Gravitational Waves: Volume 2: Astrophysics and Cosmology

Contents
Preface to Volume 2
Part III: Astrophysical sources of gravitational waves
	10 Stellar collapse
		10.1 Historical Supernovae
		10.2 Properties of Supernovae
			10.2.1 SN classification
			10.2.2 Luminosities
			10.2.3 Rates
		10.3 The dynamics of core collapse
			10.3.1 Pre-SN evolution
			10.3.2 Core collapse and neutrino-driven delayed shock
			10.3.3 The remnant of the collapse
		10.4 GW production by self-gravitating fluids
			10.4.1 Energy–momentum tensor of a perfect fluid
			10.4.2 GW production from gravitating Newtonian fluids
			10.4.3 Quadrupole radiation from axisymmetric sources
		10.5 GWs from stellar collapse
			10.5.1 GWs from collapse and bounce of rotating cores
			10.5.2 GWs from bar-mode instabilities
			10.5.3 GWs from post-bounce convective instabilities
			10.5.4 GWs from anisotropic neutrino emission
			10.5.5 GWs from magneto-rotational core collapse
			10.5.6 GWs from fragmentation during collapse
		10.6 Complements: luminosity, color and metallicity of stars
		Further reading
	11 Neutron stars
		11.1 Observations of neutron stars
			11.1.1 The discovery of pulsars
			11.1.2 Pulsar spindown and the P − P˙ plane
			11.1.3 Millisecond pulsars
			11.1.4 Pulsar demography
			11.1.5 SGRs and magnetars
		11.2 GW emission from neutron stars
			11.2.1 NS normal modes
			11.2.2 The CFS instability
			11.2.3 GWs from post-merger NS remnants
			11.2.4 GWs from deformed rotating NS
		Further reading
	12 Black-hole perturbation theory
		12.1 Scalar perturbations
		12.2 Gravitational perturbations
			12.2.1 Zerilli tensor harmonics
			12.2.2 The Regge–Wheeler gauge
			12.2.3 Axial perturbations: Regge–Wheeler equation
			12.2.4 Polar perturbations: Zerilli equation
			12.2.5 Boundary conditions
			12.2.6 The radiation field in the far zone
			12.2.7 Summary
		12.3 Black-hole quasi-normal modes
			12.3.1 General discussion
			12.3.2 QNMs from Laplace transform
			12.3.3 Power-law tails
			12.3.4 Frequency spectrum of QNMs
			12.3.5 The physical interpretation of the QNM spectrum
		12.4 Radial infall into a black hole
			12.4.1 The source term
			12.4.2 Numerical integration of the Zerilli equation
			12.4.3 Waveform and energy spectrum
		12.5 Perturbations of rotating black holes
			12.5.1 The Kerr metric
			12.5.2 Null tetrads and the Newman–Penrose formalism
			12.5.3 Teukolsky equation and QNMs of rotating BHs
		12.6 Solved problems
		12.1 Derivation of the Zerilli equation
		12.2 The source term for radial infall
		Further reading
	13 Properties of dynamical space-times
		13.1 The 3+1 decomposition of space-time
		13.2 Boundary terms in the gravitational action
		13.3 Hamiltonian formulation of GR
		13.4 Conserved quantities for isolated systems
		13.5 GWs and Newman–Penrose scalar
		Further reading
	14 GWs from compact binaries. Theory
		14.1 Non-perturbative resummations. A simple example
		14.2 Effective one-body action
			14.2.1 Equivalence to a one-body problem
			14.2.2 Conservative dynamics
			14.2.3 Inclusion of radiation reaction
			14.2.4 The EOB waveform
			14.2.5 Spinning binaries
		14.3 Numerical relativity
			14.3.1 Numerical integration of Einstein equations
			14.3.2 Equal-mass non-spinning BH binaries
			14.3.3 Unequal-mass non-spinning BH binaries
			14.3.4 Final BH recoil
			14.3.5 Spinning BHs and superkicks
			14.3.6 Astrophysical consequences of BH recoil
		14.4 GWs from NS–NS binaries
			14.4.1 Inspiral phase and tidal effects
			14.4.2 Merger phase and numerical relativity
		Further reading
	15 GWs from compact binaries. Observations
		15.1 GW150914. The first direct detection
			15.1.1 Evaluation of the statistical significance
			15.1.2 Properties of GW150914
		15.2 Further BH–BH detections
			15.2.1 GW151226
			15.2.2 GW170104
			15.2.3 GW170608
			15.2.4 GW170814: the first three-detector observation
			15.2.5 The population of BH–BH binaries
		15.3 GW170817: the first NS–NS binary
			15.3.1 GW observation
			15.3.2 The prompt γ-ray burst
			15.3.3 The electromagnetic counterpart
			15.3.4 Kilonovae and r-process nucleosynthesis
			15.3.5 The cocoon scenario
		15.4 Tests of fundamental physics
			15.4.1 BH quasi-normal modes
			15.4.2 Tests of post-Newtonian gravity
			15.4.3 Propagation and degrees of freedom of GWs
		Further reading
	16 Supermassive black holes
		16.1 The central supermassive black hole in our Galaxy
		16.2 Supermassive black-hole binaries
			16.2.1 Formation and evolution of SMBH binaries
			16.2.2 SMBH binaries at LISA
		16.3 Extreme mass ratio inspirals
			16.3.1 Formation mechanisms
			16.3.2 EMRIs at LISA
			16.3.3 Waveforms and the self-force approach
		16.4 Stochastic GWs from SMBH binaries
			16.4.1 Regime dominated by GW back-reaction
			16.4.2 Regime dominated by three-body interactions
			16.4.3 High-frequency regime and source discreteness
			16.4.4 Estimates of the SMBH merger rate
			16.4.5 Effect of the eccentricity
		Further reading
Part IV: Cosmology and gravitational waves
	17 Basics of FRW cosmology
		17.1 The FRW metric
			17.1.1 Comoving and physical coordinates
			17.1.2 Comoving and physical momenta
		17.2 Cosmological background equations for a single fluid
		17.3 Multi-component fluids
		17.4 RD–MD equilibrium, recombination and decoupling
		17.5 Effective number of relativistic species
		17.6 Conformal time and particle horizon
			17.6.1 Radiation dominance
			17.6.2 Matter dominance
			17.6.3 Analytic formulas in RD+MD
			17.6.4 Λ dominance
			17.6.5 Conformal time at significant epochs
			17.6.6 Comoving distance, angular diameter distance and luminosity distance
		17.7 Newtonian cosmology inside the horizon
			17.7.1 Newtonian dynamics in expanding backgrounds
			17.7.2 Newtonian fluid dynamics in an expanding Universe
		Further reading
	18 Helicity decomposition of metric perturbations
		18.1 Perturbations around flat space
			18.1.1 Helicity decomposition
			18.1.2 Radiative and non-radiative degrees of freedom
		18.2 Gauge invariance and helicity decomposition in FRW
			18.2.1 Linearized diffeomorphisms and gauge invariance in a curved background
			18.2.2 Bardeen variables
		18.3 Perturbed energy–momentum tensor
			18.3.1 General decomposition of Tµ
			18.3.2 Perturbations of perfect fluids
			18.3.3 Linearized energy–momentum conservation
			18.3.4 Gauge-invariant combinations
		Further reading
	19 Evolution of cosmological perturbations
		19.1 Evolution equations in the scalar sector
		19.2 Initial conditions
			19.2.1 Adiabatic and isocurvature perturbations
			19.2.2 The variables ζ and R
		19.3 Solutions of the equations for scalar perturbations
			19.3.1 Numerical integration
			19.3.2 Analytic solutions in RD
			19.3.3 Analytic solutions in MD
			19.3.4 Analytic solutions during dark-energy dominance
		19.4 Power spectra for scalar perturbations
			19.4.1 Definitions and conventions
			19.4.2 The primordial power spectrum
			19.4.3 Transfer function and growth rate
			19.4.4 The linearly processed power spectrum
		19.5 Tensor perturbations
			19.5.1 Cosmological evolution
			19.5.2 Transfer function for tensor modes
			19.5.3 GW damping from neutrino free-streaming
			19.5.4 The tensor power spectrum, Ωgw(f ) and hc(f )
		19.6 Standard sirens, dark energy and modified gravity
			19.6.1 Testing cosmological models against observations
			19.6.2 Cosmology with standard sirens
			19.6.3 Tensor perturbations in modified gravity
			19.6.4 An explicit example: non-local gravity
		Further reading
	20 The imprint of GWs on the CMB
		20.1 The CMB multipoles
		20.2 Null geodesics
		20.3 Temperature anisotropies at large angles
			20.3.1 Photon geodesics in a perturbed FRW metric
			20.3.2 Sachs–Wolfe, ISW and Doppler contributions
			20.3.3 Expression of the Cl in terms of the Θl(k)
			20.3.4 Scalar contribution to the Cl
			20.3.5 Tensor contribution to the Cl
			20.3.6 Finite thickness of the LSS
			20.3.7 The Boltzmann equation for photons
		20.4 CMB polarization
			20.4.1 Stokes parameters
			20.4.2 Polarization maps. E and B modes
			20.4.3 Polarization and tensor spherical harmonics
			20.4.4 Generation of CMB polarization
			20.4.5 Experimental situation
		Further reading
	21 Inflation and primordial perturbations
		21.1 Inflationary cosmology
			21.1.1 The flatness problem
			21.1.2 The horizon problem
			21.1.3 Single-field slow-roll inflation
			21.1.4 Large-field and small-field inflation
			21.1.5 Starobinsky model
		21.2 Quantum fields in curved space
			21.2.1 Field quantization in curved space
			21.2.2 Quantum fields in a FRW background
			21.2.3 Vacuum fluctuations in de Sitter inflation
		21.3 Primordial perturbations in single-field slow-roll inflation
			21.3.1 Mukhanov–Sasaki equation
			21.3.2 Scalar perturbations to lowest order in slowroll
			21.3.3 Scalar perturbations to first order. Spectral tilt
			21.3.4 Tensor perturbations
			21.3.5 Predictions from a sample of inflationary models
			21.3.6 The relic inflationary GW background today
			21.3.7 A full quantum computation of Ωgw(f )
		Further reading
	22 Stochastic backgrounds of cosmological origin
		22.1 Characteristic frequency of relic GWs
		22.2 GW production by classical fields
			22.2.1 General formalism
			22.2.2 GW generation by a stochastic scalar field
		22.3 GWs from preheating after inflation
			22.3.1 Parametric resonance in single-field inflation
			22.3.2 Tachyonic preheating in hybrid inflation
		22.4 GWs from first-order phase transitions
			22.4.1 Crossovers and phase transitions
			22.4.2 First-order phase transitions in cosmology
			22.4.3 Thermal tunneling theory
			22.4.4 Bubble dynamics and GW production
		22.5 Cosmic strings
			22.5.1 Global and local strings
			22.5.2 Effective description and Nambu–Goto action
			22.5.3 String dynamics. Cusps and kinks
			22.5.4 Gravitational radiation from cosmic strings
		22.6 Alternatives to inflation
		22.7 Bounds on primordial GW backgrounds
			22.7.1 The nucleosynthesis bound
			22.7.2 Bounds on extra radiation from the CMB
			22.7.3 Bounds from the CMB at large angles
			22.7.4 Limits on stochastic backgrounds from interfer- ometers
		Further reading
	23 Stochastic backgrounds and pulsar timing arrays
		23.1 GW effect on the timing of a single pulsar
		23.2 Response to a continuous signal
		23.3 Response to a stochastic GW background
		23.4 Extracting the GW signal from noise
		23.5 Searches for stochastic backgrounds with PTAs
		Further reading
Bibliography
Index