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

Abstract

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.

Figures (2)

• Figure 1: $\zeta_4(\hat{m}^2)$ in Eq. (\ref{['d=4_dS_algebra']}) is plotted for $\hat{\alpha}^{\mathrm{(inv)}}=\hat{\beta}^{\mathrm{(inv)}}=0$. The dashed line indicates the position $\hat{m}^2=-0.359$, where the denominator of $\zeta_4(\hat{m}^2)$ vanishes.
• Figure 2: $\zeta_4^M(\tilde{m}^2)$ in Eq. (\ref{['d=4_Min_algebra']}) is plotted for $\tilde{\beta}^{\mathrm{(inv)}}=0$ (blue, solid), $0.06$ (orange, dashed), $0.12$ (green, dot-dashed). As $\tilde{\beta}^{\mathrm{(inv)}}$ becomes large, the minimum value for $\gamma_4$ to have a solution with $\tilde{m}^2<0$ is lowered.