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<p>We study the stability of <i>d</i>-dimensional (<i>d</i> = 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 <i>d</i>-dimensional Lichnerowicz equation with mass-squared <i>m</i><sup>2</sup> and of semiclassical equations involving the dimensionless parameter <i>γ</i><sub><i>d</i></sub>. For <i>d</i> = 3, we find that Minkowski spacetime is always unstable against perturbations, whereas de Sitter spacetime becomes stable when a dimensionless parameter <i>γ</i><sub>3</sub> exceeds a critical value. In <i>d</i> = 4, both de Sitter and Minkowski spacetimes become unstable when the parameter <i>γ</i><sub>4</sub> exceeds its critical value. In contrast, in <i>d</i> = 5, de Sitter and Minkowski spacetimes remain stable for almost all values of the parameter <i>γ</i><sub>5</sub>, except for a regime in which higher-curvature corrections become comparable to the Einstein tensor.</p>

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

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  • 发表日期：

    2026年5月27日

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  • Akihiro Ishibashi,
  • Kengo Maeda,
  • Takashi Okamura

摘要

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 m2 and of semiclassical equations involving the dimensionless parameter γd. For d = 3, we find that Minkowski spacetime is always unstable against perturbations, whereas de Sitter spacetime becomes stable when a dimensionless parameter γ3 exceeds a critical value. In d = 4, both de Sitter and Minkowski spacetimes become unstable when the parameter γ4 exceeds its critical value. In contrast, in d = 5, de Sitter and Minkowski spacetimes remain stable for almost all values of the parameter γ5, except for a regime in which higher-curvature corrections become comparable to the Einstein tensor.