從早期宇宙到晚期宇宙與粒子物理的關聯

Abstract

本論文主要將討論粒子物理與宇宙中兩個加速膨脹時期的關聯:第一為早期 宇宙中的暴漲模型，第二是晚期宇宙的暗能量模型。關於暴漲模型，我們知道暴 漲理論為現今宇宙物理學一個重要的假說，儘管尚未被觀測所證實，但因暴漲理 論可以良好地解釋一些大爆炸理論未能解釋的宇宙學現象，因此普遍被宇宙學家 所接受。然而暴漲理論本身的來源至今仍未有定論。偉恩伯格博士於1979 年提 出之漸進安全重力論，該理論認為重力常數跟宇宙常數可能並非常數，而會隨能 量尺度改變而改變的參數，藉由量子場論中重整群的技巧，重力常數等參數將在 高能量時流動到一個固定點，如此一來可以避免量子重力理論所遭遇到在高能量 時發散產生奇異點的問題。等效地來說，漸進重力論是一個高能量完備且可重整 的重力理論。該理論將誘導出一個新的純量場，我們考慮將此純量場作為引發暴 漲的暴漲子，並同時考慮有希格子存在效應下所引發之雙場暴漲模型的物理，包 含宇宙學背景演化、膨脹規模、以及暴漲退場進入輻射支配時期的機制。我們認 為此暴漲子在暴漲末期將衰變成其他粒子，其衰變率由希格子的場值所控制，衰 變結束後，牛頓重力常數及宇宙常數將回歸到符合觀測的觀測值。此外我們也研究此雙場模型的非線性量子起伏所產生的太初曲率微擾之頻譜與非高斯項，並且 與近期普朗克衛星所發表的資料做比較。雖然觀測資料限制了本模型的參數空間， 但本模型仍然提供了一個可能的關於粒子物理與宇宙學暴漲理論的有趣連結。 關於暗能量部份，暗能量主要是解釋我們所觀測到晚期宇宙的加速膨脹現象。 與暴漲理論類似，暗能量的來源至今未有定論。本論文將討論一個可能的解釋暗 能量來源的模型。我們考慮一個非表準模型的旋量場，稱做ELKO 旋量場或暗旋 量場，該旋量場為2005 年Dr. Ahluwalia-Khalilova 和Dr. Grumiller 所提出。 不同於狄拉克旋量場，暗旋量場可以與撓場有更多交互作用，該交互作用即可能 是暗能量的來源。我們考慮暗旋量場在愛因斯坦-卡當重力底下與撓場的交互作 用，並研究其宇宙學演化。儘管假設該場的動能項具有幻能量的形式，我們發現 該模型並不像其他幻能量模型一樣遭遇到各種暗能量奇異點的問題。此模型並且 滿足能量條件定理，因此在量子層面也是穩定的。而我們的研究顯示最終擾場將消失，宇宙將進入德希特宇宙時期。 為求完整性，本論文將儘可能介紹所用到的宇宙學知識，從廣義相對論開始， 接著暴漲理論的基本知識、宇宙學微擾、非高斯性、漸進安全重力論、漸進安全 重力所引發的暴漲模型與普朗克衛星觀測資料的比較、愛因斯坦卡當重力論、暗 能量、暗旋量場及其暗能量模型與觀測之比較等等。最後我們將總結本論文並且 討論其未來相關的發展。

In this dissertation, we will study mainly two models, the first one is on inflation and second is on the dark energy. For the inationary model, we consider a model inspired on asymptotic safe gravity which can induce a scalar fi eld and we identify it as the inflaton. We also study the presence of another scalar eld which can be interpreted as the Higgs fi eld. We assume the reheating of the inflaton is controlled by the Higgs field. Firstly, we study the background trajectories of this model and it shows that our model may provide su fficient inflationary e-folds and a graceful exit to a radiation dominated phase. Then we study the possibility of generating primordial curvature perturbations through the Standard Model Higgs boson. This can be achieved under the choice of fi nely tuned parameters by making use of the modulated reheating mechanism. The primordial non-Gaussianity is expected to be sizable in this model. Though tightly constrained by the newly released Planck cosmic microwave background data, this model provides a potentially interesting connection between collider and early Universe physics. As for the dark energy, we consider a class of dynamical dark energy models which are constructed through an extended version of fermion fields called the Elko spinors, which are spin one half with mass dimension one. We wonder that if the Elko spinor interacts with torsion fields in a homogeneous and isotropic universe, then we do not expect quantum instability in this kind of dark energy model even though the fermion possesses a negative kinetic energy. In other words, this dark energy model will asymptotically approach the equation of state w = 1 from above without crossing the phantom divide. Therefore, the stability is preserved, i.e. no phantom fi eld will be created. Furthermore, we analyze as well the presence of some pressureless cold dark matter, and the result is unchanged, in this two components system. At late time, the torsion fi elds will vanish as the Elko spinors dilute, the equation of state will still converge to w = 1 and the Hubble parameter will approach a constant, the universe will eventually enter a de Sitter phase with or without the presence of this dark matter. To make it as self-contained as possible, this dissertation will contain the essential knowledge and relative important issues about these two models, including the general relativity, Einstein-Cartan theory, the cosmological inflation, the cosmological perturbations, the asymptotic safe gravity, the Higgs-modulated inflation model, the dark energy in cosmology, the Elko spinors, the dark energy of phantom dark spinor with torsion. Finally, we will briefly conclude this dissertation and discuss their future perspectives.