UJFG NATO ASI

LES HOUCHESSESSION LX

l-28Aoutl993

COSMOLOGIE ET STRUCTUREA GRANDE ECHELLE

COSMOLOGY ANDLARGE SCALE STRUCTURE

editepar

R. SCHAEFFER, J. SILK,M. SPIRO etJ. ZINN-JUSTIN

1996

ELSEVIERAmsterdam - Lausanne - New York - Oxford - Shannon - Tokyo

CONTENTS

Lecturers ix

Seminar Speakers xi

Participants xiii

Preface (French) xvii

Preface (English) xxi

Course 1. Standard Cosmological Models: Theory, byA. Blanchard 1

1. Introduction 51.1. The Olbers'paradox 61.2. Homogeneity 71.3. The Robertson—Walker element 8

2. Geometry and Dynamics 102.1. Geometry of four-dimensional space-time 102.2. Topology 102.3. Dynamics 112.4. Vacuum and the cosmological constant 12

3. Observations 133.1. Redshift 133.2. The proper distance 143.3. The angular distance 153.4. The luminosity distance 153.5. Distance along the line of sight • 15

4. Solutions 164.1. Case(A0 = 0,p = 0) 164.2. Case(A0 > 0 , p = 0) . 174.3. Radiation dominated case 18

5. The early universe 185.1. The primordial nucleosynthesis 19

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5.2. The cosmic background radiation 226. Conclusion 23References 24

Course 2. Observational Cosmology, byM. Rowan-Robinson

1. Introduction1.1. Contents of universe

1.1.1.1.1.1.1.1.1.1.

. 1. Our Galaxy

.2. Limitations our Galaxy imposes on cosmological observations

.3. Other galaxies

.4. Groups, clusters, walls and voids

.5. Intergalactic medium

.6. Radiation

.7. Neutrinos

.8. Dark matter

.9. Cosmic rays

.10. Gravitational radiation1.2. Observational evidence for Big Bang models.1.3. Brief outline of history of universe1.4. Summary of Friedmann models and cosmological parameters

1.4.1. Friedmann models1.4.2. Cosmological parameters1.4.3. Age of the universe1.4.4. Horizons

2. The distance scale and Ho2.1. Reviews of the distance scale and Ho2.2. The local distance scale2.3. Primary extragalactic distance indicators

2.3.1. Cepheid variable stars2.3.2. Supernovae2.3.3. Novae2.3.4. Tip of the red giant branch2.3.5. Gravitational lens time delay2.3.6. Sunyaev—Zeldovich effect

2.4. Secondary extragalactic distance indicators2.4.1. Tully—Fisher method for spirals2.4.2. Dn-o method for ellipticals2.4.3. Globular cluster luminosity function2.4.4. Planetary nebula luminosity function2.4.5. Surface brightness fluctuations2.4.6. Brightest red stars in galaxies

27

313131313232323333333334343435353536373737383838394041414142424243434343

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Contents

2.5. Summary of distances to Local Group galaxies, M81, Virgo 432.6. The Hubble constant, Ho 45

3. Age of the universe, to . 453.1. Nucleocosmochronology 453.2. Globular cluster ages 463.3. White dwarf luminosity function and age of the Galaxy 47

4. Density of the universe, fio 474.1. M/L + integrated light from galaxies 474.2. Primordial nucleosynthesis 484.3. Cosmic virial theorem 484.4. Large-scale flows 49

4.4.1. Using the peculiar velocity of the Local Group of galaxies 504.4.2. Using the peculiar velocities of field and cluster galaxies 514.4.3. Infall pattern to a single cluster 524.4.4. Issues and problems 524.4.5. Three-dimensional dipole from IRAS PSC to 0.6 Jy 54

4.5. The value of n 0 575. Cosmological constant, A 58

5.1. Some consequences of A > 0 585.2. Standard cosmological tests for (q, Cl) 585.3. Statistics of gravitational lenses 595.4. Statistics of quasar abosorption line systems 595.5. Summary on A 59

6. Implications of observed values of Ho, io, &o, 9o, A 597. Evolution of normal, active and starburst galaxies 60

7.1. Normal galaxies 607.2. Active galaxies 607.3. Starburst galaxies 617.4. Summary on evolution 62

8. High redshift galaxies and protogalaxies 628.1. Models for protogalaxies 628.2. Lyman a galaxies at high redshift 648.3. High redshift quasars 648.4. High redshift radio-galaxies 648.5. Lyman a clouds 658.6. IRAS F10214+4724 - protogalaxy? 66

References 67

Course 3. Baryonic Dark Matter, by J. Silk 75

1. Introduction 792. The evidence for baryonic dark matter 80

2.1. Primordial nucleosynthesis 80

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2.2. Evidence from rotation curves 812.3. Dark halos may be flattened 812.4. Continuity with population II 822.5. Gravitational microlensing experiments 83

3. The possible forms of baryonic dark matter 853.1. A star formation primer 85

3.1.1. Initial mass function 853.1.2. Star formation efficiency 883.1.3. Star formation rate 88

3.2. The primordial IMF 893.3. What could the (dark) matter be? 91

3.3.1. Brown dwarfs 923.3.2. Halo white dwarfs 933.3.3. Diffuse gas clouds 943.3.4. Exotica ' 96

4. Cosmogonic implications 974.1. Galaxy morphology 974.2. Large-scale structure 974.3. Primordial density fluctuation power spectrum 994.4. 6T/T on intermediate and small angular scales 1014.5. The Compton y constraint . 1024.6. A BDM scenario 103

5. Conclusions 103References 105

Course 4. Mapping the Large-Scale Structure, byV. de Lapparent 107

1. Introduction 1112. The nearby galaxy distribution 1123. Comparison of the data with the theoretical models 117

3.1. Theoretical framework for the formation of the large-scale structure 1173.2. Statistical characterization of the large-scale structure 119

4. Constraints from new surveys 1214.1. Wide-angle deep surveys 1214.2. Configuration of redshift surveys 1244.3. Ultra-deep pencil-beam probes 126

5. Conclusions and prospects 128References 129

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Course 5. Observations of Large-Scale Structure in theUniverse, by G. Efstathiou 133

1. Introduction 1372. The galaxy luminosity function 137

2.1. Background 1382.2. Estimating the luminosity function 140

3. Galaxy clustering in two dimensions 1483.1. Catalogues of galaxies 1483.2. The two-point correlation function 149

3.2.1. Definition 1493.2.2. Relationship of £(r) to the power spectrum 1503.2.3. The angular two-point correlation function 1513.2.4. Scaling of w(9) with depth 153

3.3. Results from the APM Galaxy Survey 1543.4. Some remarks on estimating correlation functions 163

4. Three-dimensional statistics from two-dimensional surveys 1684.1. Inversion of w(0) 1684.2. Inversion of the two-dimensional power spectrum P2 (A') 1714.3 • Comparison of power spectra with theoretical models 173

5. Three-dimensional statistics from redshift surveys 1785.1. A summary of some important redshift surveys 178

5.1.1. Pencil beam surveys 1795.1.2. Slices of the Universe 1805.1.3. Large-angle surveys 180

5.2. Counts-in-cells and high-order correlations 1815.3. Measuring the mean density in a flux-limited redshift survey 1835.4. Estimating £(s) from a redshift survey 1865.5. Counts-in-cells analysis of redshift surveys 1915.6. Power spectram measured from three-dimensional surveys 1975.7. Clustering in real space and redshift space 2065.8. Spherical-harmonic analysis of redshift surveys 213

6. Cluster-cluster and cluster—galaxy correlations 2166.1. Clustering of rich clusters of galaxies 2166.2. The cluster-galaxy cross-correlation function 225

7. Large-scale motions in the Universe 2277.1. Measurements of peculiar motions 2277.2. Analysis of bulk flows 2297.3. Velocity correlation function 2357.4. Computing velocities from density maps 2377.5. Computing density fields from velocity maps 2397.6. Cluster peculiar motions 242

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8. Future prospects 243References 246

Course 6. Statistical Aspects of the Large Scale GalaxyDistribution, by A.S. Szalay 253

1. Introduction 2572. Quantifying large scale structure 257

2.1. Key questions 2572.1.1. The fluctuation spectrum today: power on COBE scales 2592.1.2. Measuring the evolution of structure 2592.1.3. How non-Gaussian is the Universe today? 259

2.2. Measuring structure on 100-1000 h~l Mpc scales 2602.2.1. Problems in power spectrum estimation 2602.2.2. Cross-correlation power spectrum 2602.2.3. Eigenmode analysis of redshift surveys 261

2.3. Measuring evolution and clustering 2632.3.1. Photometric redshifts 2642.3.2. Galaxy colors and angular correlation functions 265

2.4. Practical applications of higher order correlations 2682.4.1. Effects of sparse sampling * 2682.4.2. Bayesian density reconstruction j 269

3. New surveys, new methods 270References 271

Course 7. Cosmological Dynamics, by E. Bertschinger 273

0. Preface 2771. Elementary mechanics 277

1.1. Newtonian dynamics in cosmology 2771.2. Lagrangian and Hamiltonian formulations 2821.3. Conservation of momentum and energy? 284

2. Eulerian fluid dynamics 2852.1. Cosmological fluid equations 2852.2. Linear instability 1: isentropic fluctuations and Jeans criterion 2882.3. Linear instability 2: entropy fluctuations and isocurvature mode 2912.4. Vorticity - or potential flow? 292

3. Hot dark matter 2943.1. Tremaine-Gunn bound 2953.2. Vlasov equation 2973.3. Nonrelativistic evolution in an external gravitational field 3003.4. Nonrelativistic evolution including self-gravity 304

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4. Relativistic cosmological perturbation theory 3054.1. Introduction 305

4.1.1. Synopsis 3064.1.2. Summary of essential relativity 307

4.2. Classification of metric perturbations 3104.3. Stress-energy tensor 3134.4. Synchronous gauge 3164.5. Gauge modes 3204.6. Poisson gauge 3234.7. Physical content of the Einstein equations 3264.8. Hamiltonian dynamics of particles 3294.9. Lagrangian field equations 335

References 345

Course 8. Formation and Evolution of Galaxies, byS.D.M. White 349

1. Introduction 3532. Gravitational dynamics 353

2.L Linear and quasilinear theory 3542.1.1. Linear fluctuation growth 3542.1.2. Lagrangian theory and the Zel'dovich approximation 3562.1.3. The origin of galactic spin 3582.1.4. Linear scaling laws 3602.1.5. Nonlinear scaling laws 363

2.2. Nonlinear models for gravitational collapse 3642.2.1. The spherical top-hat 3642.2.2. Similarity solutions for collapse 3652.2.3. Similarity solutions for voids 3682.2.4. The ellipsoidal top-hat 369

2.3. The statistics of hierarchical clustering 3732.3.1. The peaks formalism 3742.3.2. Press-Schechter theory 3752.3.3. The excursion set derivation of the P&S formula 3762.3.4. Progenitor distributions 3792.3.5. Merging histories 3842.3.6. Tests of the Press—Schechter formalism 386

2.4. Internal structure of clumps 3873. iV-body simulations 388

3.1. Solution of the iV-body equations 3893.2. Boundary conditions 3913.3. Initial conditions 3923.4. Hierarchical clustering in TV-body simulations 394

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4. Models for galaxy formation 3984.1. Cooling and the luminosity and structure of galaxies 400

. 1. Compton cooling 400

.2. Radiative cooling 401

.3. Cooling times for uniform clouds 402

.4. Derivation of a galaxy "luminosity function" 404

.5. Cooling in an isothermal halo 407

.6. Disk galaxy formation 408

.7. Mergers, disk disruption, and elliptical formation 4104.2. Galaxy formation through hierarchical clustering 411

4.2.1. The dark matter 4124.2.2. Supply of cold gas - 4134.2.3. Feedback and star formation 4144.2.4. Synthesizing a model 4154.2.5. The halo abundance in fi = 1 CDM 4164.2.6. Monte Carlo models for galaxy formation 418

5. Smoothed particle hydrodynamics (SPH) 421References 429

Course 9. Faint Galaxies and Dark Matter, by J.A. Tyson 431

1. Introduction 4352. Faint surface brightness surveys 435

2.1. CCD surveys 4362.2. Colors of faint galaxies 437

3. The nature of the faint blue galaxies 4383.1. Observed redshift distribution 4403.2. Sizes of faint galaxies 4413.3. Cosmology from FBG number counts? 4433.4. Are evolution models unique? 443

4. Mapping dark matter with FBGs 444,4.1. Gravitational light-bending: displacements and distortions 4444.2. Mass in galaxy clusters 4464.3. The inverse problem: mass from image distortion 4474.4. Prospecting for dark lenses 451

References 452

Course 10. Results from the Cosmic Background Explorer,by G.F. Smoot 455

1. Introduction 4592. DMR and CMB anisotropy 460

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3. CMB Fluctuation Power Spectrum 4614. FIRAS and CMB Spectrum Observations 4635. DIRBE and the Cosmic Infrared Background 4656. COBE Data Products Release 4667. Discussion and Summary 466References 467

Course 11. Theory and Observations of the CosmicBackground Radiation, byJ.R. Bond 469

1.' Introduction and basic properties 4752. Spectral observations and constraints 4793. Spectral distortion theory 483

3.1. Radiative transport in the expanding universe 4833.2. Source functions for spectral distortions 487

3.2.1. Compton scattering and the Kompaneets source term 4873.2.2. Bremsstrahlung 4903.2.3. Double Compton scattering 4923.2.4. Rayleigh scattering 492

0 3.2.5. Line radiation 4933.2.6. Synchrotron 4933.2.7. Dust grains 493

3.3. The cosmic photosphere and Bose—Einstein distortions 4973.4. Recombination and photon decoupling 499

3.4.1. Hydrogen and Helium Recombination 4993.4.2. Visibility and decoupling 504

3.5. Reionization of the universe 5053.6. Post-recombination energy sources 507

4. Phenomenology of CMB anisotropy 5124.1. Statistical measures of the radiation pattern: C(9), Ce,... 5134.2. Experimental arrangements and their filters 516

4.2.1. Pixel-pixel correlation filters 5164.2.2. Beams and dmr and firs 5194.2.3. 2-Beams, 3-beams, oscillating beams,... 520

4.3. Primary power spectra for inflation-based theories 5224.4. 2D spectra with tilt and a Gaussian coherence angle 5264.5. Experimental band-powers: past and present 5274.6. Measuring cosmological parameters with the CMB 535

5. Primary and secondary sources of anisotropy 5465.1. Angular power spectra from 3D random source-fields 547

5.1.1. Simple sample sources 5485.1.2. Angular power spectra for simple sample sources 5495.1.3. Products of Bessel functions 551

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5.1.4. Fourier derivation of the simple sample spectra at high £ 5535.1.5. Narrow and broad visibilities 5545.1.6. Power-law spectra with coherence scales in 3D and 2D 555

5.2. The primary primary anisotropy effects 5565.2.1. Sachs-Wolfe, photon-bunching and Doppler sources 5575.2.2. Longitudinal and synchronous pictures of the Sachs—Wolfe effect 5585.2.3. Differential power spectrum and form factors 5585.2.4. Damping , 5605.2.5. Early reionization form factors 5615.2.6. The isocurvature effect on low multipoles 561

5.3. Secondary anisotropies 5625.3.1. Sample secondary anisotropy power spectra 5635.3.2. Anisotropy power from dusty primeval galaxies 5645.3.3. SZ and nonlinear Thomson scattering from clusters 5665.3.4. Single-cluster observations of the SZ effect 5675.3.5. The maximum entropy nature of Gaussian anisotropies 5715.3.6. Quadratic nonlinearities in Thomson scattering 5715.3.7. The influence of weak gravitational lensing on the CMB 574

6. Perturbation theory of primary anisotropies 5756.1. Overview of fluctuation formalism 5756.2. Perturbed Einstein equations 577

6.2.1. Time-hypersurface and gauge freedom 5776.2.2. Scalar mode Einstein equations 5796.2.3. Useful gauge invariant combinations for scalar modes 5816.2.4. Longitudinal and synchronous gauges 5836.2.5. Tensor mode metric equations 584

6.3. Connection with primordial post-inflation power spectra 5866.4. Relating scalar and tensor power measures to the dmr band-power 5896.5. The Boltzmann transport equation 591

6.5.1. Scalar mode transfer equations 5926.5.2. Tensor mode transfer equations 603

7. Connection with other cosmic probes of fc-space 605\.7.1. Density power spectra and characteristic scales 6057.2. The observable range in fc-space 6087.3. Relating the cluster-amplitude as and the dmr band-power 6117.4. The future 616

Appendix A. The ADM formalism and perturbation theory • 617A. 1. The ADM equations 618A.2. Scalar perturbations 623A.3. Tensor perturbations 627

Appendix B. Transport theory in General Relativity 627B.I. The distribution function and the BTE in GR 627B.2. Number, energy and momentum conservation equations 631B.3. The transport of extremely relativistic particles 634

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B.4. momentum space gauge transformations 635Appendix C. Polarized transport for Thomson scattering 638

C.I. The polarization matrix and Stokes parameters 638C.2. Scalar perturbation source terms 644

C.2.1. Thomson source functions 644C.2.2. The moment equations for photons 645C.2.3. CDM and baryon transport 646C.2.4. The transport of massless neutrinos 647C.2.5. Hot and warm dark matter transport 648

C.3. Numerically useful regimes for scalar perturbations 651C.3.1. Tight-coupling, shear viscosity and thermal diffusion 651C.3.2. Free-streaming 655

C.4. Modifications with mean curvature 657C.5. Lensing 659C.6. Tensor perturbation source terms 662

References 666

Course 12. Nonbaryonic Dark Matter, by B. Sadoulet 675

1. Introduction 6792. The value of Q 681

2.1. Direct summation 681, 2.2. Dynamical methods 682

2.3. Geometry measurements 6842.4. Conclusion: current uncertainties of O 686

3. Astrophysical evidence for nonbaryonic dark matter 6873.1. Astrophysical constraints on baryonic dark matter 6873.2. Astrophysical constraints on nonbaryonic dark matter 689

4. Nonbaryonic dark matter candidates 6924.1. Axions . 6924.2. Neutrinos \ 6934.3. Weakly Massive Interactive Particles 6944.4. A multi-component dark matter? 695

5. Direct searches for WIMPs 6955.1. The challenges of the detection of WIMPs 6965.2. Reduction of the radioactive background 6985.3. Current strategies in searches for WIMPs 701

5.3.1. Germanium detectors 7015.3.2. Large mass scintillators 7025.3.3. Mica 7025.3.4. Low-pressure time projection chambers 7035.3.5. Cryogenic detectors 703

5.4. The Center for Particle Astrophysics cryogenic search 705

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6. Indirect detection of WIMPs 7077. Conclusion 709References 710

Course 13. The Very Early Universe and Particle Physics,by J.Ellis ' 715

1. Introduction to early cosmology and the Standard Model 7191.1. The first second — a general overview 7191.2. Ingredients in the Standard Model 7251.3. Field theory primer 7261.4. How to make a model and win a prize 730

2. Testing the Standard Model 7302.1. Setting up the electroweak theory 7302.2. The Z° peak in e+e~ annihilation 7342.3. Quantum corrections 7372.4. Electroweak symmetry breaking 743

3. The quark—hadron phase transition and Big Bang nucleosynthesis 7433.1. The strong interactions 7433.2. General description of phase transitions, 7483.3. Modelling the QCD phase transition 7503.4. Standard Big Bang nucleosynthesis 754

3.4.1. 4He 7543.4.2. D + 3He 7563.4.3. 7Li 7563.4.4. Be + B 756

3.5. Inhomogeneous Big Bang nucleosynthesis 7574. The electroweak phase transition and baryogenesis 759

4.1. Finite-temperature field theory 7594.2. Modelling the electroweak phase transition 7644.3. Sphalerons 7674.4. Electroweak scenarios for baryogenesis 770

5. Supersymmetry 7735.1. Why supersymmetry? 7735.2. The naturalness/hierarchy problem 7745.3. What is supersymmetry? 7785.4. Model-building 7805.5. The lightest supersymmetric particle 785

6. Grand Unification 7876.1. Strategy for Grand Unification 7876.2. Simple GUT models 7936.3. Baryon decay 7976.4. Neutrino masses, mixing and oscillations 799

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1. Inflation 8057.1. The psychology of inflation 8057.2. Some inflationary models 8097.3. Inflationary perturbations 8127.4. Measuring the inflaton potential 815

8. Particle dark matter candidates 8188.1. Motivations 8188.2. Axions 8198.3. Massive neutrinos 8258.4. Lightest supersymmetric particle 830

8.4.1. Sneutrino£ 8308.4.2. GravitinoG 8318.4.3. Neutralinox 831

9. Searches for dark matter particles 8339.1. Annihilations in the galactic halo 8339.2. Annihilations in the Sun or Earth 8359.3. Dark matter searches in the laboratory 839

10. Some stringy things 84910.1. Motivations 84910.2. Basic principles 85210.3. The supersymmetric flipped 517(5) GUT 85510.4. Problems of quantum gravity 858

References 863

Seminar 1. X-ray Astronomy and ROSAT Observations ofClusters of Galaxies, by M. Pierre 871

1. Introduction 8732. The ROSAT observatory 874

2.1. The project 8742.2. The scientific payload ; 875

3. X-ray emission mechanisms 8764. Applications of X-ray observations of clusters to cosmology 8785. X-ray mass determination of clusters of galaxies 8816. Cluster detection and identification in the ROSAT survey 884

6.1. Clusters in the survey 8846.2. Optical identifications 885

7. Conclusions and future prospects 886References 887

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Seminar 2. Mapping the Galaxy Distribution, byL.N. da Costa 891

1. Introduction 8932. The nearby Universe 8933. Conclusions 896References 896

Seminar 3. Clustering in the Universe, by R. Schaeffer 899

1. Introduction 9012. The void probability 9023. Counts in cells 9054. The mass function 9075. Hierarchical clustering 9106. Conclusions 910References 912

Seminar 4. Faint Galaxies: Observations andInterpretations, byB.A. Peterson 913

1. Introduction 9152. Models of galaxy luminosity evolution 9173. Angular correlations 9174. Selection effects and the redshift distribution 9195. Number counts 9196. Merging 9207. Conclusions 920References 921

Seminar 5. Solar Neutrinos, by M. Spiro and Th. Stolarczyk 923

1. Introduction 9252. Are the predictions right? 927

2.1. i/sBflux 9272.2. uiBe flux 927

3. Consistent predictions for gallium experiments 9284. Results of the gallium experiments 929

4.1. SAGE 9294.2. GALLEX 929

5. Interpretations 930References 934

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Seminar 6. Experimental and Astrophysical Status ofNeutrino Masses, by G. Raffelt 935

1. Introduction 9372. Direct bounds 937

2.1. Tritium beta decay 9372.2. Mu and tau neutrinos 9382.3. Supernova neutrinos 939

3. Indirect searches 9393.1. Oscillation experiments 9393.2. Solar neutrinos 9403.3. Atmospheric neutrinos 9413.4. r-Process in supernovae 9413.5. Neutrinoless double beta decay 942

4. Summary 942References 943

Seminar 7. EROS, by E. Aubourg et al. 945

References 9500

Seminar 8. The Early Nucleosynthesis: Comments on thePresent Situation, by J. Audouze 953

1. Introduction 9552. The "glory" of the standard model 9553. To sum up . . . 9574. Note added in proof 957References 958

Seminar 9. Gauge Triplet Neutrinos as the Missing Mass,byP.Salati 959

1. Introduction 9612. Heavy neutrinos as gauge triplets 9613. Cosmological behaviour 9634. Discussion and prospects 966References 968

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