视界问题的新图示(英文)

A NEW DIAGRAM FOR ILLUSTRATING THE HORIZON PROBLEM

在用定义为径向距离除以尺度因子的径向坐标r和宇宙时间t的r-t图中,大爆炸时向我们发射、现在到达我们这里的光子的轨迹,r_(t),是大爆炸时我们向外发射光子轨迹,r+(t)的镜象。前者画出我们现今时刻的“世界图象”(world picture),而后者则描绘(粒子)视界自从大爆炸以来的增长。方程,r_(t)=～(1/2)r+(t)决定时刻t_D,它有如下性质:世界图象中凡早于t_D的事件多少都有视界问题,晚于t_D的事件就没有视界问题。 对于平直的Friedmann宇宙,算得t_D颇晚(相应的红移仅是z_D≈1.25!),远晚于微波背景辐射的时刻t_M(其红移为～10~3)。对于Guth的暴涨宇宙,算得t_D很接近暴涨期的开始,远早于t_M。 对于一个弯曲的Friedmann宇宙,Penrose图的时间轴可被证认为通常用来表述尺度因子演化的参数方程中的参数η,而其空间轴可被证认为径向角坐标x,由此马上得出:当哈勃时间H_0^(-1)=20×10~9年时,对于一个减速参数q_0=1.65的封闭宇宙,z_D=0.86;对于一个密度参数Q_0=0.05的开放宇宙,z_D=3.66。

In the r-t diagram, where t is the cosmic time and r is the radial co- ordinate defined as the proper radial distance divided by the scale factor, the locus of the incoming photon emitted at the big bang and reaching us now, r_(t), is a mirror image of the locus of the outgoing photon emitted at the big bang with r = 0, r+(t). The former graphs our present world picture while the latter traces the growth of the (particle) horizon sincethe big bang. The equation r_(t) = 1/2r+(t) determines an epoch tD withthe property that, for all events on the world picture before tD, the horizon problem exists to varying degrees of severity, while for events after tD, there is no horizon problem.For the flat Friedmann universe tD turns out to be quite recent (ZD≈ 1.25!), long after than the epoch of the MBR (microwave background radiation z≈103); for the inflationary model of Guth, to is near the beginning of the inflationary era, long before the MBR epoch.For a curved Friedmann universe the time axis of the Penrose diagram can be identified with the parameter η in the usual parametric representation of the scale factor and the space axis, with the angular radial coordinate X. Thus interpreted, the diagram readily gives ZD = 0.86 (3.66) for a closed (open) universe corresponding to H0-1= 20 × 109 yR and q0 = 1.65(Ω0 = 0.05).