Gravitational Waves from a Quantum Field Theory Perspective

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