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Positivity from Negativity: M theory on hyperbolic geometry and Lambda>0

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We will describe a mechanism under development for accelerated expansion in the generic case of negative-curvature compactifications (based on work in progress with B. de Luca and G. Torroba). These manifolds are well-studied mathematically, with an important rigidity property at fixed volume. They exhibit precise generalizations of string dualities and connect to other areas of the landscape. M theory on a fiducial hyperbolic manifold with asymmetric cusp cross section, along with its automatically generated Casimir energy and a single source (7-form flux) contains an immediate 3-term structure for volume stabilization at positive potential energy. We analyze the equations of motion and off-shell effective potential, derived in beautiful work by M. Douglas taking proper account of the constraints of general relativity, using both human and artificial neural networks. After deriving a Maldacena-Nunez style no-go theorem for anti-de Sitter extrema for a range of parameters, and observing that standard integrated inequalities are all consistent with de Sitter solutions, we discuss ongoing work on the full equations of motion, including smooth internal field configurations with small slow roll parameters.

This talk is part of the Cosmology Lunch series.

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