Birkhoff Integrability of Truncated Hořava–Lifshitz Mixmaster Model near the Cosmological Singularity

Abstract

The Hořava–Lifshitz mixmaster cosmological model near the cosmological singularity is presented as a generalized Euclidean Toda chain. Restricting to dominant vectors of the spectrum, we get a truncated model that qualitatively well describes the mixmaster model. The truncated model is associated with an affine Kac–Moody Lie algebra \(A_{2}^{+}\). According to the Adler–van Moerbeke criterion, the truncated Hamiltonian system is algebraically completely integrable.