世界线的经典散焦--宇宙学意义
Classical defocussing of world lines -- Cosmological Implications
摘要：
我们用标量$ψ(r)$的五维理论修正了早期引力，推广了我们关于世界线散焦的结果。Raychaudhuri方程中的加速度项对于平坦FRW度规是正的。标量$ψ(r)$满足求解的非线性微分方程。虽然是奇异的，但加速度项是有限的。由此得到哈勃参数H（t）和比例因子$a(t)$的方程。这些都是使用“固定点分析”进行分析。如果没有标量场，宇宙的年龄是有限的，表明宇宙的开始和没有反弹。考虑到标量的贡献，宇宙的年龄被证明是无限的，从而解决了奇异性。比例因子$a(t)$表现出经典反弹，该反弹与标量场的效应成比例。早期宇宙中的5维引力效应是引起世界线的散焦，给出无限大的宇宙年龄，从而解决了FRW尺度因子的大爆炸奇点和经典反弹。
英文摘要：
We have extended our result on defocussing of world lines [1] by modifying gravity in the early epoch by a 5-d theory with scalar $ψ(r)$. The acceleration term in the Raychaudhuri equation has been shown to be positive for flat FRW metric. The scalar $ψ(r)$ satisfies a non-linear differential equation which is solved. Though singular, the acceleration term turns out to be finite. With this, the equations for the Hubble parameter H(t) and the scale factor $a(t)$ are obtained. These are analyzed using 'fixed point analysis'. Without the scalar field, the age of the universe is finite showing a beginning of the universe and with out bounce. With the contribution of the scalar included, the age of the universe is shown to be infinite, thereby resolving the singularity. The scale factor $a(t)$ exhibits classical bounce, the bounce being proportional to the effect of the scalar field. The effect of the 5-d gravity in the early universe is to cause defocussing of the world lines, give infinite age of the universe thereby resolving the big bang singularity and classical bounce for the FRW scale factor.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
