Instability thresholds for de Sitter and Minkowski spacetimes in holographic semiclassical gravity

A bstract We study the stability of d -dimensional ( d = 3, 4, 5) de Sitter and Minkowski spacetimes within the framework of semiclassical gravity sourced by a strongly coupled quantum field with a gravity dual. Our stability results are derived from a careful analysis of the d -dimensional Lichnerowicz equation with mass-squared m 2 and of semiclassical equations involving the dimensionless parameter γ d . For d = 3, we find that Minkowski spacetime is always unstable against perturbations, whereas de Sitter spacetime becomes stable when a dimensionless parameter γ 3 exceeds a critical value. In d = 4, both de Sitter and Minkowski spacetimes become unstable when the parameter γ 4 exceeds its critical value. In contrast, in d = 5, de Sitter and Minkowski spacetimes remain stable for almost all values of the parameter γ 5 , except for a regime in which higher-curvature corrections become comparable to the Einstein tensor.