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

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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√Λ, 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 10⁴. In this high-energy case, the null cosmological constant result reduces to the Schwarzschild value 27πrg²/4.