Holographic duality and mode stability of de Sitter space in semiclassical gravity

Abstract

We employ holographic duality to compute ⟨ Tμ ν ⟩ in strongly coupled \U0001d4a9 = 4 supersymmetric Yang-Mills theory and then study evolution of the semiclassical Einstein field equations sourced by ⟨ Tμ ν ⟩. Linearizing about de Sitter space, we find that the semiclassical equations of motion reduce to a four dimensional scalar wave equation coupled to a five dimensional scalar wave equation. We compute the mode spectrum of these equations and find that there exists a critical value of the Hubble constant Hc for which de Sitter space is unstable when H < Hc and mode stable when H > Hc.