軸子是一種假想的贗標量粒子，最初提出的動機是為了解決強作用力的CP問題，而現在已被視為具有前途的暗物質候選者。QCD軸子和類軸子粒子都有可能通過引力互相吸引和自身的相互作用在早期宇宙中形成一種稱作軸子星的緊緻天體。在這項研究中，我們研究由軸子星的引力和軸子-光子耦合效應所引起的銀河系外快速電波爆發的透鏡現象，而後者的效應在過去的文獻中尚未被考慮。我們計算被位於銀河系外和銀河系中的軸子星透鏡化的快速電波爆發的光學深度。根據尚未觀察到被透鏡化的快速電波爆發信號，我們對軸子的參數如質量、衰變常數、軸子-光子耦合常數與軸子對暗物質比例進行了約束。

Axions are hypothetical pseudoscalar particles that were originally proposed to resolve the strong $CP$ problem and have been viewed as promising dark matter candidates. Both QCD axions and axion-like particles have the potential to form an astrophysical compact star called axion star through gravitational attraction and self-interaction in the early universe. In this work, we study the lensing of fast radio bursts (FRBs) induced by gravity and axion-photon coupling effects from the axion stars, while the latter effect hasn't been considered in the past literature. We calculate the integrated optical depth of FRB being lensed by axion stars located in both extragalactic space and the Milky Way. From the null observational result of the lensed FRB signal, we have placed the constraints on axion parameters, such as mass, decay constant, axion-photon coupling constant, and its fraction to dark matter abundance.

Contents I
List of Tables III
List of Figures IV
1 Introduction 1
1.1 Dark Matter . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Axion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Fast Radio Burst . . . . . . . . . . . . . . . . . . . . . . 12
2 Gravitational Lensing 18
2.1 Point-Like Lens . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 Finite-Lens Size Effect . . . . . . . . . . . . . . . . . . . 24
2.3 Finite-Source Size Effect . . . . . . . . . . . . . . . . . . 27
3 Axion-Photon Coupling-Induced Bending Angle, Magnification and
Time Delay 30
4 Fast Radio Burst Lensing 34
5 Results 38
5.1 Case: QCD Axion . . . . . . . . . . . . . . . . . . . . . . . 38
5.2 Case: ALP . . . . . . . . . . . . . . . . . . . . . . . . . . 41
6 Conclusion 49
Bibliography 51

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