Effect of the Brane-Dicke coupling parameter on weak gravitational lensing

In this paper, we analyze the deflection angle of light by the Brane-Dicke wormhole in the weak field limit approximation to find the effect of the Brane-Dicke coupling parameter on the weak gravitation lensing. For this purpose, we consider new geometric techniques, i.e., Gauss-Bonnet theorem and optical geometry in order to calculate the deflection angle. Furthermore, we verify our results by considering the most familiar geodesic technique. Moreover, we establish the quantum corrected metric of the Brane-Dicke wormhole by replacing the classical geodesic with Bohmian trajectories, whose matter source and anisotropic pressure are influenced by Bohmian quantum effects and calculate its quantum corrected deflection angle. Then, we calculate the deflection angle by naked singularities and compare with the result of the wormhole. Such a novel lensing feature might serve as a way to detect wormholes, naked singularities and also the evidence of Brane-Dicke theory.