in Sec \[sec:introduction\], the most important cosmological consequence in the string landscape was that there was a tunneling event in our past. Let us consider an effective potential $V(\phi )$ with a local minimum at $\phi_{\rm L}$, a slow-roll inflationary plateau at $\phi_{\rm R}$ and a point where the field emerges at $\phi_{*}$, as shown in Fig. \[fig:open\_potential\]. The action is given by $$\begin{aligned}
S=\int \sqrt{-g}{{\rm d}}^{4}x
\Biggl[\frac{1}{2\kappa}R
-\frac{1}{2}g^{\mu\nu}\partial_{\mu}\phi\partial_{\nu}\phi
-V(\phi )\Biggr]\,. \end{aligned}$$ In this paper, we assume that the final tunneling transition occurs through the CDL instanton. Let us consider the $O(4)$-symmetric bounce solution [@Coleman:1977py; @Coleman:1980aw]. An $O(4)$-symmetric bubble nucleation is described by the Euclidean solution (instanton). The metric is given by $$\begin{aligned}
ds^2={{\rm d}}t_{\rm E}^{2}
+a_{\rm E}^2(t_{\rm E} )\left( {{\rm d}}\chi_{\rm E}^{2}
+\sin^{2}\chi_{\rm E} {{\rm d}}\Omega^{2}\right)\,,\end{aligned}$$ and the background scalar field is denoted by $\phi =\phi (t_{\rm E})$.

The Euclidean background equations are given by $$\begin{aligned}
&&\left(\frac{\dot{a}_{\rm E}}{a_{\rm E}}\right)^{2}
-\frac{1}{a_{\rm E}^2}
=\frac{\kappa}{3}\left( \frac{1}{2}\dot{\phi}^2
-V(\phi )\right)
\,,\label{eq:Friedmann eq}
\\
&&\left(\frac{\dot{a}_{\rm E}}{a_{\rm E}}\right)^{\cdot}
+\frac{1}{a_{\rm E}^2}
=-\frac{\kappa}{2}\dot{\phi}^2
\,,
\label{eq:Friedmann2}
\\
&&\ddot{\phi}+3\frac{\dot{a}_{\rm E}}{a_{\rm E}}\dot{\phi} 
-V'(\phi )=0
\,,\label{eq:scalar field eq}\end{aligned}$$ where a dot represents differentiation with respect to $t_{\rm E}$.

The background geometry and the field configuration in the Lorentzian regime are obtained by 