Effect of the Cosmological Constant on Light Deflection: Time Transfer Function Approach

We revisit the role of the cosmological constant L in the deflection of light by means of the Schwarzschild-de Sitter/Kottler metric. In order to obtain the total deflection angle a, the time transfer function approach is adopted, instead of the commonly used approach of solving the geodesic equation of photon. We show that the cosmological constant does appear in expression of the deflection angle, and it diminishes light bending due to the mass of the central body M. However, in contrast to previous results, for instance, that by Rindler and Ishak (Phys. Rev. D. 2007), the leading order effect due to the cosmological constant does not couple with the mass of the central body M.