Power Law Inflation
Power Law Inflation
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DOI：
10.1007/s00220-009-0812-6
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发表时间：
2009-04
影响因子：
2.4
通讯作者：
H. Ringström
中科院分区：
文献类型：
--
作者：
H. Ringström
本文的主题是耦合到具有指数势的非线性标量场的爱因斯坦方程。我们考虑的问题是证明一类方程的空间局部齐次解的未来全局非线性稳定性。幂律型的加速展开有解。我们证明了这样一个结果，即如果我们的初始数据在一定半径的球上与这样的解足够接近，那么在我们开始的数据的最大全局双曲发展中，所有的因果测地线都是完整的。换句话说，我们只是在空间上做局部假设，在时间上得到全局结论。我们还在我们控制的区域内得到渐近展开式。根据这一结果以及在大多数空间齐次情况下可以分析其渐近行为的事实，我们在空间局部齐次情况下得到了一个相当一般的稳定性陈述。
The subject of this paper is Einstein’s equations coupled to a non-linear scalar field with an exponential potential. The problem we consider is that of proving future global non-linear stability of a class of spatially locally homogeneous solutions to the equations. There are solutions onwith accelerated expansion of power law type. We prove a result stating that if we have initial data that are close enough to those of such a solution on a ball of a certain radius, say, then all causal geodesics starting inare complete to the future in the maximal globally hyperbolic development of the data we started with. In other words, we only make local assumptions in space and obtain global conclusions in time. We also obtain asymptotic expansions in the region over which we have control. As a consequence of this result and the fact that one can analyze the asymptotic behaviour in most of the spatially homogeneous cases, we obtain quite a general stability statement in the spatially locally homogeneous setting.