在這篇論文中，我將會簡介暴漲模型的想法，以及其中一種模型“自然暴
漲模型”。自然暴漲模型有其缺點，也就是裡面的f scale需遠大於Planck scale。為了解決此問題，進而引進另一種暴漲模型“軸子暴漲模型”。
軸子暴漲理論可以解決f scale太大的問題。軸子可以自然地與規範波色子
起交互作用，在這篇論文中，我們將考慮最簡單的情況，也就是與光子交互作用。在暴漲期間，我們會把光子當作隨機場,並且來影響暴漲子。
最後我們會發現，在暴漲期間，右手偏振光的效應會遠遠大於左手偏振
光。而我們在軸子暴漲模型中，自然地得到2-point correlator，以及3-point correlator。3-point correlator則會與non-Gaussianity效應有直接的關聯。也就是說軸子暴漲場理論可以自然地給出non-Gaussianity效應。

In this thesis, I will introduce the idea of inflationary Universe, and will give the
“Natural inflation model” as an example. This model has some disadvantages. The best known one is that the f scale is much larger than the Planck scale. But the “axion inflation model” can heal this problem. Axion can naturally interact with the gauge boson . In our case , we choose the most simple situation in which the gauge boson is the photon.We then consider the Electromagnetic field as a stochastic field, which affects inflaton. In our calculation, we discover that light with the right hand polarization can have more effect than the one with the left hand polarization during the inflation epoch. And we can naturally get 2-point correlators and 3-point correlators in the axion inflation model. 3-point correlators are related to non-Gaussianity. Therefore, axion inflation model can naturally supply non-Gaussianity effect.

簡介 ---------------------------------------------------------- 1
暴漲機制
2.1 宇宙學模型 ------------------------------------------------------- 6
2.2 宇宙常數項與de-Sitter宇宙 --------------------------------- 12
2.3 暴漲模型 --------------------------------------------------------- 14
2.4 在暴漲模型下的不均勻宇宙 -------------------------------- 21
2.5 自然暴漲模型 --------------------------------------------------- 27
Axion暴漲模型
3.1 in-in formalism --------------------------------------------------- 32
3.2 Axion model ------------------------------------------------------ 38
3.3 Photon in Axion Inflation model ------------------------------- 42
3.4 光子場的Green’s Function ------------------------------------ 51
3.5 光子場與φ場 ---------------------------------------------------54
3.6 Langevin equation與Non-Gaussianity ----------------------66
結論與未來工作-----------------------------------------77
參考文獻 -------------------------------------------------------------80

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