Quantum Supersymmetric Bianchi IX Cosmology

Understand

We study the quantum dynamics of a supersymmetric squashed three-sphere by dimensionally reducing to one timelike dimension the action of D=4 simple supergravity for a Bianchi IX cosmological model.

• After imposition of the diffeomorphism constraints, the wave function of the Universe becomes a spinor of Spin(8,4) depending on the three squashing parameters, which satisfies Dirac, and Klein-Gordon-like, wave equations describing the propagation of a quantum spinning particle reflecting off spin-dependent potential walls.
• The algebra of the susy constraints and of the Hamiltonian one is found to close.
• One finds that the quantum Hamiltonian is built from operators that generate a 64-dimensional representation of the maximally compact sub-algebra of the rank-3 hyperbolic Kac-Moody algebra AE3.