Asymptotic Silence of Generic Cosmological Singularities

In this Letter we investigate the nature of generic cosmological singularities using the framework developed by Uggla et al. We study the past asymptotic dynamics of general vacuum $G_2$ cosmologies, which are expected to capture the singular behavior of generic cosmologies with no symmetries at all. Our results indicate that asymptotic silence holds, i.e., particle horizons along all time lines shrink to zero for generic solutions. Moreover, we provide evidence that spatial derivatives become dynamically insignificant along generic time lines, and that the evolution into the past along such time lines is governed by an asymptotic dynamical system which is associated with an invariant set—the silent boundary. We identify an attracting subset on the silent boundary that organizes the oscillatory dynamics of generic time lines in the singular regime. Finally, we discuss the dynamics associated with recurring spike formation.

Figure 1

(a) Unstable variables on $\mathcal{K}$, and (b) single transition sets associated with $N_{-}$ (dotted lines), ${\Sigma }_{\times }$ (dash-dotted lines) and ${\Sigma }_2$ (solid lines).

Figure 2

Projections onto the $({\Sigma }_{+}{\Sigma }_{-})$-plane of a state space orbit along the typical time line $x=0.3$ for (a) the full $G_2$ system, and (b) its restriction to the silent boundary. In both cases the orbits approach ${\mathcal{U}}_{\mathrm{v}\mathrm{a}\mathrm{c}}^{-}$, i.e., $\Delta \to 0$ in (a), and $(E_1{}^1,\mathit{C})\to 0$ in both (a) and (b).

Figure 3

Projection onto the $({\Sigma }_{+}{\Sigma }_{-})$-plane of a state space orbit undergoing a spike transition, followed by ${\Sigma }_2$ and ${\Sigma }_{\times }$ induced frame transitions and another spike transition (solid lines). The combination of $N_{-}$ curvature and ${\Sigma }_{\times }$ frame transitions corresponding to the second spike transition is shown (dashed lines). See also p. 152 in Ref. 15.