= (2/3)\ln F'(A)$. Using this relation between $\sigma(x,\phi)$ and $A(x,\phi)$, one lands up with the following scalar-tensor action $$\begin{aligned}
 S=(1/2\kappa^2)\int d^4x dy \sqrt{\tilde{G}} \bigg[\tilde{R} + 3\tilde{G}^{MN}\partial_M\sigma \partial_N\sigma 
 - (\frac{A}{F'(A)^{2/3}} - \frac{F(A)}{F'(A)^{5/3}})\bigg]
 \nonumber\end{aligned}$$ where $\tilde{R}$ is the Ricci scalar formed by $\tilde{G}_{MN}$. $\sigma(x,\phi)$ is the scalar field emerged from higher curvature degrees of freedom. Clearly kinetic part of $\sigma(x,\phi)$ is non canonical. In order to make the scalar field canonical, transform $\sigma$ $\rightarrow$ $\Phi(x,\phi) = \sqrt{3}\frac{\sigma(x,\phi)}{\kappa}$. In terms of $\Phi(x,\phi)$, the above action takes the following form, $$S=\int d^4x dy \sqrt{\tilde{G}} \bigg[\frac{\tilde{R}}{2\kappa^2} + \frac{1}{2}\tilde{G}^{MN}\partial_M\Phi 
 \partial_N\Phi - V(\Phi)\bigg]
 \nonumber\\$$

where $V(\Phi) = \frac{1}{2\kappa^2}[\frac{A}{F'(A)^{2/3}} - \frac{F(A)}{F'(A)^{5/3}}]$ is the scalar field potential which depends on the form of $F(R)$. Thus the action of $F(R)$ gravity in five dimension can be transformed into the action of a scalar-tensor theory by a conformal transformation of the metric.

Warped spacetime in F(R) model and corresponding scalar-tensor theory
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In the present paper, we consider a five dimensional AdS spacetime with two 3-brane scenario in F(R) model. The form of $F(R)$ is taken as $F(R) = R + \alpha R^2$ where $\alpha$ is a constant with square of the inverse mass dimension. Considering $\phi$ as the extra dimensional 