Title Page
Abstract
Contents
Chapter 1. Introduction 16
1.1. Brief review of cosmology 16
1.2. Gravity in cosmology 20
1.3. Dissertation objective 21
Chapter 2. Background knowledge: gravitational wave, gravitational lensing, and inflation 23
2.1. Gravitational waves 23
2.1.1. Ripples in spacetime 24
2.1.2. Gravitational waves from binary merger 26
2.1.3. Observable of gravitational wave detection 29
2.2. Gravitational lensing 32
2.2.1. Wave propagation in weakly curved spacetime 33
2.2.2. Thin lens approximation 35
2.2.3. Geometrical optics limit 38
2.2.4. Application to point mass lens 40
2.3. Inflation 43
2.3.1. FRW universe 44
2.3.2. The flatness and the horizon problem 45
2.3.3. The solution: inflation 47
2.3.4. Giving perturbations to FRW universe 48
2.3.5. Quantum theory of perturbations in inflation 52
2.3.6. Evolution of perturbation and horizon crossing 55
2.3.7. Classical universe from quantum fluctuation 57
2.3.8. Stochastic description of light scalar fields in inflation 65
Chapter 3. Probing Cosmic Strings with Gravitational-Wave Fringe 71
3.1. Introduction 72
3.2. Lensing fringe from cosmic strings 73
3.2.1. Straight strings 73
3.2.2. Loops 77
3.3. Lensing detection estimation 79
3.3.1. Detection criteria 79
3.3.2. Leading-order waveforms 81
3.4. Prospects at future detectors 83
3.5. Discussion 85
3.5.1. Distinction from point-mass fringes 85
3.5.2. Prospect comparison with lensing of light 86
3.5.3. Robustness against astrophysical uncertainties 87
3.6. Conclusion 88
Appendix 89
3.A. More on - ln L and relative likelihood 89
3.B. Detection rate calculation 90
3.C. Detection rate for each mass bins 92
Chapter 4. Gamma-ray burst lensing parallax: Closing the primordial black hole dark matter mass window 94
4.1. Introduction 95
4.2. Lensing Parallax 95
4.3. GRB Parameters 98
4.4. GRB Results 99
4.4.1. Nearby-Stars Results 101
4.5. Discussion 102
Appendix 102
4.A. Useful numbers and formulas 102
4.B. Finite source-size effect 103
4.C. Computing optical depth and constraints 104
4.D. Effects of PBH clustering 105
4.E. GRB source parameter distribution 106
Chapter 5. Constraining the gravitational coupling of axion dark matter at LIGO 111
5.1. Introduction 112
5.2. Overview 114
5.3. Propagation through coherent axions 115
5.3.1. Coupled wave equations 115
5.3.2. Solution for finite propagation 117
5.4. Signal 119
5.4.1. Signal 1: Resonance with finite coherence 119
5.4.2. Signal 2: Explosion 121
5.4.3. Modeling an axion halo with multiple coherent patches 122
5.4.4. Summing effects from multiple patches 123
5.5. LIGO bounds and prospects 125
5.5.1. Detection criteria 125
5.5.2. Results 126
5.5.3. Time-delay of a resonance from dispersion 128
5.5.4. Similar bounds on the axion-photon coupling 129
5.6. Discussions 130
5.6.1. Energy conservation and axion backreaction 130
5.6.2. Stimulated axion decay rate 130
5.6.3. Effective 'graviton' mass 131
5.6.4. Axions in the source galaxy and intergalactic region 131
5.7. Corollary: Absence of parity-violation observables on the chirping GW 132
5.8. Conclusions 133
Appendix 135
5.A. Solving wave equation through the Mathieu equation 135
5.B. Sketch for the axion search in the frequency-time plane 139
Chapter 6. Hubble selection of the weak scale from QCD quantum critical point 143
6.1. Introduction 144
6.2. Model 145
6.3. QCD quantum critical points 147
6.4. Hubble selection 149
6.5. The weak scale criticality 152
6.6. Discussion 155
Appendix 156
6.A. Quantum critical points of LSM 156
6.B. Quantum regimes 158
6.C. Numerical calculation of the equilibrium distribution 162
Chapter 7. PBH Formation from Overdensities in Delayed Vacuum Transitions 164
7.1. Introduction 165
7.2. First-order Phase Transition 166
7.3. PBH Formation Mechanism 168
7.3.1. Formation criterion 169
7.3.2. Formation probability 170
7.3.3. Comparison with 2106.05637 173
7.4. PBH Abundance Calculation 174
7.4.1. Numerical setup 174
7.4.2. Semi-quantitative analysis on PBH formation probability 177
7.5. Discussion 179
Appendix 180
7.A. Consistency check for completion of FOPT 180
Chapter 8. Conclusion 186
Bibliography 189
초록 219
Table 1.1. Corresponding papers of the chapters. 22
Table 4.1. Benchmarks for GRB lensing-parallax detection. Fractional brightness resolution є, the highest frequency used in our analysis, number of GRB... 100
Table 6.1. Predictions of the benchmark SM point [Eq. (6.6) and (6.7)], compared with data from the Particle Data Group [195]. In units of MeV. 147
Table 7.1. FOPT parameters for models A (PBH mass window), B (HSC), and C (OGLE) in Fig. 7.5. Γ₀ and β are for equation (7.2) with t*=tcri, and β/H and...[이미지참조] 174
Figure 3.1. GW fringes from cosmic-string lensing in the frequency domain. The benchmark GW is from 30 M⊙-30M⊙ binary at 400 Mpc of luminosity...[이미지참조] 75
Figure 3.2. Expected detection rates of the GW fringe from cosmic strings at aLIGO, ET, AI, and BBO. The former two are high-frequency LIGO-band... 82
Figure 3.3. The comoving coordinate system and the placement of a cosmic string used for lensing detection calculation. The hatched region indicates the... 91
Figure 3.4. Detection rate of the GW fringe with four aLIGOs (left) and one ET (right) in each binary mass bin. Several values of string tensions △=8 πGµ=... 93
Figure 4.1. Expected 95% CL upper limits on the PBH abundance, f, from lensing parallaxes of GRBs (red) and stars (blue). The (a) upper and (b) lower... 108
Figure 4.2. Optical depth τ for the lensing parallax of GRBs(red) at zS=2 and stars(blue) at 75 kpc. The inset shows the zS-dependence for M=10⁻¹²M⊙ as...[이미지참조] 109
Figure 4.3. Single lensing probability P₁ for selected values of RH (equivalently, τH); the smaller the halo size RH of the given mass MH=10¹²M⊙, the higher...[이미지참조] 109
Figure 4.4. Histograms of (a) redshift (upper panel) and (b) transverse size (lower panel) of observed GRBs that we use. Using a total of 2105 observed... 110
Figure 5.1. An example axion signal in the chirping GW spectrum. The sharp peak is at the resonance frequency f₀=50 Hz of the stimulated decay of axions... 120
Figure 5.2. The expected upper limit on the axion Chern-Simons coupling ℓ, assuming the absence of resonance peaks in the GW observations at... 127
Figure 5.3. The contours (solid) of the arrival-time delay of a resonance peak with respect to the chirping part, induced from the propagation through a 100... 129
Figure 5.4. Example spectrograms (normalized amplitudes) of axion signals in association with chirping GWs, for the resonance frequency 50 Hz (upper) and... 142
Figure 6.1. Vacuum energies of benchmark coexisting QCD vacua at T=0, as functions of vh. The critical point is at vh* ≃ 20MeV, with a ΛQCD-scale energy difference.[이미지참조] 150
Figure 6.2. Top: Total potential energy near the critical point as a function of φ, for the benchmark Eq. (6.18); dashed line for comparison. Inset: Zoom-in near... 153
Figure 6.3. The probability distribution of vh among Hubble patches that have reached reheating. σvh ≃ 0.1 MeV ≪vh* for the benchmark Eq. (6.18); dashed...[이미지참조] 154
Figure 6.4. (Top): Quantum critical point vh* in the Nf=3 LSM. Other parameters are fixed to benchmark values; scale factors are relative to the...[이미지참조] 157
Figure 6.5. Effects of the boundary at φ₀=0 on the volume-weighted distribution ρ(φ). For several choices of σφ with fixed △φ=100 in the solution Eq. (6.31)...[이미지참조] 161
Figure 7.1. Wall cone diagram for PBH formation. A nucleation in either the horizon volume (red) or the causative past wall cone (blue) would trigger the... 170
Figure 7.2. The underlying spacetime diagram for Ref. with the missing wall cones, which should have been somewhere between the solid and... 173
Figure 7.3. The average radiation density ρR(t), average FV energy density ρv, and average total density ρ(t) as a function of time. ρfv (t) is the local density of...[이미지참조] 176
Figure 7.4. Top: The transition probability p(t) for a Hubble volume as a function of time in Model A. Transitions in the shaded region can only form... 184
Figure 7.5. The PBH mass function f PBH(M). The excluded regions by existing bounds are shown by the shaded regions. H₀=67.66 km/s/Mpc and ΩDM=...[이미지참조] 185
Figure 7.6. The normalized FV volume of a FV region at t₁.₄₅, simplified to be a separated de Sitter universe. Black: the FV volume fraction, equivalent to... 185