Ochi-Hubble

\[\begin{align}\begin{split} S(\omega) = & E_1 G_1 \omega_{n, 1}^{-(4\lambda_1 + 1)} \exp\left[-\left(\lambda_1 + 0.25\right)\omega_{n,1}^{-4}\right] \\ & + E_2 G_2 \omega_{n, 2}^{-(4\lambda_2 + 1)} \exp\left[-\left(\lambda_2 + 0.25\right)\omega_{n,2}^{-4}\right] \end{split}\end{align}\]

\[\begin{align}\begin{split} \omega_{n,1} &= \frac{\omega}{w_{p,1}} \\ \omega_{n,2} &= \frac{\omega}{w_{p,2}} \\ E_1 &= \frac{H_{s,1}^2}{16\omega_{p,1}} \\ E_2 &= \frac{H_{s,2}^2}{16\omega_{p,2}} \\ G_1 &= \frac{4(\lambda_1 + 0.25)^{\lambda_1}}{\gamma(\lambda_1)} \\ G_2 &= \frac{4(\lambda_2 + 0.25)^{\lambda_2}}{\gamma(\lambda_2)} \\ \lambda_1 &= 3.0 \\ \lambda_2 &= 1.54 e^{-0.062 H_s} \\ \omega_{p,1} &= 0.7 e^{-0.046 H_s} \\ \omega_{p,2} &= 1.15 e^{-0.039 H_s} \\ H_{s,1} &= 0.84 H_s \\ H_{s,2} &= 0.54 H_s \end{split}\end{align}\]