, restricts the bare mass parameter of the additional doublet to $m_{22}=400.0$ GeV, demanding GUT-scale perturbative unitarity for $Y_N=0.01$. The right-handed neutrino effect is studied here only through the running of Yukawa coupling, i.e. $Y_N$. The running of Yukawa coupling for different values at the electroweak scale restricts the perturbative unitarity at different scales, and affects the strength of the phase transition. The increase in $Y_N$ reduces the strength of the phase transition, and it is no longer satisfied even for a vanishing bare mass parameter. The Planck-scale perturbative unitarity allows for the first-order phase transition, $\frac{\phi _{+}(T_c)}{T_c} \ge 0.6$, up to $m_{22}=70.0$ GeV for $Y_N=0.01$, and none of the mass values satisfy the first-order phase transition for $Y_N=0.4$. The thermal corrections also affect the probability of tunneling from the false vacuum to the true vacuum, and hence the finite-temperature stability of the electroweak vacuum has been studied including the finite-temperature effects.