论文标题
EGB模型中具有三个因子空间的稳定指数宇宙学类型解决方案，具有$λ$ - 期
Stable exponential cosmological type solutions with three factor spaces in EGB model with a $Λ$-term
论文作者
论文摘要
我们研究了$ d $二维的爱因斯坦 - 加斯 - 邦网络模型，其中包括高斯式术语，宇宙学术语$λ$和两个非零常数：$α_1$和$α_2$。在将指标强加于对角线的情况下，我们发现宇宙学类型的解决方案在可变$ u $中具有指数依赖性的宇宙学类型解决方案，由三个非固定性的hubble类似参数（$ h \ neq 0 $，$ h_1 $ and $ h_1 $ and $ h_1 $ and $ h_2 $）$ h + k_1 H + k_1 h_1 h_1 h_1 h_1 + k_1 + k_2 > 1 $，$ k_1> 1 $和$ k_2> 1 $，具体取决于符号参数$ \ varepsilon = \ pm 1 $，其中$ \ varepsilon = 1 $对应于宇宙案例，$ \ varepsilon = -1 $ - 至静态一个）。我们处理两种情况：i）$ m <k_1 <k_2 $和ii）$ 1 <k_1 = k_2 = k $，$ k \ neq m $。我们表明，在这两种情况下，如果$ \varepsilonα= \varepsilonα_2 /α_1> 0 $和$αλ> 0 $满足某些（上和下部）边界，则解决方案存在。解决方案定义为四个（或更少）的某些多项式主方程的解，该方程可能在自由基中解决。在情况II中）提出了明确的解决方案。在这两种情况下，我们都将稳定和非稳定解决方案列为$ u \ to \ pm \ infty $。还考虑了$ h = 0 $的情况。
We study a $D$-dimensional Einstein-Gauss-Bonnet model which includes the Gauss-Bonnet term, the cosmological term $Λ$ and two non-zero constants: $α_1$ and $α_2$. Under imposing the metric to be diagonal one, we find cosmological type solutions with exponential dependence of three scale factors in a variable $u$, governed by three non-coinciding Hubble-like parameters: $H \neq 0$, $h_1$ and $h_2$, obeying $m H + k_1 h_1 + k_2 h_2 \neq 0$, corresponding to factor spaces of dimensions $m > 1$, $k_1 > 1$ and $k_2 > 1$, respectively, and depending upon sign parameter $\varepsilon = \pm 1$, where $\varepsilon = 1$ corresponds to cosmological case and $\varepsilon = - 1$ - to static one). We deal with two cases: i) $m < k_1 < k_2$ and ii) $1< k_1 = k_2 = k$, $k \neq m$. We show that in both cases the solutions exist if $\varepsilon α= \varepsilon α_2 / α_1 > 0$ and $αΛ> 0$ satisfies certain (upper and lower) bounds. The solutions are defined up to solutions of certain polynomial master equation of order four (or less) which may be solved in radicals. In case ii) explicit solutions are presented. In both cases we single out stable and non-stable solutions as $u \to \pm \infty$. The case $H = 0$ is also considered.
