fermion field in the backdrop of higher curvature scenario and its consequences. The paper ends with some concluding remarks.

Transformation of a F(R) theory to scalar-tensor theory
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In this section, we briefly describe how a higher curvature F(R) gravity model in five dimensional scenario can be recast into Einstein gravity with a scalar field. The F(R) action is expressed as, $$S=(1/2\kappa^2)\int d^4x dy \sqrt{G} F(R)
 \label{action0}$$ where $x^{\mu} = (x^0, x^1, x^2, x^3)$ are usual four dimensional coordinate and $y$ is the extra dimensional spatial linear coordinate. $R$ is the five dimensional Ricci curvature and $G$ is the determinant of the metric. Moreover $\frac{1}{2\kappa^2}$ as taken as $2M^3$ where $M$ is the five dimensional Planck scale. Introducing an auxiliary field $A(x,\phi)$, above action (\[action0\]) can be equivalently written as, $$S=(1/2\kappa^2)\int d^4x dy \sqrt{G} [F'(A)(R-A) + F(A)]
 \label{action00}$$ By the variation of the auxiliary field $A(x,\phi)$, one easily obtains $A=R$. Plugging back this solution $A=R$ into action (\[action00\]), initial action (\[action0\]) can be reproduced. At this stage, perform a conformal transformation of the metric as $$G_{MN}(x,\phi) \rightarrow \tilde{G}_{MN} = \exp{(\sigma(x,\phi)}G_{MN}(x,\phi)
 \nonumber\\$$ $M, N$ run form 0 to 5. $\sigma(x,\phi)$ is conformal factor and related to the auxiliary field as $\sigma 