6+1維度宇宙學模型

Abstract

在本篇論文中，我們在SO(4)群6維的均項性(homogenous)空間，建立一個均項性但各向異性(anisotropic)的度規(metric)，使得這個6維空間分開成3個大的空間維度，以及另外3個極小的額外維度。再利用建立的度規計算在 空間中的曲率，並推導在6+1維度下的愛因斯坦方程式，討論額外維度收縮的過程。 接著我們讓此模型做演化，並分別與古典宇宙學中宇宙演化的各個階段：暴漲(Inflation)、輻射主控時期(Radiation dominated era)、物質主控時期(Matter dominated era)分別做對照。並且計算在此模型中一些重要的數值。

In this thesis, we use SO(4) group as a 6 dimensional homogenous space, we can build up a homogenous but anisotropic metric such that the 6 dimensional space become 3 large ordinary dimension and 3 compact extra-dimension. We will calculate the space curvature on the metric. Finally, we will obtain an Einstein’s equation for such a space describing the evolution of space compactification and topology. Then we will evolve this model with every phase of universe: inflation, radiation dominated era and matter dominated era. Fit this model with cosmology. Finally we will give some estimation and evaluate important quantities in this model.