De Sitter horizons & holographic liquids

We explore asymptotically AdS₂ solutions of a particular two-dimensional dilaton-gravity theory. In the deep interior, these solutions flow to the cosmological horizon of dS₂. We calculate various matter perturbations at the linearised and non-linear level. We consider both Euclidean and Lorentzian perturbations. The results can be used to characterise the features of a putative dual quantum mechanics. The chaotic nature of the de Sitter horizon is assessed through the soft mode action at the AdS₂ boundary, as well as the behaviour of shockwave type solutions.