Conformal boundaries near cosmological horizons

Abstract: We investigate the dynamics of linearised perturbations around the de Sitter static patch, in the presence of a timelike boundary with conformal boundary conditions. Inspired by the case of global AdS4, for which the limit in which the conformal boundary approaches the asymptotic boundary reveals a hierarchy of real modes, we consider the limit in dS4 in which the conformal boundary approaches the cosmological horizon. In this limit, potential perturbations that grow exponentially in time are attenuated. We find a hierarchy of modes that localise near the conformal boundary, suggesting a holographic interpretation. In particular, we uncover sound and shear fluid-dynamical modes that we interpret in terms of a conformal fluid with shear viscosity over entropy density ratio eta/s=1/4pi.