Cosmological stochastic Higgs field stabilization

We show that the stochastic evolution of an interacting system of the Higgs field and a spectator scalar field naturally gives rise to an enhanced probability of settling down at the electroweak vacuum at the end of inflation. Subsequent destabilization due to parametric resonance between the Higgs field and the spectator field can be avoided in a wide parameter range. We further argue that the spectator field can play the role of dark matter.

Figure 1

Equal probability contours corresponding to 68% (blue) and 95% (green) inside them. We have taken $H_{\inf }={10}^{11}\mathrm{GeV}$, $N=60$, ${\lambda }_S=0.01$ and ${\lambda }_{hS}=0.1$ (${10}^{-4}$) in the left (right) panel. The solid red lines represent the local maximum of the potential and the right side of the hatched region corresponds to the unstable region. The magenta and cyan dotted lines correspond to the boundary for $h$ and $S$, respectively, beyond which $\delta {\varphi }_{\mathrm{cl}}>\delta {\varphi }_{\mathrm{qm}}$ so that stochastic approach is no longer valid.

Figure 2

Survival probability in terms of the inflationary Hubble parameter. We have taken $N=60$, ${\lambda }_S=0.01$, and ${\lambda }_{hS}=0,{10}^{-4},{10}^{-3},{10}^{-2},{10}^{-1}$ from bottom to top. Each point and line correspond, respectively, to the numerical results and the analytic formula (12) with $p=2$ and $q=5$.

Figure 3

Postinflationary stability chart for the Higgs from the numerical calculation of the homogeneous mode. The colored region corresponds to our metastable Universe. We have taken $H_{\inf }={10}^{12}\mathrm{GeV}$, ${\lambda }_S=0.01$, and ${\lambda }_{hS}=0.1(0.03)$ in the left (right) panel. The blue dots are the results from two-dimensional lattice computations.

Figure 4

Survival probability well after the end of inflation in terms of ${\lambda }_{hS}$. We have taken ${\lambda }_S=0.01$ and $H_{\inf }={10}^{13}\mathrm{GeV}$ (circle), $10^{12}\mathrm{GeV}$ (square), and $10^{11}\mathrm{GeV}$ (triangle). Each solid line with same color corresponds to the probability at the end of inflation without destabilization due to parametric resonance.