Hyperbolic compactification of M-theory and de Sitter quantum gravity
  We present a mechanism for accelerated expansion of the universe in the
generic case of negative-curvature compactifications of M-theory, with minimal
ingredients. M-theory on a hyperbolic manifold with small closed geodesics
supporting Casimir energy -- along with a single classical source (7-form flux)
-- contains an immediate 3-term structure for volume stabilization at positive
potential energy. Hyperbolic manifolds are well-studied mathematically, with an
important rigidity property at fixed volume. They and their Dehn fillings to
more general Einstein spaces exhibit explicit discrete parameters that yield
small closed geodesics supporting Casimir energy. The off-shell effective
potential derived by M. Douglas incorporates the warped product structure via
the constraints of general relativity, screening negative energy. Analyzing the
fields sourced by the localized Casimir energy and the available discrete
choices of manifolds and fluxes, we find a regime where the net curvature,
Casimir energy, and flux compete at large radius and stabilize the volume.
Further metric and form field deformations are highly constrained by hyperbolic
rigidity and warping effects, leading to calculations giving strong indications
of a positive Hessian, and residual tadpoles are small. We test this via
explicit back reacted solutions and perturbations in patches including the Dehn
filling regions, initiate a neural network study of further aspects of the
internal fields, and derive a Maldacena-Nunez style no-go theorem for Anti-de
Sitter extrema. A simple generalization incorporating 4-form flux produces
axion monodromy inflation. As a relatively simple de Sitter uplift of the
large-N M2-brane theory, the construction applies to de Sitter holography as
well as to cosmological modeling, and introduces new connections between
mathematics and the physics of string/M theory compactifications.
