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arXiv 1607.01244hep-thgr-qc
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Einstein-Gauss-Bonnet模型中具有非静态体积因子的指数宇宙学解的稳定性

On stability of exponential cosmological solutions with non-static volume factor in the Einstein-Gauss-Bonnet model

V. D. Ivashchuk

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20 pages, no figures, LaTex; two Remarks (1 and 4) and 7 references are added
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摘要：

考虑一个具有Gauss-Bonnet项和宇宙学常数项的（n+1）维引力模型。当采用对角宇宙度规时，得到了尺度因子为指数依赖的解：a_i ~ exp（v^it），i = 1，.，n，分析n > 3。研究了具有非静态体积因子的解的稳定性，即当K（v）= \sum_{k = 1}^{n} v^k \neq 0.我们证明了在一定的限制R下，K（v）> 0的解是稳定的，而K（v）< 0的解是不稳定的.一些稳定的解决方案的例子。我们证明了当有效引力常量为零变化且满足v^1 = v^2 = v^3 = H > 0的解在满足约束R的条件下是稳定的.

英文摘要：

A (n+1)-dimensional gravitational model with Gauss-Bonnet term and cosmological constant term is considered. When ansatz with diagonal cosmological metrics is adopted, the solutions with exponential dependence of scale factors: a_i ~ exp( v^i t), i = 1, ..., n, are analysed for n > 3. We study the stability of the solutions with non-static volume factor, i.e. if K(v) = \sum_{k = 1}^{n} v^k \neq 0. We prove that under certain restriction R imposed solutions with K(v) > 0 are stable while solutions with K(v) < 0 are unstable. Certain examples of stable solutions are presented. We show that the solutions with v^1 = v^2 = v^3 = H > 0 and zero variation of the effective gravitational constant are stable if the restriction R is obeyed.

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