标题： 宇宙学扰动在(1+3+6)维时空中的情况 显示英文标题

标题： Cosmological perturbations in the (1+3+6)-dimensional space-times

摘要： 在不包含粘性过程的光子气体的(1+3+6)维时空中的宇宙扰动是基于Abbott等人的方式进行研究的。 时空由外空间（三维膨胀部分）和内空间（六维部分）组成。 内空间最初膨胀，之后收缩。 Abbott等人仅在小波数极限下得到了幂次型解，这些解出现在时空的最终阶段。 在本文中，我们不仅得到了小波数解，还得到了大波数解。 发现后者解依赖于两个波数k_r和k_R（分别在外空间和内空间中定义），并且当(k_r/r(t))/(k_R/R(t)) >> 1或<< 1时，k_r相关的部分和k_R相关的部分分别主导总扰动，其中r(t)和R(t)是外空间和内空间的尺度因子。 此外，通过比较这些扰动的行为，讨论了随时间变化的外空间扰动谱的变化。 显示英文摘要

摘要： Cosmological perturbations in the (1+3+6)-dimensional space-times including photon gas without viscous processes are studied on the basis of Abbott et al.'s formalism. Space-times consist of the outer space (the 3-dimensional expanding section) and the inner space (the 6-dimensional section). The inner space expands initially and contracts later. Abbott et al. derived only power-type solutions in the small wave-number limit which appear at the final stage of the space-times. In this paper, we derive not only small wave-number solutions, but also large wave-number solutions. It is found that the latter solutions depend on the two wave-numbers k_r and k_R (which are defined in the outer and inner spaces, respectively), and that the k_r-dependent and k_R-dependent parts dominate the total perturbations when (k_r/r(t))/(k_R/R(t)) >> 1 or << 1, respectively, where r(t) and R(t) are the scale-factors in the outer and inner spaces. By comparing the behaviors of these perturbations, moreover, changes in the spectrum of perturbations in the outer space with time are discussed.