The mixmaster universe in HoavaLifshitz gravity

Ioannis Bakas (1) , Francois Bourliot (2) , Dieter Lüst (3, 4) , Marios Petropoulos (2)

1 Department of Physics
2 CPHT - Centre de Physique Théorique [Palaiseau]
3 MPI-P - Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)
4 Arnold-Sommerfeld-Center für Theoretische Physik Department für Physik

We consider spatially homogeneous (but generally non-isotropic) cosmologies in the recently proposed Hořava-Lifshitz gravity and compare them to those of general relativity using Hamiltonian methods. In all cases, the problem is described by an effective point particle moving in a potential well with exponentially steep walls. Focusing on the closed-space cosmological model (Bianchi type IX), the mixmaster dynamics is now completely dominated by the quadratic Cotton tensor potential term for very small volume of the universe. Unlike general relativity, where the evolution towards the initial singularity always exhibits chaotic behavior with alternating Kasner epochs, the anisotropic universe in Hořava-Lifshitz gravity (with parameter λ > 1/3) is described by a particle moving in a frozen potential well with fixed (but arbitrary) energy E. Alternating Kasner epochs still provide a good description of the early universe for very large E, but the evolution appears to be non-ergodic. For very small E there are harmonic oscillations around the fully isotropic model. The question of chaos remains open for intermediate energy levels.

Mots clés: Physical Sciences

Ioannis Bakas, Francois Bourliot, Dieter Lüst, Marios Petropoulos. The mixmaster universe in HoavaLifshitz gravity. Classical and Quantum Gravity, 2010, 27 (4), pp.45013. ⟨10.1088/0264-9381/27/4/045013⟩. ⟨hal-00569784⟩