论文标题
世界界线的古典散布 - 宇宙学的含义
Classical defocussing of world lines -- Cosmological Implications
论文作者
论文摘要
我们通过用标量$ψ（r）$修改早期时代的重力来散布世界线的结果[1]。 Raychaudhuri方程中的加速度项已被证明对平面FRW度量呈阳性。标量$ψ（r）$满足已解决的非线性微分方程。尽管奇异，但加速度术语被证明是有限的。这样，获得了哈勃参数h（t）和比例因子$ a（t）$的方程。使用“固定点分析”对这些进行分析。没有标量场，宇宙的年龄是有限的，显示了宇宙的开头，并且反弹。随着标量的贡献，宇宙的年龄被证明是无限的，从而解决了奇异之处。比例因子$ a（t）$表现出经典的反弹，反弹与标量场的效果成正比。 5-D重力在早期宇宙中的影响是引起世界界线的散焦，给予宇宙的无限年龄，从而解决了FRW量表因子的大爆炸奇点和经典的反弹。
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.
