Gravitational Waves from a Quantum Field Theory Perspective

Description

Preface Contents Units and Acronyms 1 Introduction 1.1 Overview References 2 Prologue: Gravitational Waves in Classical General Relativity 2.1 General Relativity 2.2 Linearised Gravity 2.3 Gravitational Waves in Minkowski Background 2.4 Interaction of Gravitational Waves with Test Masses 2.5 Polarisations of Gravitons in Theories Beyond Einstein's Gravity 2.6 Generation of Gravitational Waves 2.7 Energy Flux of Gravitational Waves 2.8 Waveforms from Compact Binaries 2.9 Energy Radiated by Compact Binary Stars 2.10 Chirp Signal of Coalescing Binaries 2.11 Post-newtonian Corrections to Binary Orbit 2.12 Gravitational Waveform from Sources at Cosmological Distances References 3 Field Theory of Linearised Gravity 3.1 Field Theory of Linearised Gravity 3.2 Graviton–Matter Coupling 3.3 Gauge Invariance and Conservation of Stress Tensor 3.4 Newtonian Gravity 3.5 Non-relativistic Effective Theory of Gravity: NRGR 3.6 First Post-newtonian Correction: Einstein–Infeld–Hoffmann Action 3.7 Potentials and Waves 3.8 Quantum Gravity Corrections to Newtonian Potential 3.9 Massive Gravity Theories 3.10 Bending of Light 3.11 Eikonal Method 3.12 Gravitational Waveform from Scattering Amplitude 3.13 Gravitational Radiation: Fermi's Golden Rule 3.14 Gravitational Radiation: Imaginary Part of Second Order Action References 4 Gravitational Wave Radiation from Compact Binaries 4.1 Introduction 4.2 Gravitational Wave Radiation by Binaries in Circular Orbit 4.3 Gravitational Wave Radiation from Compact Binary Stars in Elliptical Orbits 4.4 Waveforms of Elliptical Orbit Binaries 4.5 Gravitational Radiation from Binaries in the Non-relativistic Effective Theory 4.6 Multipole Expansion 4.7 Radiation of Ultralight-Scalars from Binary Stars 4.8 Vector Boson Radiation by Neutron Star Binaries 4.9 Gravitational Waveforms from Coalescing Binaries 4.10 Gravitational Waves from Hyperbolic Orbits 4.11 Waveform of Gravitational Waves from Hyperbolic Encounters 4.12 Memory Effect in Hyperbolic Orbits References 5 Gravitational Memory and Soft-Graviton Theorem 5.1 Introduction 5.2 Soft-Graviton Amplitudes 5.3 Soft-Graviton Amplitudes in the NLO 5.4 Memory Effect from Soft-Graviton Amplitudes 5.5 Gravitational Energy Radiated in Particle Collisions 5.5.1 Graviton Emission from Non-relativistic Particle Scattering 5.5.2 Graviton Emission from Massless Particle Collisions 5.6 Gravitational Wave from Sudden Impulse 5.7 Gravitational Waves from Relativistic Bremsstrahlung 5.8 Non-linear Memory 5.9 Non-linear Memory from Binary Orbits 5.10 Gravitational Wave Signal from Supernova Neutrino Burst References 6 Backreaction and Dissipation: The In-In Formalism 6.1 Introduction 6.2 Radiation Reaction in the In-Out Formalism 6.3 Propagators 6.4 Lagrangian Dynamics of Dissipative Systems 6.5 Path Integral: In-Out Formalism 6.6 Closed Time Path (CTP) Formulation 6.7 The Keldysh Representation 6.8 Gravitational Waves in Keldysh Formulation 6.9 Dissipative Force from Backreaction of Gravitational Radiation 6.10 Thermal Bath 6.11 Non-equilibrium Propagators in a Thermal Bath References 7 Gravitational Waves from Blackhole Quasi-Normal Mode Oscillations 7.1 Introduction 7.2 Wave Equation in Spherically Symmetric Blackhole Background 7.3 Regge-Wheeler and Zerilli Equations 7.4 Isospectral Property of Odd and Even Perturbation Equations 7.5 Quasi-Normal Modes: Eikonal Calculation 7.6 Gravitational Waves from Quasi-Normal Oscillations 7.7 Quasi-Normal Frequencies of Kerr Blackholes 7.8 Greens Functions and Late Time Tails 7.9 Testing Blackhole No Hair Theorems 7.10 Traversable Wormholes 7.11 Quasi-Normal Modes of Wormholes References 8 Gravitational Radiation from Spin Dynamics in Binary Orbits 8.1 Dynamics of Spinning Bodies in General Relativity 8.2 Binary System of Spinning Black Holes 8.3 Signature of Black Hole Spins in Gravitational Wave Events References 9 Refractive Index and Damping of Gravitational Waves in a Medium 9.1 Introduction 9.2 Graviton Propagation in a Medium 9.3 Propagation of Gravitational Waves Through Perfect Fluid Medium 9.4 Propagation Through Dissipative Medium 9.5 Propagation Through Scalar Field Dark Matter 9.6 Modified Gravity Theories 9.7 Čerenkov Radiation of Gravitational Waves 9.8 Gravitational Radiation in a Background of Gravitons: Stimulated Emission 9.9 The Thermal Background of Gravitons 9.10 Ensemble of Binaries in Thermal Graviton Background 9.11 Einstein's A and B Coefficients for an Ensemble of Binary Stars in Thermal Graviton Background 9.12 Absorption of Gravitational Waves by Bound State Systems 9.12.1 Absorption of Gravitational Waves by Compact Binaries 9.12.2 Absorption of Gravitational Waves by Scalar Cloud Around Blackholes References 10 Stochastic Gravitational Waves 10.1 Introduction 10.2 Gravitational Waves from Extended Sources 10.3 Energy Density of Gravitational Waves from Extended Sources 10.4 Symmetry Breaking and Topological Defects 10.5 Domain Walls 10.6 Cosmological Evolution of Domain Walls 10.7 Gravitational Waves from Domain Wall Annihilation 10.8 Gravitational Radiation from Cosmic Strings References 11 Inflation 11.1 Inflation 11.2 Perturbations of de-Sitter background 11.3 Curvature Perturbation During Inflation 11.4 Power Spectrum of Curvature Perturbation 11.5 Quantum Fluctuations of the Inflaton 11.6 Scalar Power Spectrum 11.7 Tensor Power Spectrum 11.8 Tensor-to-Scalar Ratio and Energy Scale of Inflation 11.9 Inflationary Observables in CMB 11.10 Stochastic Gravity Waves from Inflation 11.11 The In-in Formalism for Evaluating Cosmological Correlators 11.12 Non-Gaussianity in the In-in Formalism 11.13 Schwinger-Keldysh Treatment of Cosmological Correlations 11.14 Tensor Propagators in de-Sitter Space 11.15 Enhancement of Inflation Power Spectrum by Thermal Background 11.16 Second Order Gravitational Waves from Scalar Perturbations 11.17 Gravitational Wave from Pre-Heating References Index