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