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We employ holographic duality to compute $\langle T_{\mu \nu} \rangle$ instrongly coupled $\mathcal N = 4$ supersymmetric Yang-Mills theory and thenstudy evolution of the semiclassical Einstein field equations sourced by$\langle T_{\mu \nu} \rangle$. Linearizing about de Sitter space, we find thatthe semiclassical equations of motion reduce to a four dimensional scalar waveequation coupled to a five dimensional scalar wave equation. We compute themode spectrum of these equations and find that there exists a critical value ofthe Hubble constant $H_c$ for which de Sitter space is unstable when $H < H_c$and mode stable when $H > H_c$.

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