April 11, 2013 A Survey of Dark Matter and Related Topics in Cosmology Bing-Lin Young To readers: This is a drift. As reflect in the organization of and the topics contained, the lecture notes is intended for students of high energy physics who are interested in dark matter and curious about cosmology. The notes' first one-third consists of topics of dark matter. The rests deals topics in cosmology which are relevant to dark matter and which high energy students may not be familiar with. The notes has been revised a couple of time but it is not yet completed. Appendix D on CMB anisotropy and some other topics which should be included are still missing. If you see some dangling references, they probably belong to Appendix. So please do not pay any attention to them for this version of the notes. I welcome your comments and suggestions. Please contact me at <[email protected]>. Thanks. CONTENTS iii Contents Bibliography vi 1 Introduction 1 2 Observational evidence 5 2.1 Galactic rotation curve . .5 2.2 Large scale structures . .8 2.3 Gravitational lensing . .9 2.4 Cosmic microwave background anisotropy . 13 2.5 Primordial Nucleosysthesis: The baryon content of the universe . 15 2.6 Alternatives to dark matter . 15 2.7 Finding a solution . 16 3 Dark matter candidates 16 3.1 Dark matter-kinematic types and production mechanisms . 17 3.2 Dark matter-particle types . 18 3.3 Summary of viable dark matter candidates . 21 3.4 A brief remark on dark matter mass bounds . 22 4 WIMPs 24 4.1 Weakly interacting massive particles (WMIPs) . 24 4.2 Supersymmetric particles as WIMPs . 24 4.3 WIMP physics and cosmology . 25 4.4 Comments on thermal vs non-thermal production . 27 5 Milky Way and galactic dark matter 28 5.1 Relevant parameters . 28 5.2 A couple brief remarks . 29 5.2.1 Possible problems with cold dark matter . 29 5.2.2 Reviews on dark matter searches . 30 6 Dark matter searches I-light particles 31 6.1 Searches for axions . 31 6.2 KeV sterile neutrinos . 34 7 Dark matter searches II-WIMPs 36 7.1 Worldwide deep underground laboratories . 37 7.2 Direct searches - dark matter in terrestrial laboratories . 38 7.2.1 A cursory look of the basic formulation . 40 7.2.2 Direct search experiments . 43 7.3 Indirect searches-galactic dark matter . 46 7.4 High energy collider-Accelerator Production . 48 CONTENTS iv 8 A brief summary of the status of dark matter searches 50 8.1 Direct searches . 50 8.1.1 Direct search: DAMA/LIBRA . 50 8.1.2 Direct search: CDMS-II . 52 8.1.3 Direct search: CoGeNT . 52 8.1.4 Direct search: CRESST . 53 8.2 Indirect searches . 54 8.2.1 Indirect searches: charged particles, positrons and antiproton . 54 8.2.2 Indirect searches: Photons . 57 8.2.3 Indirect searches: neutrinos . 57 8.2.4 Anti-deuterons . 59 8.2.5 Searches of other anti-particles . 62 8.3 Summary . 62 8.3.1 Status of experimental searches . 62 8.3.2 A glance in the future . 62 8.3.3 Some miscellaneous theoretical remarks . 63 A An introductory cosmology for pedestrians 69 A.1 The Einstein's equation and the FLRW metric . 69 A.1.1 Review of some generality . 69 A.1.2 The FLRW metric . 70 A.1.3 The Einstein's equations in the FLRW metric . 73 A.1.4 Cosmological redshift . 78 A.1.5 Energy components in the early universe as functions of the redshift . 80 A.1.6 Age of the universe . 81 A.2 Kinetic theory-thermodynamics . 82 A.2.1 Equilibrium distributions . 82 A.2.2 Chemical potential . 83 A.2.3 Entropy . 83 A.2.4 Lorentz invariant phase space element and distribution functions . 85 A.3 Relativistic and non-relativistic behaviors of particle densities . 88 A.3.1 Ultra-relativistic limit . 88 A.3.2 Non-relativistic limit . 89 A.3.3 Internal degrees of freedom gj .......................... 91 A.3.4 Some detailed properties . 92 A.4 Beyond equilibrium, decoupling of particles . 96 A.4.1 Mechanism of equilibrium . 97 A.4.2 Decoupling-breakaway from equilibrium . 98 A.5 Thermal history of the early universe . 100 A.5.1 Temperature chronology of the early universe . 103 A.5.2 Baryon-photon ratio in the equilibrium era . 105 A.5.3 Effective decoupling of radiation and electrons . 106 A.5.4 Radiation-matter equality . 106 A.5.5 Recombination and the last scattering surface . 107 A.5.6 Decoupling of the photon and the last scattering surface . 111 A.5.7 A cheat sheet of the cosmo-history . 113 CONTENTS v B Big Bang nucleosynthesis: Primordial helium synthesis 115 B.1 Introduction . 115 B.2 Estimate decoupling . 117 B.2.1 Cosmic expansion rate . 118 B.2.2 Interaction rate . 119 B.2.3 Approximate decoupling temperature Tf and neutron freezing fraction . 120 B.3 Differential equation and initial condition for the neutron fraction . 120 B.3.1 Nucleon conversion rates . 123 B.3.2 Solution of the differential equation . 128 B.4 Freezing out neutron fraction . 131 B.5 Effect of neutron decay . 133 B.6 Arresting neutron decay-Formation of light elements . 135 B.6.1 Deuteron bottleneck . 138 B.7 Primordial fraction of helium-4 . 141 B.8 Counting the baryonic matter and the lithium problem . 142 C Freeze-out of heavy particles 145 C.1 Boltzmann equation for particle productionn and annihilation . 145 C.2 The rate of change of particle number density . 146 C.3 Digression-Riccati equation and some of its properties . 150 C.3.1 Transforming to a linear equation . 151 C.3.2 Multiple solutions . 151 C.3.3 Boundary condition . 152 C.4 Solution of rate of change of particle number density . 152 C.5 Freeze-out: freeze-out temperature and particle abundance . 155 C.5.1 Relic abundance due to freeze-out . 156 C.5.2 The freeze-out epoch . 156 C.6 Evaluation of λ and the Physical implication . 157 C.6.1 Estimate of λ ................................... 157 C.6.2 Fraction of critical density . 158 C.6.3 Estimate of the mass of heavy particle . 159 D CMB anisotropy (incomplete) 161 E Useful cross section formulae 163 E.1 Electromagnetic interaction cross sections . 163 E.1.1 Klein-Nishina formula . 163 E.1.2 Thomas scattering cross section . 163 E.2 Weak interactions cross sections . 164 E.2.1 Muon lifetime . 164 E.2.2 Leptonic elastic cross sections . 164 E.2.3 Leptonic inelastic cross sections . 165 E.2.4 More neutrino leptonic and annihilation cross sections . 165 E.2.5 Neutrino nucleon elastic cross sections . 165 E.2.6 Two-body neutrino nucleon inelastic cross sections . 165 CONTENTS vi F Useful constants and units conversion 167 F.1 Natural units and units conversion . ..