Speaker
Description
Near a spacelike singularity, the BKL approximation reduces gravitational dynamics to the motion of logarithmic scale factors in a Lorentzian minisuperspace. In the late-time limit, this becomes a billiard motion on a hyperbolic domain. Quantisation then gives a Wheeler–DeWitt equation which can be interpreted as a Laplace-type spectral problem on the corresponding hyperbolic billiard.
This talk focuses on the four- and five-dimensional cases. In these cases, the Wheeler–DeWitt eigenfunctions are naturally organised as Maass-type waveforms. I will then describe an auxiliary Fock-space representation of the Mellin-transformed wavefunction, where the wavefunction is written as a trace over charged harmonic oscillators whose modes are labelled by primes in the four-dimensional case, and by the relevant complex primes in the five-dimensional case. This gives a “dual” primon-gas picture of the Wheeler–DeWitt wavefunction near a cosmological singularity.
I will also briefly describe ongoing work in seven dimensions, where the BKL billiard may serve as a quaternionic bridge between the commutative arithmetics and the octonionic structures associated with the maximal-supergravity billiard.