Bending of light in a universe filled with quintessential dark energy

As a local effect of dynamical dark energy, bending of light in the presence of a spherically symmetric and static black hole surrounded by quintessence has been studied. Having in mind recent observational data, we have treated the problem as a deviation from Kottler space-time. This deviation is measured by a perturbation parameter $ϵ$ included in the equation of state parameter of quintessence as ${\omega }_q=-1+\frac{1}{3}ϵ$. Here, the deflection angle is calculated and then the result is compared with [H. Arakida and M. Kasai, Phys. Rev. D 85, 023006 (2012)] in the limit $ϵ\to 0$ where the quintessence behaves like the cosmological constant. It is shown that unlike the cosmological constant, the effect of quintessence on the photon energy equation can not be absorbed into the definition of impact parameter. Moreover in this paper, we generalize the Kiselev black hole to the case that there is a modified Chaplygin gas as the dark energy component of the universe and show that the resulted metric can be reduced to the Kiselev metric by adjusting some arbitrary parameters.