Asymptotic states of the bounce geometry

TL;DR

The paper analyzes how to define asymptotic observables in cosmology within a string-landscape framework by studying the Coleman–De Luccia bounce and a proposed S-matrix between past and future Λ=0 regions. It derives a covariant entropy bound that limits the number of semiclassical states and finds that the past half of the bounce violates the second law, complicating a boundary S-matrix description. The authors show that generic perturbations drive the evolution toward a big crunch, making non-crunching asymptotic states rare, and identify halo-like and future-boundary states as the only tractable near-boundary configurations, with halo entropy saturating the same bound. Consequently, the S-matrix picture spanning both infinities appears problematic, suggesting a shift toward amplitudes defined at late times, akin to a no-boundary–style, future-boundary framework for cosmological observables.

Abstract

We consider the question of asymptotic observables in cosmology. We assume that string theory contains a landscape of vacua, and that metastable de Sitter regions can decay to zero cosmological constant by bubble nucleation. The asymptotic properties of the corresponding bounce solution should be incorporated in a nonperturbative quantum theory of cosmology. A recent proposal for such a framework defines an S-matrix between the past and future boundaries of the bounce. We analyze in detail the properties of asymptotic states in this proposal, finding that generic small perturbations of the initial state cause a global crunch. We conclude that late-time amplitudes should be computed directly. This would require a string theory analogue of the no-boundary proposal.

Figures (7)

• Figure 1: A potential which has a metastable minimum with positive energy and a stable minimum with zero energy.
• Figure 2: The Coleman-De Luccia bounce geometry, as an embedding in Minkowski space. The flat piece has zero cosmological constant, while the curved piece has positive cosmological constant. A domain wall separates the two regions.
• Figure 3: Conformal diagram of the Coleman-De Luccia solution, including orbits of the symmetry group $SO(1,3)$. The thick orbit is the domain wall. The radius of spheres goes to zero at the left and right boundaries and to infinity on the remaining boundaries.
• Figure 4: A wedged conformal diagram CEB2 for the bounce geometry. Normal ($>$, $<$), trapped ($\vee$), and anti-trapped ($\wedge$) regions are separated by apparent horizons (thick lines). Their shape is determined by matter sources (the domain wall, and the matter created by it in regions II and III). We treat the domain wall (dotted line) as a delta function source. $L_1$ and $L_2$ are light-sheets of the sphere $P$. The tightest entropy bound on the spacetime is obtained from $L$, a single light-sheet whose maximal area is the de Sitter horizon in the top right corner.
• Figure 5: Two ordinary particles collide with a large center of mass energy if they begin far apart. The backreaction will cause a crunch (heavy line). The regions above this line are included only to guide the eye. The diagram has been doubled: every point represents a hemisphere, not a sphere.