Lambda does not Lens: Deflection of Light in the Schwarzschild-de Sitter Spacetime

Debate persists as to whether the cosmological constant $\mathrm{\Lambda }$ can directly modify the power of a gravitational lens. With the aim of reestablishing a consensus on this issue, I conduct a comprehensive analysis of gravitational lensing in the Schwarzschild–de Sitter spacetime, wherein the effects of $\mathrm{\Lambda }$ should be most apparent. The effective lensing law is found to be in precise agreement with the $\mathrm{\Lambda }=0$ result: $\alpha_$\mathrm{e}\mathrm{f}\mathrm{f}$ = 4m/b_$\mathrm{e}\mathrm{f}\mathrm{f}$+15\pi m^2/4b_$\mathrm{e}\mathrm{f}\mathrm{f}$^2 +O(m^3/b_$\mathrm{e}\mathrm{f}\mathrm{f}$^3)$,wheretheeffectivebendingangle$\alpha_$\mathrm{e}\mathrm{f}\mathrm{f}$$andimpactparameter$b_$\mathrm{e}\mathrm{f}\mathrm{f}$$ are defined by the angles and angular diameter distances measured by a comoving cosmological observer. [These observers follow the timelike geodesic congruence which (i) respects the continuous symmetries of the spacetime and (ii) approaches local isotropy most rapidly at large distance from the lens.] The effective lensing law can be derived using lensed or unlensed angular diameter distances, although the inherent ambiguity of unlensed distances generates an additional uncertainty $O(m^5\mathrm{/}\mathrm{\Lambda }{b}_{\mathrm{e}\mathrm{f}\mathrm{f}}^7)$. I conclude that the cosmological constant does not interfere with the standard gravitational lensing formalism.