angular coordinate, two branes are located at $\phi = 0$ (hidden brane) and at $\phi = \pi$ (visible brane) respectively while the latter one is identified with the visible universe. Moreover the spacetime is $S^1/Z_2$ orbifolded along the coordinate $\phi$. The action for this model is : $$\begin{aligned}
 S = \int d^4x dy \sqrt{G} \bigg[\frac{1}{2\kappa^2}(R + \alpha R^2) + \Lambda + V_h\delta(\phi) + V_v\delta(\phi-\pi)\bigg]
 \label{actionF(R)}\end{aligned}$$ where $\Lambda (< 0)$ is the bulk cosmological constant and $V_h$, $V_v$ are the brane tensions on hidden, visible brane respectively.

This higher curvature like $F(R)$ model (in eqn.(\[actionF(R)\])) can be transformed into scalar-tensor theory by using the technique discussed in the previous section. Performing a conformal transformation of the metric as $$G_{MN}(x,\phi) \rightarrow \tilde{G}_{MN} = \exp{(\frac{1}{\sqrt{3}}\kappa\Phi(x,\phi))}G_{MN}(x,\phi)
 \label{conformal}$$ the above action (in eqn.(\[actionF(R)\])) can be expressed as a scalar-tensor theory with the action given by : $$\begin{aligned}
 S&=&\int d^4x dy \sqrt{\tilde{G}} \bigg[\frac{\tilde{R}}{2\kappa^2} + \frac{1}{2}\tilde{G}^{MN}\partial_M\Phi \partial_N\Phi - V(\Phi) + \Lambda\nonumber\\ 
 &+&\exp{(-\frac{5}{2\sqrt{3}}\kappa\Phi)} V_h\delta(\phi) + \exp{(-\frac{5}{2\sqrt{3}}\kappa\Phi)} V_v\delta(\phi-\pi)\bigg]
 \label{action1ST}\end{aligned}$$ where the quantities in tilde are reserved for ST theory. $\tilde{R}$ is the Ricci curvature formed by the transformed metric $\tilde{G}_{MN}$. $\Phi(x,\phi)$ is the scalar field corresponds to higher curvature degrees of freedom and $V(\Phi)$ is the scalar potential which 