On the Classical Stability of Orientifold Cosmologies

TL;DR

The paper investigates the classical stability of orientifold cosmologies, showing that orientifold boundaries can resolve the Horowitz–Polchinski instability by excising regions responsible for black-hole formation. By reducing the three-dimensional setup to a two-dimensional dilaton gravity model and analyzing shock-wave backreaction, it demonstrates that the uplifted HP surface can be reconciled with a boundary that eliminates CTC-induced instabilities. It also proves that localized perturbations do not destabilize the cosmological Cauchy horizon at the classical level, though a full quantum stress-energy analysis remains for future work. Overall, the work provides a concrete mechanism by which stringy orientifolds can tame cosmological singularities and horizon instabilities, advancing our understanding of time-dependent backgrounds.

Abstract

We analyze the classical stability of string cosmologies driven by the dynamics of orientifold planes. These models are related to time-dependent orbifolds, and resolve the orbifold singularities which are otherwise problematic by introducing orientifold planes. In particular, we show that the instability discussed by Horowitz and Polchinski for pure orbifold models is resolved by the presence of the orientifolds. Moreover, we discuss the issue of stability of the cosmological Cauchy horizon, and we show that it is stable to small perturbations due to in-falling matter.

Figures (13)

• Figure 1: The curves given by equation (\ref{['surxpxm']}), which represent the surfaces $S_a$ for the values of $a$ indicated in the figure. The surface $S_1$ is clearly singled out, and is the unique null surface.
• Figure 2: Scattering of light rays in three dimensions. The holonomies $U_1$ and $U_2$ are null boosts, whereas $U$ is a boost for center of mass energies greater then a specific threshold. In this case, the geometry has CTC's, as indicated.
• Figure 3: Shock wave solution in two--dimensional dilaton gravity.
• Figure 4: The cosmological vacuum solution for $V=2\Phi^{-3}$. Regions I$_{in}$, I$_{out}$ are the contracting and expanding cosmologies, whereas regions II$_{L,R}$ are the intermediate regions. Regions III$_{L,R}$ are after the singularities, and correspond, when uplifted to three dimensions, to the regions where the Killing vector $\kappa$ becomes timelike.
• Figure 5: Shock wave solutions in the cosmological geometry.