arXiv 0811.15802008-11-10hep-thastro-phgr-qchep-ph

N+1维FRW宇宙中的p膜动力学

p-brane dynamics in N+1-dimensional FRW universes

P. P. Avelino, R. Menezes, L. Sousa

备注：: 6 pages, 3 figures
发表信息：: Phys.Rev.D79:043519,2009
DOI：: 10.1103/PhysRevD.79.043519

摘要：

我们研究了具有$S_{p-i}\otimes \mathbbm{R}^i$拓扑的极大对称$p$ -膜在具有$N+1$维数的平坦膨胀或坍缩的均匀各向同性宇宙中的演化（$N \ge 3$，$p < N$，$0 \le i < p$）.我们找到相应的运动方程，并计算新的解析解的轨迹在相空间。对于一个恒定的哈勃参数，$H$，$i=0$，我们表明，所有最初的静态解决方案的物理半径低于一定的临界值，$r_c^0$，是周期性的，而那些具有较大的初始半径成为冻结在后期的共动坐标。我们找到一个固定的解决方案与恒定的速度和物理半径，$r_c$，并计算均方根速度的周期$p$膜解决方案和相应的（平均）状态方程的$p$膜气体。我们还调查了$p$ -膜动力学$H \neq {\rm constant}$的模型中，宇宙的演化是由一个完美的流体与恒定的状态方程参数，$w={\cal P}_p/ρ_p$，并表明，一个临界半径，$r_c$，仍然可以定义为$ -1 \le w < w_c$与$w_c=(2-N)/N$。我们进一步表明，对于$w \sim w_c$的临界半径给出近似的$r_c H \propto (w_c-w)^{γ_c}$与$γ_c=-1/2$（$r_c H \to \infty$时$w \to w_c$）。最后，我们讨论了宇宙的大尺度动力学对非常小的环的宏观演化的影响。

英文摘要：

We study the evolution of maximally symmetric $p$-branes with a $S_{p-i}\otimes \mathbbm{R}^i$ topology in flat expanding or collapsing homogeneous and isotropic universes with $N+1$ dimensions (with $N \ge 3$, $p < N$, $0 \le i < p$). We find the corresponding equations of motion and compute new analytical solutions for the trajectories in phase space. For a constant Hubble parameter, $H$, and $i=0$ we show that all initially static solutions with a physical radius below a certain critical value, $r_c^0$, are periodic while those with a larger initial radius become frozen in comoving coordinates at late times. We find a stationary solution with constant velocity and physical radius, $r_c$, and compute the root mean square velocity of the periodic $p$-brane solutions and the corresponding (average) equation of state of the $p$-brane gas. We also investigate the $p$-brane dynamics for $H \neq {\rm constant}$ in models where the evolution of the universe is driven by a perfect fluid with constant equation of state parameter, $w={\cal P}_p/ρ_p$, and show that a critical radius, $r_c$, can still be defined for $ -1 \le w < w_c$ with $w_c=(2-N)/N$. We further show that for $w \sim w_c$ the critical radius is given approximately by $r_c H \propto (w_c-w)^{γ_c}$ with $γ_c=-1/2$ ($r_c H \to \infty$ when $w \to w_c$). Finally, we discuss the impact that the large scale dynamics of the universe can have on the macroscopic evolution of very small loops.

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