挑戰廣義相對論在極端尺度下的非線性效應

Abstract

本碩士論文依據作者過去發表的文章分成兩大部分。 首先，我們認為與以往的微擾計算結果相反，廣義相對論的非線性效應會讓宇宙小尺度的不均勻性足以改變超新星亮度距離與紅移的關係，使得從超新星推得的哈伯常數與從宇宙微波背景輻射得來的數值不同。我們計算並顯示已知的3.4個標準差的差距確實可以用一個約莫三億秒差距大小的空洞來解釋，同時該空洞與亮物質密度觀測數據暗示可能存在的空洞大小位置相符。 然後在第二部分，我們基於廣義相對論中常常出現的旋量變數，透過將弦世界面理論對稱轉變為旋量對稱來建立一個新形式的時空量子化。由於是從幾種常見的重力理論共有的特性出發，我們相信此理論可以將如量子迴圈重力理論與超弦理論等熱門理論連結起來。我們也推導了廣義測不準原理並顯示理論具有全相性。由於時空被量子化，世界線會變得比較模糊。我們計算了模糊的程度，並顯示即便是在宇宙學尺度下也極難測量到該現象。因此我們無需擔心這個時空量子化理論會與任何宇宙觀測結果相衝突。

The whole thesis is divided into two parts, each of which is based on papers published before. First, we suggest that contrary to the usual perturbation result, the increasingly severe Hubble parameter tension between observations by utilizing low-redshift supernovae luminosity distance and the cosmological microwave background can be explained away by considering the nonlinear effect of the local inhomogeneity. We also compare the density profile from galaxy survey to what we obtained from the assumption that the tension of Hubble parameter comes solely from the local inhomogeneity, and find that they agree with each other. Second, we introduce a new type of spacetime quantization based on the spinorial description suggested by loop quantum gravity. Specifically, we build our theory on a string theory inspired Spin(3, 1) worldsheet action. Because of its connection with quantum gravity theories, our proposal may in principle link back to string theory, connect to loop quantum gravity where SU(2) is suggested as the fundamental symmetry, or serve as a Lorentzian spin network. We derive the generalized uncertainty principle and demonstrate the holographic nature of our theory. Due to the quantization of spacetime, geodesics in our theory are fuzzy, but the fuzziness is shown to be much below conceivable astrophysical bounds, which makes our theory safe from deleterious effects.