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In this study, we investigate the quasinormal modes (QNMs), pseudospectrum and time evolution of a massive vector field around a quantum corrected black hole in de-Sitter spacetime. We start by parametrization and using orthonormal tetrads to get the effective potential. Methodologically we use the hyperboloidal framework together with discretizing the nonself-adjoint operator through Chebyshev-Gauss-Labatto grid to attain the QNMs. We explore the parametric instability of QNMs caused by quantum correction, cosmological constant and Proca mass, and these three factors show very different influences on the QNMs' migration flow. On the other hand, we discuss the instability of QNMs with arbitrary-shape perturbation and the effectiveness of numerical results through pseudospectrum. We use high frequency approximation to attain the expression of the time domain Green function and clarify the origin of two different stages in time evolution. Through numerical methods we confirm that no power-law late time tail is expected, and the possible impact on time evolution caused by quantum correction is discussed.
Shu Luo (Mon,) studied this question.