Cosmological horizons as new examples of the membrane paradigm

In this paper we aim to provide new examples of the application and the generality of the membrane paradigm. The membrane paradigm is a formalism for studying the event horizon of black holes. After analyzing it with some technical details and realizing it in the Reissner-Nordström black hole, we apply the paradigm to cosmological horizons, first to the pure de Sitter horizon, and then to the trapping horizon of the Friedmann-Lemaître-Robertson-Walker Universe. In the latter case, the cosmological stretched horizon is oblique, thus the running of the renormalization parameter is nonzero in the timelike direction and gives a correction to the membrane pressure. In this paradigm, the cosmological equations come from continuity equations of the membrane fluid and the bulk fluid respectively.