暴脹磁場與太初黑洞的形成

Abstract

本論文探索太初磁場與太初黑洞在宇宙暴脹中形成的機制。我們首先利用軸子與光子的耦合，並計入暴脹前的快滾階段，因而在宇宙暴脹下成功製造出可延續至今的大尺度種子磁場，但卻發現過程中存在著能量守恆的限制。於是，我們在軸子與伸縮子雙重驅動的暴脹電磁場中，成功找到可滿足各項物理條件限制的太初磁場解。 然後，我們將來自於規範場中粒子的反饋作用納入計算，透過適當的數值方法計算暴脹場和光子耦合的模態微分方程後，發現在接近暴脹結束前所產生的能量密度峰值，可能會導致太初黑洞的形成。接著，我們在單一位能項與正弦波疊加的組合位能中，試著分析由超普朗克軸子場所驅動的宇宙暴脹。我們發現在軸子單延拓暴脹模型裡，適當的軸子-規範場耦合確實能夠產生質量範圍在10^8公克到10太陽質量的太初磁場。我們也研究了模型中所產生的重力波強度與脈衝星計時陣列和干涉儀實驗的關聯。We first discuss the generation of primordial magnetic fields during inflation by a simple axion-photon coupling with a fast-roll stage. Though a large enough coherent magnetic seed field could be produced, there exists an energy budget barrier. We then explore the inflationary dilaton-axion magnetogenesis and find plausible solutions to resolve the energy budget problem. We also consider the backreaction from the particle production of gauge fields during inflation era. By solving the coupled differential equations of motion numerically, we obtain proper mode functions for both the inflaton and photons. The energy density peaks produced near the end of inflation may lead to the formation of primordial black holes. We consider driving the inflation by the axion with super-Planckian field values in a monomial potential with superimposed sinusoidal modulations. In the axion monodromy inflation model, the axion-gauge field coupling constant favors the formation of primordial black holes with masses ranging from 10^8 grams to 10 solar masses. We also study the associated gravitational waves and their detection in pulsar timing arrays and interferometry experiments.