  We employ holographic duality to compute $\langle T_{\mu \nu} \rangle$ in
strongly coupled $\mathcal N = 4$ supersymmetric Yang-Mills theory and then
study evolution of the semiclassical Einstein field equations sourced by
$\langle T_{\mu \nu} \rangle$. 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 $H_c$ for which de Sitter space is unstable when $H < H_c$
and mode stable when $H > H_c$.
