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arXiv 0911.2665hep-thgr-qc
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Horava-Lifshitz引力中的Mixmaster宇宙

Mixmaster universe in Horava-Lifshitz gravity

Ioannis Bakas, Francois Bourliot, Dieter Lust, Marios Petropoulos

摘要:

我们考虑空间均匀的(但一般非各向同性)宇宙学在最近提出的Horava-Lifshitz引力和比较他们的广义相对论使用哈密顿方法。在所有情况下,问题描述为一个有效的点粒子运动的势阱与指数陡峭的墙壁。聚焦于封闭空间宇宙学模型(Bianchi IX型),对于非常小的宇宙体积,混合主动力学现在完全由二次Cotton张量势项主导。与广义相对论不同的是,在广义相对论中,朝向初始奇点的演化总是表现出卡斯纳历元交替的混沌行为,霍拉瓦-利夫希茨引力(参数λ> 1/3)中的各向异性宇宙是由一个在冻结势阱中运动的粒子描述的,该粒子具有固定(但任意)的能量E。交替卡斯纳历元仍然提供了一个很好的描述早期宇宙非常大的E,但演变似乎是非遍历。对于非常小的E,在完全各向同性模型周围存在谐波振荡。对于中间能级,混沌的问题仍然是开放的。

英文摘要:

We consider spatially homogeneous (but generally non-isotropic) cosmologies in the recently proposed Horava-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 Horava-Lifshitz gravity (with parameter lambda > 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.

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