Bending of light in the Universe filled with quintessential dark energy

TL;DR

This paper investigates how quintessence dark energy influences light bending around black holes, comparing it to the cosmological constant case, and extends the analysis to include modified Chaplygin gas as dark energy.

Contribution

It provides a detailed calculation of light deflection in a universe with quintessence and generalizes the Kiselev black hole to include modified Chaplygin gas dark energy.

Findings

Quintessence affects photon energy differently than the cosmological constant.

The deflection angle deviates from the Kottler spacetime when quintessence is considered.

The metric can be reduced to the Kiselev form with appropriate parameters.

Abstract

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 $\varepsilon$ included in the equation of state parameter of quintessence as $\omega_q=-1+\frac{1}{3}\varepsilon$. Here, the deflection angle is calculated and then the result is compared with \cite{Arakida:2011th} in the limit $\varepsilon\rightarrow 0$ 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.