$$\frac{\mathcal{L}}{a^3} = \frac{1}{2}\!\left[\dot{\pi}_c^2 - c_{\rm rel}^2\frac{(\partial_i\pi_c)^2}{a^2}\right] + \frac{1}{2}\!\left[\dot{\sigma}_c^2 - \frac{(\partial_i\sigma_c)^2}{a^2} - m^2\sigma_c^2\right] + \color{#ff7f0e}{\rho\,\dot{\pi}_c\,\sigma_c}$$
$$\quad \color{#1f77b4}{-\,\lambda_1\frac{(\partial_i\pi_c)^2}{a^2}\dot{\pi}_c - \lambda_2\,\dot{\pi}_c^3} \;\;\color{#ff7f0e}{-\,\frac{\kappa_1}{2}\frac{(\partial_i\pi_c)^2}{a^2}\sigma_c - \frac{\kappa_2}{2}\dot{\pi}_c^2\,\sigma_c}$$
where $\pi_c,\,\sigma_c$ are canonically normalized fields and
$$c_{\rm rel} = \frac{c_\pi}{c_\sigma},\quad \lambda_1 = \frac{(1-c_\pi^2)}{2\,f_\pi^2\,c_\sigma^2}\,c_{\rm rel}^{3/2},\quad \lambda_2 = -\frac{(1-c_\pi^2)}{2\,f_\pi^2}\,c_{\rm rel}^{3/2}\!\left(1+\frac{2}{3}\frac{\tilde{c}_3}{c_\pi^2}\right)$$
$$m = c_\sigma\,m_\sigma,\quad \kappa_1 = \frac{\rho}{f_\pi^2\,c_\sigma^2}\,c_{\rm rel}^{3/2},\quad \kappa_2 = \frac{\tilde{\rho}}{f_\pi^2}\,c_{\rm rel}^{3/2}$$
with $\mu = \sqrt{m^2/H^2 - 9/4}$ and $f_\pi = H\,(4\pi^2\Delta_\zeta^2)^{-1/4}$.
Blue: self-interactions | Orange: mixing/exchange