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Résumé : A bstract We consider four-dimensional general relativity with a positive cosmological constant, Λ, in the presence of a boundary, Γ, of finite spatial size. The boundary is located near a cosmological event horizon, and is subject to boundary conditions that fix the conformal class of the induced metric, and, K , the trace of the extrinsic curvature along Γ. The proximity of Γ to the horizon is controlled by the dimensionless parameter $$ {K\Lambda}^{-\frac{1}{2}} $$ K Λ − 1 2 . We provide an exhaustive analysis of linearised gravitational perturbations for the setup. This is performed both for a Γ encasing a portion of the static patch that ends just before the cosmological horizon (pole patch), as well as a Γ containing only the region near the cosmological horizon (cosmic patch). In the pole patch, we uncover a layered hierarchy of modes: ordinary normal modes, a novel type of boundary gapless mode, and boundary soft modes of frequency ω ≈ ±2 πiT dS , with T dS the horizon temperature. Minkowskian behaviour is recovered only for angular momenta l ≳ $$ {K\Lambda}^{-\frac{1}{2}} $$ K Λ − 1 2 which can be made parametrically large, thus attenuating previously found growing modes. In the cosmic patch, we uncover sound and shear fluid-dynamical modes that we interpret in terms of a conformal fluid with shear viscosity over entropy density ratio $$ \frac{\eta }{s} $$ η s = $$ \frac{1}{4\pi } $$ 1 4 π and vanishing bulk viscosity ζ = 0. The fluid dynamical sector is shown to admit a non-linear treatment. We describe a scaling regime in which the stretched horizon gravitational dynamics is dictated by a universal Rindler geometry, independent to the details of the infilling horizon. We briefly discuss quantitative features that distinguish cosmological and black hole horizons away from the Rindler regime.