Bianchi IX 宇宙模型的探討

Abstract

爆漲理論可以解釋視界、平坦等微調問題。然而，若限制宇宙一開始就是如FRW度規所描述的各向同性，亦是一種不自然。因此我們放寬各向同性的限制但仍要求宇宙是空間均勻的，亦即，我們把Bianchi空間引入重力誘發爆漲裡頭。我們最後重新檢驗了在變分法裡頭容易被忽略的一個問題，最後我們發現，在Lagrangian放入一些高階修正項的Bianchi II, VIII, IX模型都可以直接對尺度因子變分而得到正確的場方程式。

The inflation theory is known to solve the horizon and flatness problems. However, to restrict the initial universe to be isotropic as described by FRW metric is not natural. Hence, we release the constraint of isotropy but still require the universe to be homogeneous, i.e. we take Bianchi spaces into induced gravity inflation. We re-examine a problem about action principle which may be easily ignored in the end. After some detailed study, we find that it is correct to do variation of the action with respect to scale factors for Bianchi IX model up to some higher derivative Lagrangian corrections.