Hunting for primordial black holes with stochastic gravitational-wave background ; 用引力波隨機背景探索原初黑洞 ; Yong yin li bo sui ji bei jing tan suo yuan chu hei dong

Ph.D. ; The direct detection of gravitational waves has ushered in a new era of observational astronomy. It has opened a unique window to investigate astrophysics and probe some of the most mysterious matter in the Universe such as dark matter. This thesis is focused on hunting for primordial black holes, a candidate for dark matter, with a stochastic background of gravitational waves. ; In Chapter 1, we briefly review the basic aspects of the gravitational-wave astronomy, including the Einstein field equation, gravitational wave as a perturbative solution, and the data analysis techniques for gravitational waves from binary compact objects such as black holes or neutron stars. This chapter lays the foundation for the rest of the thesis. ; Chapter 2 is dedicated to an overview of stochastic gravitational-wave background. Besides the gravitational-wave transient signals which are strong enough to be detectable individually, there exist numerous sub-threshold gravitational waves in the Universe whose incoherent superposition forms a stochastic background. The mathematical characteristics and the cross-correlation data analysis techniques are reviewed. ; In Chapter 3 we discuss an original work which derives the stochastic background energy density spectrum from the coalescence of primordial black holes, which is generated by the direct collapse from the quantum fluctuations of the early Universe. Using the current upper limit on stochastic background measured by LIGO and Virgo collaboration, we constrain the abundance of primordial black hole with 1 to 100 solar mass. The stochastic background has given the most stringent upper limit on abundance in this mass range compared with other electromagnetic observations such as microlensing. ; Chapter 4 is another original work investigating the stochastic background ii from extreme mass-ratio inspiral systems including a primordial black hole and a massive black hole at the galactic center using the space-based gravitational-wave detector. We model the event rate based ...