  The double-cone geometry is a saddle of the gravitational path integral,
which explains the chaotic statistics of the spectrum of black hole
microstates. This geometry is the usual AdS-Schwarzschild black hole, but with
a periodic identification of the time coordinate; the resulting singularity at
the black hole horizon is regulated by making the geometry slightly complex.
Here, we consider generalizations of the double-cone geometry which include the
Lorentzian cosmology that sits between the event horizon and the black hole
singularity. We analyze this in two and three dimensions, where the cosmology
has compact spatial sections and big bang/crunch singularities. These
singularities are regulated in the same way by slightly complexifying the
metric. We show that this is possible while satisfying the Kontsevich-Segal
criterion, implying that these geometries can be interpreted as perturbatively
stable saddle points in general relativity. This procedure leads to a novel
description of the cosmology in terms of standard observables in the dual
boundary CFT. In three dimensions, the cosmological solution gives a new
contribution to the two-point function of the density of states in the boundary
CFT. Unlike the usual double cone, it describes correlations between black hole
microstates with different masses, and in a limit describes correlations
between the statistics of heavy states and states near the BTZ threshold.
