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Scattering of scalar perturbations with cosmological constant in low-energy and high-energy regimes

We study the absorption and scattering of massless scalar waves propagating in spherically symmetric spacetimes with dynamical cosmological constant both in low-energy and high-energy zones. In the former low-energy regime, we solve analytically the Regge-Wheeler wave equation and obtain an analytic absorption probability expression which varies with $M\sqrtΛ$, where $M$ is the central mass and $Λ$ is cosmological constant. The low-energy absorption probability, which is in the range of $[0, 0.986701]$, increases monotonically with increase in $Λ$. In the latter high-energy regime, the scalar particles adopt their geometric optics limit value. The trajectory equation with effective potential emerges and the analytic high-energy greybody factor, which is relevant with the area of classically accessible regime, also increases monotonically with increase in $Λ$, as long $Λ$ is less than or of the order of $10^4$. In this high-energy case, the null cosmological constant result reduces to the Schwarzschild value $27πr_g^2/4$.