标题： α变化宇宙的定性分析 显示英文标题

标题： Qualitative Analysis of Universes with Varying Alpha

摘要： 假设一个以幂律标度因子演化的弗里德曼宇宙，$a=t^{n}$，我们分析描述相对论广义化中随时间变化的精细结构“常数”$\alpha$的方程组的相空间。在贝肯斯坦-桑迪克-巴罗-马奎霍的广义相对论推广中，我们已经分类了所有可能的$\alpha (t)$行为，适用于具有不同$n$的永恒膨胀宇宙，并找到了$\alpha (t)$的新精确解。我们发现在相空间中所有$n$的吸引子点。 一般而言，当宇宙膨胀处于尘埃主导阶段（$n=2/3$）时，$\alpha $将是时间的非减函数，并且以对数方式随时间增加，但在$n>2/3$成立时变为常数。 这包括负曲率主导的情况（$n=1$）。 当膨胀尺度因子呈指数增长时，$\alpha $也迅速趋于常数。 在膨胀宇宙中，建立了$\alpha $在晚期趋于渐近常数的一般条件集。 显示英文摘要

摘要： Assuming a Friedmann universe which evolves with a power-law scale factor, $a=t^{n}$, we analyse the phase space of the system of equations that describes a time-varying fine structure 'constant', $\alpha$, in the Bekenstein-Sandvik-Barrow-Magueijo generalisation of general relativity. We have classified all the possible behaviours of $\alpha (t)$ in ever-expanding universes with different $n$ and find new exact solutions for $\alpha (t)$. We find the attractors points in the phase space for all $n$. In general, $\alpha $ will be a non-decreasing function of time that increases logarithmically in time during a period when the expansion is dust dominated ($n=2/3$), but becomes constant when $n>2/3$. This includes the case of negative-curvature domination ($n=1$). $\alpha $ also tends rapidly to a constant when the expansion scale factor increases exponentially. A general set of conditions is established for $\alpha $ to become asymptotically constant at late times in an expanding universe.