Effect of quintessence on geodesics and Hawking radiation of Schwarzschild black hole

We study the timelike geodesics and the greybody radiation of the Schwarzschild black hole surrounded by quintessence field. Quintessence field is one of the highly plausible models for the dark energy. The effective potential along with the structure of the possible orbits for test particles in view of the various values of quintessence parameter are analyzed in detail. The exact solution of radial timelike geodesics for a test particle is obtained. Remarkably, it is shown that an increase in quintessence parameter decelerates the particles following the radial timelike geodesics so that the particles reach the singularity slower than the bare Schwarzschild case. The circular orbits of the test particles in case of non-radial geodesics are studied. We also discuss the Lyapunov exponent and the effective force acting on the particle in the presence of quintessence field. The effect of quintessence parameter on the greybody factor is also investigated. We consider the Miller-Good transformation method to compute the greybody factor and therefore to discuss how the Hawking radiation is affected from the quintessence field.