Table of Contents
Preface v
Acknowledgments vii
Introduction 1
1 Superfluidity and the order parameter 5
1.1 Bose-Einstein condensation 5
1.2 The order parameter 8
1.3 Spontaneous symmetry breaking 10
1.4 Quantized vorticity 12
1.5 Superconductivity 15
1.6 Higgs mechanism 17
2 Quantum turbulence 19
2.1 Vortex dynamics 19
2.2 Vortex reconnections 23
2.3 The vortex tangle: quantum turbulence 25
2.4 Vinen's equation 28
2.5 String theory of relativistic quantized vorticity 29
3 Higgs 35
3.1 Why Higgs 35
3.2 The vorticon 37
3.3 The Higgs field as order parameter 39
3.4 Relativistic superfluidity 41
3.5 Persistence of long-ranged order 41
3.6 Non-relativistic limit 43
4 Renormalization 45
4.1 Virtual processes in quantum field theory 45
4.2 Wilson's theory of renormalization 46
4.3 RG trajectories 48
4.4 Fixed points 48
4.5 Asymptotic freedom 49
4.6 Triviality 49
4.7 Polchinski's equation 51
5 Halpern-Huang scalar field 55
5.1 The Gaussian fixed point 55
5.2 Eigenpotential 56
5.3 Asymptotic freedom 59
5.4 Superposition of eigenpotentials 60
6 The dynamics of spacetime 63
6.1 Spacetime curvature 63
6.2 Einstein's equation 64
6.3 Metrics 65
6.4 The expanding universe 66
6.5 Perfect-fluid cosmology 69
7 Black holes 73
7.1 The Schwarzschild radius 73
7.2 Oppenheimer-Snyder solution: inside 75
7.3 Oppenheimer-Snyder solution: outside 77
7.4 Rotating black holes in a cosmic superfluid 78
8 The big bang 81
8.1 Scalar-field cosmology 81
8.2 There is only one scale 83
8.3 Initial conditions 84
8.4 Numerical solutions 85
9 Creation of matter 89
9.1 Quantum turbulence creates all matter 89
9.2 Homogeneous vorticity 90
9.3 Vinen's equation 92
9.4 Cosmological equations with quantum turbulence 93
9.5 Decoupling 95
9.6 The inflation era 97
10 Dark energy and dark matter 101
10.1 Evidence of dark energy and dark matter 101
10.2 Galactic redshift 103
10.3 Galactic halo 105
11 Quantum vorticity in the universe 109
11.1 Voids in galactic distribution 109
11.2 Galaxy rotations 110
11.3 Galaxy formation 112
11.4 The CMB, ACDM, and DM 114
Epilogue 117
Index 119
