this expression, we find that efficiently reflected at the wall are only low frequency modes with $p\lesssim \Delta s/2$, which are thought to be interpreted as the wall fluctuation [@Sasaki:1997ex]. Notice that the reflection rate at $p=0$ is unity. Without this reflection by the wall, the square amplitude of fluctuation is divergent. In this sense, one might be able to interpret that the so-called wall fluctuation mode represents the penetration of the waves from the false vacuum side, and its amplitude is reduced if the wall efficiently reflects back the waves. Substituting the expression (\[eq:reflection\]), the spectrum becomes $$\begin{aligned}
&&\frac{p^3}{2\pi^{2}}P_{\rm T}(p)
=4\kappa\left(\frac{{\mathbb H}_p}{2\pi}\right)^{2}
\frac{p^2\coth\pi p}{1+p^2}
\nonumber\\
&&\ \ \times
\Biggl[ 1-\frac{(\Delta s)^2\cos [b_pp] 
+2p\Delta s\sin [b_pp]}
{[4p^2+(\Delta s)^2]\cosh\pi p}\Biggr]\,,
\label{eq:power spectrum}\end{aligned}$$ where $b_p:=2\left(\eta_{\rm W}-\eta_{\rm T}^p\right)$. Once parameters $\eta_{\rm W}\,,\Delta s$ and the late-time asymptotic value of $\tilde{\bm w}^p$ are fixed, we can immediately calculate the power spectrum using this formula. The power spectra for the tensor-type perturbation are shown in Fig. \[fig:constHubble\] for $(\alpha ,\beta )=(100,1)$, $(1,100)$, $(10^{-3},10^{-3})$ and $(1,1)$, setting ${\mathbb H}_p=H_R$ and $\eta_T^p=0$. As a reference, we plot the spectrum for ${\mathbb H}_p=H_R$, $\Delta s=\infty$ and $b_p=0$, which we denote by “plain spectrum” in this paper, as a 