[论文解读] Are we living in a string-dominated universe?

Michael Petri|ArXiv.org|May 3, 2004

Cosmology and Gravitation Theories参考文献 17被引用 5

一句话总结

本文提出宇宙在本质上由弦主导，将其建模为全息星——一种无奇点、紧凑的物体，其引力半径外两普朗克长度处存在边界膜。该解由零宇宙学常数的爱因斯坦方程导出，预测 Ht = 1 且 CDM 与重子物质之比约为 6.45，与 WMAP 数据高度吻合，表明弦理论支配大尺度宇宙学。

ABSTRACT

The holographic solution is a new exact solution to the Einstein field equations. It describes a compact self-gravitating object with properties similar to a black hole. Its entropy and temperature at infinity are proportional to the Hawking result. Instead of an event horizon, the holographic solution has a real spherical boundary membrane, situated roughly two Planck distances outside of the object's gravitational radius. The interior matter-state is singularity free. It consists out of string type matter, which is densely packed. Each string has a transverse extension of exactly one Planck area. This dense package of strings might be the reason, why the solution does not collapse to a singularity. The local string tension is inverse proportional to the average string length. This purely classical result has its almost exact correspondence in a recent result in string theory. The holographic solution suggest, that string theory is relevant also on cosmological scales. The large scale phenomena in the universe can be explained naturally in a string context. Due to the zero active gravitational mass-density of the strings the Hubble constant in a string dominated universe is related to its age by H t = 1. The WMAP measurements have determined H t \approx 1.02 \pm 0.02 experimentally. The nearly unaccelerated expansion in a string dominated universe is compatible with the recent supernova measurements. Under the assumption, that the cold dark matter (CDM) consists out of strings, the ratio of CDM to baryonic matter is estimated as Ω_CDM / Ω_b \approx 6.45. Some arguments are given, which suggest that the universe might be constructed hierarchically out of its most basic building blocks: strings and membranes.

研究动机与目标

• 探索爱因斯坦方程的新精确解，提出一种无奇点的黑洞替代模型。
• 研究密集、径向排列的类弦物质是否能解释大尺度宇宙学观测。
• 检验宇宙中观测到的哈勃常数与物质密度比是否与经典弦基宇宙学模型一致。
• 评估弦理论作为低能宇宙学框架的可行性，而不仅限于高能粒子物理。

提出的方法

• 推导出零宇宙学常数下爱因斯坦场方程的精确球对称解，以物理边界膜取代事件视界。
• 将内部建模为密集、径向排列的弦阵列，每根弦占据恰好一个普朗克面积，张力与平均弦长成反比。
• 使用经典弦的物态方程（P_r = -ρ, P_⊥ = 0）描述内部各向异性的压强分布。
• 通过全息原理，将熵与穿刺边界膜的弦段数量关联，其规模与膜的面积成正比。
• 从引力势的径向依赖关系推导哈勃参数，表明在无宇宙学常数下 Ht = 1。
• 利用膨胀全息星解中局部能量密度与熵密度之比恒定，估算 CDM 与重子物质之比。

实验结果

研究问题

• RQ1 能否通过无奇点的、基于弦的爱因斯坦方程解重现宇宙的大尺度观测特性？
• RQ2 由经典弦主导的宇宙是否自然预测 Ht = 1，正如 WMAP 所测得的那样？
• RQ3 能否从基本弦模型中推导出观测到的冷暗物质与重子物质之比（≈6）？
• RQ4 黑洞的熵-面积定律是否能由全息星的弦结构自然解释？
• RQ5 该解中无宇宙学常数是否能与观测到的近乎无加速膨胀相协调？

主要发现

• 该模型精确预测 Ht = 1，与 WMAP 测得的 Ht = 1.02 ± 0.02 一致。
• 冷暗物质与重子物质之比估算为 Ω_CDM/Ω_b ≈ 6.45，与 WMAP 的 ≈6 值极为接近。
• 宇宙的能量密度满足 ρ/T⁴ ≈ 2⁶π³√3/ħ⁴（自然单位下），与实验数据相差仅几个百分点。
• 膨胀接近匀速（减速参数 q ≈ 0），当 H ≈ 60–63 km s⁻¹ Mpc⁻¹ 时与超新星观测一致。
• 哈勃常数预测值为 H ≈ 63 km s⁻¹ Mpc⁻¹，与其它绝对测量结果及一致 ΛCDM 模型相符。
• 该解的熵与边界膜的面积成正比，且每段弦占据一个普朗克面积，自然实现了贝肯斯坦-霍金熵公式。