Effects of quintessence dark energy on the action growth and butterfly velocity

In this work we are about to investigate the effects of quintessence dark energy on evolution of the computational complexity relating to the AdS/CFT correspondence. We use $"complexity=action"$ conjecture for a charged AdS black hole surrounded by the dark energy at the quintessence regime. Then we try to find some conditions on the quintessence parameters where the Lloyd bound is satisfied in presence of affects of the quintessence dark energy on the complexity growth at the late time approximations. We compare late time approximation of the action growth by perturbed geometry in small limits of shift function. Actually we investigate the evolution of complexity when thermofield double state on the boundaries is perturbed by local operator corresponding to a shock wave geometry as holographically. Furthermore we seek spread of local shock wave on the black hole horizon in presence of the quintessence dark energy.