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Dark Matter and Dark Energy components chapter 7 Lecture 3 The early universe chapters 5 to 8 Particle Astrophysics , D. Perkins, 2nd edition, Oxford 5. 6. 7. 8. The expanding universe Nucleosynthesis and baryogenesis Dark matter and dark energy components Development of structure in early universe exercises Slides + book http://w3.iihe.ac.be/~cdeclerc/astroparticles Overview • Part 1: Observation of dark matter as gravitational effects – – – – – Rotation curves galaxies, mass/light ratios in galaxies Velocities of galaxies in clusters Gravitational lensing Bullet cluster Alternatives to dark matter • Part 2: Nature of the dark matter : – Baryons and MACHO’s, primordial black holes – Standard neutrinos – Axions • Part 3: Weakly Interacting Massive Particles (WIMPs) • Part 4: Experimental WIMP searches (partly today) • Part 5: Dark energy (next lecture) 2014-15 Dark Matter lect3 3 Previously • Universe is flat k=0 • Dynamics given by Friedman equation • Cosmological redshift • Closure parameter 1 z R t0 R t t t c t • Energy density evolves with time 2014-15 z t0 0 Dark Matter lect3 Ωk=0 4 Dark matter : Why and how much? • Several gravitational observations show that more matter is in the Universe than we can ‘see’ • It these are particles they interact only through weak interactions and gravity • The energy density of Dark Matter today is obtained from fitting the ΛCDM model to CMB and other observations luminous 1% dark baryonic 4% dark energy ~70% Neutrino HDM <1% cold dark matter ~24% Planck, 2013 rad t0 105 matter t0 0.30 3 4 H t H m t0 1 z r t0 1 z t0 2 2014-15 2 0 Dark Matter lect3 5 Dark matter nature • The nature of most of the dark matter is still unknown Is it a particle? Candidates from several models of physics beyond the standard model of particles and their interactions Is it something else? Modified newtonian dynamics? • the answer will come from experiment 2014-15 Dark Matter lect3 6 Velocities of galaxies in clusters and M/L ratio Galaxy rotation curves Gravitational lensing Bullet Cluster PART 1 GRAVITATIONAL EFFECTS OF DARK MATTER 2014-15 Dark Matter lect3 7 Dark matter at different scales • Observations at different scales : more matter in the universe than what is measured as electromagnetic radiation (visible light, radio, IR, X-rays, γ-rays) • Visible matter = stars, interstellar gas, dust : light & atomic spectra (mainly H) • Velocities of galaxies in clusters -> high mass/light ratios M⊙ L⊙ =1 M MW » 10 LMW M cluster » 500 Lcluster L is much smaller than expected from value of M • Rotation curves of stars in galaxies large missing mass up to large distance from centre 2014-15 Dark Matter lect3 8 Dark matter in galaxy clusters 1 • Zwicky (1937): measured mass/light ratio in COMA cluster is much larger than expected – Velocity from Doppler shifts (blue & red) of spectra of galaxies – Light output from luminosities of galaxies v COMA cluster 1000 galaxies 20Mpc diameter 100 Mpc(330 Mly) from Earth Optical (Sloan Digital Sky Survey) + IR(Spitzer Space Telescope 2014-15 Dark Matter lect3 NASA 9 Dark matter in galaxy clusters 2 • Mass from velocity of galaxies around centre of mass of cluster using virial theorem () ( ) 1 GPE M 2 æM ö M (velocities) >1010 M ⊙ üï æ M ö » 500 ´ ç ÷ ýÞç ÷ 7 è L øsun L » 10 L⊙ ïþ è L øcluster KE v = æM ö æM ö ⊙ ç ÷ ç ÷ è L øCOMA è L øSUN L should be larger Most of the mass M does not emit light • Proposed explanation: missing ‘dark’ = invisible mass • Missing mass has no interaction with electromagnetic radiation 2014-15 Dark Matter lect3 10 Galaxy rotation curves • Stars orbiting in spiral galaxies • gravitational force = centrifugal force mv 2 mM r G r r2 • Star inside hub v ⊙ r • Star far away from hub v⊙ 2014-15 1 r Dark Matter lect3 11 NGC 1560 galaxy optical HI 21cm radio emission from gas 2014-15 Dark Matter lect3 12 Universal features • Large number of rotation curves of spiral galaxies measured by Vera Rubin – up to 110kpc from centre • Show a universal behaviour 2014-15 Dark Matter lect3 13 Dark matter halo • Galaxies are embedded in dark matter halo • Halo extends to far outside visible region HALO DISK 2014-15 Dark Matter lect3 14 Dark matter halo models Milky Way halo models DM Density (GeV cm-3) • Density of dark matter is larger near centre due to gravitational attraction near black hole • Halo extends to far outside visible region • dark matter profile inside Milky Way is modelled from simulations Solar system Dark Matter lect3 Distance from centre (kpc) 2014-15 15 2014-15 Dark Matter lect3 16 Gravitational lensing • Gavitational lensing by galaxy clusters -> effect larger than expected from visible matter only 2014-15 Dark Matter lect3 17 Gravitational lensing principle • Photons emitted by source S (e.g. quasar) are deflected by massive object L (e.g. galaxy cluster) = ‘lens’ • Observer O sees multiple images 2014-15 Dark Matter lect3 18 Lens geometries and images 2014-15 Dark Matter lect3 19 Observation of gravitational lenses • First observation in 1979: effect on twin quasars Q0957+561 • Mass of ‘lens’ can be deduced from distortion of image • only possible for massive lenses : galaxy clusters Distorted images of remote quasar Lens = cluster Abell 2218 2014-15 Dark Matter lect3 20 Different lensing effects • Strong lensing: – clearly distorted images, e.g. Abell 2218 cluster – Sets tight constraints on the total mass • Weak lensing: – only detectable with large sample of sources – Allows to reconstruct the mass distribution over whole observed field • Microlensing: – no distorted images, but intensity of source changes with time when lens passes in front of source – Used to detect Machos 2014-15 Dark Matter lect3 21 Collision of 2 clusters : Bullet cluster • Optical images of galaxies at different redshift: Hubble Space Telescope and Magellan observatory • Mass map contours show 2 distinct mass concentrations – weak lensing of many background galaxies – Lens = bullet cluster 0.72 Mpc Cluster 1E0657-558 2014-15 Dark Matter lect3 22 Bullet cluster in X-rays • X rays from hot gas and dust - Chandra observatory • mass map contours from weak lensing of many galaxies 2014-15 Dark Matter lect3 23 Bullet cluster = proof of dark matter • Blue = dark matter reconstructed from gravitational lensing • Is faster than gas and dust : no electromagnetic interactions • Red = gas and dust = baryonic matter – slowed down because of electromagnetic interactions • Modified Newtonian Dynamics cannot explain this 2014-15 Dark Matter lect3 24 Another example • Abell 1689 cluster • Blue = reconstructed dark matter map 2014-15 Dark Matter lect3 25 Alternative theories • MOND theory proposed by Milgrom in 1983 • Modification of Newtonian Dynamics over (inter)-galactic distances • Far away from centre of cluster or galaxy the acceleration of an object becomes small -> no need for hidden mass • Explains rotation curves • Does not explain Bullet Cluster 2014-15 Dark Matter lect3 26 2014-15 Dark Matter lect3 27 Overview • Part 1: Observation of dark matter as gravitational effects – – – – – Rotation curves galaxies, mass/light ratios in galaxies Velocities of galaxies in clusters Gravitational lensing Bullet cluster Alternatives to dark matter • Part 2: Nature of the dark matter : – Baryons and MACHO’s, primordial black holes – Standard neutrinos – Axions • Part 3: Weakly Interacting Massive Particles (WIMPs) • Part 4: Experimental WIMP searches (partly today) • Part 5: Dark energy (next lecture) 2014-15 Dark Matter lect3 28 Baryons MACHOs = Massive Compact Halo Objects Primordial black holes Standard neutrinos Axions WIMPs = Weakly Interacting Massive Particles →Part 3 PART 2 THE NATURE OF DARK MATTER 2014-15 Dark Matter lect3 29 What are we looking for? • Particles with mass – interact gravitationally • Particles which are not observed in radio, visible, X-rays, γ-rays, .. : neutral and possibly weakly interacting • • • • Candidates: Dark baryonic matter: baryons, MACHOs, primordial black holes light particles : primordial neutrinos, axions Heavy particles : need new type of particles like neutralinos, … = WIMPs • To explain formation of structures majority of dark matter particles had to be non-relativistic at time of freeze-out -> Cold Dark Matter 2014-15 Dark Matter lect3 30 Total baryon content Visible baryons Neutral and ionised hydrogen – dark baryons Mini black holes MACHOs BARYONIC MATTER 2014-15 Dark Matter lect3 31 Baryon content of universe • measurement of light element abundances • and of He mass fraction Y • And of CMB anisotropies • Interpreted in Big Bang Nucleosynthesis model NB 6.047 0.074 1010 N ΩBh2=.022 He mass fraction D/H abundance PDG 2013 ΩB h 2 = 0.02207 0.00027 2014-15 Dark Matter lect3 32 Baryon budget of universe • From BB nucleosynthesis and CMB fluctuations: • Related to history of universe at z=109 and z=1000 • Most of baryonic matter is in stars, gas, dust • Small contribution of luminous matter • 80% of baryonic mass is dark • Ionised hydrogen H+, MACHOs, mini black holes baryons 0.05 lum 0.01 • Inter Gallactic Matter = gas of hydrogen in clusters of galaxies • Absorption of Lyα emission from distant quasars yields neutral hydrogen fraction in inter gallactic regions • Most hydrogen is ionised and invisible in absorption spectra form dark baryonic matter 2014-15 Dark Matter lect3 33 Lyα forest and neutral hydrogen gas Hydrogen atoms Absorb UV light Emission of UV light by quasar λ= 1216 Å Lyman α transition in H Measurement of absorption spectra yields amount of neutral H 2014-15 Dark Matter lect3 34 tiny black holes • Primordial black holes could make up dark matter if created early enough in history of universe and survive inflation • PBH of 1011kg could have lifetime = age of universe • Emit Hawking radiation in form of γ–rays -> signal expected • If present in Milky Way halo they would be detected by gravitational microlensing (see MACHO’s, next part) • no events were observed • -> contribution to DM negligible 2014-15 Dark Matter lect3 35 Massive Astrophysical Compact Halo Objects Dark stars in the halo of the Milky Way Observed through microlensing of large number of stars MACHOS 2014-15 Dark Matter lect3 36 Microlensing • Light of source is amplified by gravitational lens • When lens is small (star, planet) multiple images of source cannot be distinguished : addition of images = amplification • But : amplification effect varies with time as lens passes in front of source - period T • Efficient for observation of e.g. faint stars Period T 2014-15 Dark Matter lect3 37 Microlensing - MACHOs • Amplification of signal by addition of multiple images of source • Amplification varies with time of passage of lens in front of source 2 2 x x A 1 / x 1 2 4 x t T • Typical time T : days to months – depends on distance & velocity • MACHO = dark astronomical object seen in microlensing • M ≈ 0.001-0.1M • Account for very small fraction of dark baryonic matter • MACHO project launched in 1991: monitoring during 8 years of microlensing in direction of Large Magellanic Cloud 2014-15 Dark Matter lect3 38 Optical depth – experimental challenge • Optical depth τ = probability that one source undergoes gravitational lensing • For ρ = NLM = Mass density of lenses along line of sight 2 • Optical depth depends on DS 2 G – distance to source D c 3 S – number of lenses per source 107 • Near periphery of bulge of Milky Way Need to record microlensing for millions of stars • Experiments: MACHO, EROS, superMACHO, EROS-2 • EROS-2: – 7x106 bright stars monitored in ~7 years – one candidate MACHO found – less than 8% of halo mass are MACHOs 2014-15 Dark Matter lect3 39 schema 2014-15 Dark Matter lect3 40 Example of microlensing • source = star in Large Magellanic Cloud (LMC, distance = 50kpc) • Dark matter lens in form of MACHO between LMC star and Earth • Could it be a variable star? • No: because same observation of luminosity in red and blue light : expect that gravitational deflection is independent of wavelength 2014-15 Blue filter Dark Matter lect3 red filter 41 2014-15 Dark Matter lect3 42 STANDARD NEUTRINOS AS DARK MATTER 2014-15 Dark Matter lect3 43 Standard neutrinos • Standard Model of Particle Physics – measured at LEP N fermion families 2.984 0.009 → 3 types of light neutrinos with Mν<45GeV/c2 • Fit of observed light element abundances to BBN model (lecture 2) N neutrino species 3.5 • Neutrinos have only weak and gravitational interactions 2014-15 Dark Matter lect3 44 Relic standard neutrinos • Non-baryonic dark matter = particles Lecture 2 – created during radiation dominated era – Stable and surviving till today • Neutrino from Standard Model = weakly interacting, small mass, stable → dark matter candidate • Neutrino production and annihilation in early universe weak interactions e e i i i e, , • Neutrinos freeze-out at kT ~ 3MeV and t ~ 1s • When interaction rate W << H expansion rate 2014-15 Dark Matter lect3 45 Cosmic Neutrino Background • Relic neutrino density and temperature today • for given species (νe, νμ, ντ ) (lecture 2) N N 113 cm-3 T t0 1.95K meV 3 N 340 cm • Total density today for all flavours • High density, of order of CMB – but difficult to detect! • At freeze-out : relativistic kT FO >> m ( ) 2014-15 Dark Matter lect3 n 46 Neutrino mass • If all critical density today is built up of neutrinos 1 c 2 2 m c 47 eV m < 16 eV c ν e , , • Direct mass measurement: Measure end of electron energy spectrum in beta decay Count rate 3 1 2014-15 H 23 He e e m eV c Electron energy (keV) Dark Matter lect3 2 47 Neutrinos as hot dark matter • Relic neutrinos are numerous • have very small mass < eV • Were relativistic when decoupling from other matter at kT~3MeV • → can only be Hot Dark Matter – HDM • Relativistic particles prevent formation of large-scale structures – through free streaming they ‘iron away’ the structures • → HDM should be limited • From simulations of structures: maximum 30% of DM is hot 2014-15 Dark Matter lect3 48 Simulations and data: majority must be CDM Hot dark matter warm dark matter cold dark matter See eg work of Carlos Frenk http://star-www.dur.ac.uk/~csf/ simulations Observations 2dF galaxy survey 2014-15 Dark Matter lect3 49 2014-15 Dark Matter lect3 50 Postulated to solve ‘strong CP’ problem Could be cold dark matter particle AXIONS 2014-15 Dark Matter lect3 51 Strong CP problem • QCD lagrangian for strong interactions LQCD Lquark Lgauge standard L • Term Lθ is generally neglected • violates P and T symmetry → violates CP symmetry • Violation of T symmetry would yield a non-zero neutron electric dipole moment e.d.m. -(15-16) predicted » q ´10 e.cm • Experimental upper limits experiment e.d .m. 2014-15 10 25 e.cm Dark Matter lect3 10 10 52 Strong CP problem • Solution by Peccei-Quinn : introduce higher global U(1) symmetry, which is broken at an energy scale fa • This extra term cancels the Lθ term • With broken symmetry comes a boson field φa = axion with mass 1010 GeV m A ~ 0.6meV fA • Axion is very light and weakly interacting • Is a pseudo-scalar with spin 0- ; Behaves like π0 2 3 G m • Decay rate to photons A A A 2014-15 Dark Matter lect3 64 53 Axion as cold dark matter • formed boson condensate in very early universe during inflation • Is candidate for cold dark matter • if mass < eV its lifetime is larger than the lifetime of universe stable • Production in plasma in Sun or SuperNovae • Searches via decay to photons in magnetic field A production decay A GA2 m3A 64 • CAST experiment @ CERN: axions from Sun • If axion density = critical density today then A 1 A c 2014-15 mA 106 103 eV c2 Dark Matter lect3 54 Axion-γ coupling (GeV-1) Axions were not yet observed Axion model predictions Some are excluded by CAST limits Combination of mass and coupling below CAST Axion mass (eV) limit are still allowed by experiment CAST has best sensitivity 2014-15 Dark Matter lect3 55 Pauze Overview • Part 1: Observation of dark matter as gravitational effects – – – – – Rotation curves galaxies, mass/light ratios in galaxies Velocities of galaxies in clusters Gravitational lensing Bullet cluster Alternatives to dark matter • Part 2: Nature of the dark matter : – Baryons and MACHO’s, primordial black holes – Standard neutrinos – Axions • Part 3: Weakly Interacting Massive Particles (WIMPs) • Part 4: Experimental WIMP searches (partly today) • Part 5: Dark energy (next lecture) 2014-15 Dark Matter lect3 57 Which candidates Short recall of SuperSymmetry Expected abundances of neutralinos today Expected mass range Weakly Interacting Massive Particles PART 3 WIMPS AS DARK MATTER 2014-15 Dark Matter lect3 58 summary up to now • Standard neutrinos can be Hot DM • Most of baryonic matter is dark luminous 1% dark baryonic 4% – MACHO? PBH? • cold dark matter (CDM) is still of unknow type • Need to search for candidates for non-baryonic cold dark matter in particle physics beyond the SM Neutrino HDM <1% cold dark matter ~24% dark energy ~70% matter Baryons HDM CDM 0.05 0.01 0.24 0.30 2014-15 Dark Matter lect3 59 Non-baryonic CDM candidates • Axions – To reach density of order ρc their mass must be very small mAc2 106 103 eV – No experimental evidence yet • • • • • Most popular candidate for CDM : Weakly Interacting Massive Particles : WIMPs present in early hot universe – stable – relics of early universe Cold : Non-relativistic at time of freeze-out Weakly interacting : conventional weak couplings to standard model particles - no electromagnetic or strong interactions • Massive: gravitational interactions (gravitational lensing …) 2014-15 Dark Matter lect3 60 Weakly interacting and massive • Massive neutrinos: – The 3 standard neutrinos have very low masses – contribute to Hot DM – Massive non-standard neutrinos : 4th generation of leptons and quarks? No evidence yet • Neutralino χ = Lightest SuperSymmetric Particle (LSP) in Rparity conserving Minimal SuperSymmetry (SUSY) theory – Lower limit from accelerators > 50 GeV/c2 MSSM – Stable particle – survived from primordial era of universe • Other SUSY candidates: sneutrinos • New particles from models with extra space dimensions • ……. 2014-15 Dark Matter lect3 61 SuperSymmetry in short • Gives a unified picture of matter (quarks and leptons) and interactions (gauge bosons and Higgs bosons) • Introduces symmetry between fermions and bosons Q fermion boson Q boson fermion • Fills the gap between electroweak and Planck scale M W 102 GeV 19 1017 M PL 10 GeV • Solves problems of Standard Model, like the hierarchy problem: = divergence of radiative corrections to Higgs mass • Provides a dark matter candidate 2014-15 Dark Matter lect3 62 SuperSymmetric particles • Need to introduce new particles: supersymmetric particles • Associate to all SM particles a superpartner with spin ±1/2 (fermion ↔ boson) -> sparticles • minimal SUSY: minimal supersymmetric extension of the SM – reasonable assumptions to reduce nb of parameters • If R-parity is conserved there is a stable Lightest SUSY Particle: neutralino 3B+L+2S RP = (-1) • Neutralino could be dark matter particle • Is searched for at LHC 2014-15 Dark Matter lect3 63 WIMP annihilation rate at freeze-out • WIMP with mass M must be non-relativistic at freeze-out Could be neutralino or • gas in thermal equilibrium other weakly interacting massive particle kT ⊙ M c c 2 ® Boltzman gas æ -M c 2 ö c 3 ç ÷÷ ç 2 æ M T ö è kT ø N T = çç c ÷÷ e è 2p ø ( ) TFO number density • Annihilation rate W T N T Annihilationv χ WIMP velocity at FO • Cross section σ depends on model parameters : e.g. weak interactions 2014-15 Dark Matter lect3 64 Freeze-out temperature • assume that couplings are of order of weak interactions GF = Fermi constant H T • Rewrite expansion rate • Freeze-out condition W TFO H TFO é ê êM T ê c ê ë ( • f = constants ≈ 100 2 M c • Set P solve for P ) 1 2 T2 M PL æ -M c c2 ö ù ç kT ÷ ú 2 3 T è ø 2 úéG 2 M 2 ù = e f F cû ë ú M PL ú û P FO kT 2014-15 1.66 g * Dark Matter lect3 M c2 kTFO ~ 25 kTFO ~ M c2 25 65 Number density N(T) Depends on model Increasing <σAv> P~25 today P=M/T (time ->) 2014-15 Dark Matter lect3 66 Relic abundance today Ω(T0) - 1 • At freeze-out annihilation rate ~ expansion rate N TFO Av H TFO • WIMP number density today for T0 = 2.73K R3 TFO N T0 N TFO 3 R T0 • Energy density today r c (T0 ) = M c N (T0 ) ⊙ PFOT03 M PL s Av 2 MPL T0 TFO TFO 3 N T0 PFO Av T0 M PL 6 ´10-31 r c T0 ⊙ GeV s-1 s Av ( ) 2014-15 Dark Matter lect3 67 Relic abundance today Ω(t0) - 2 • Relic abundance of WIMPs today WIMP miracle • For 1 1025 t0 ~ cm3 s 1 vFO X 1035 cm2 O pb • O(weak interactions) weakly interacting particles can make up cold dark matter with correct abundance • Velocity of relic WIMPs at freeze-out from kinetic energy 3kTFO 1 2 Mv 2 2 2014-15 v 3 ~ P FO c Dark Matter lect3 1 2 0.3 v FO ≈ 0.3 c 68 Expected mass range: GeV-TeV • Assume WIMP interacts weakly and is non-relativistic at freeze-out • Which mass ranges are allowed? Ω • Cross section for WIMP annihilation vs mass leads to abundance vs mass HDM neutrinos CDM WIMPs MWIMP (eV) 2014-15 Dark Matter lect3 69 2014-15 Dark Matter lect3 70 Overview • Part 1: Observation of dark matter as gravitational effects – – – – – Rotation curves galaxies, mass/light ratios in galaxies Velocities of galaxies in clusters Gravitational lensing Bullet cluster Alternatives to dark matter • Part 2: Nature of the dark matter : – Baryons and MACHO’s, primordial black holes – Standard neutrinos – Axions • Part 3: Weakly Interacting Massive Particles (WIMPs) • Part 4: Experimental WIMP searches (partly today) • Part 5: Dark energy (next lecture) 2014-15 Dark Matter lect3 71 Direct dark matter detection Indirect detection Searches at colliders The difficult path to discovery PART 4: EXPERIMENTAL WIMP SEARCHES 2014-15 Dark Matter lect3 72 Where should we look? • Search for WIMPs in the Milky Way halo Indirect detection: expect WIMPs from the halo to annihilate with each other to known particles Direct detection: expect WIMPs from the halo to interact in a detector on Earth Dark matter halo Solar system Luminous disk © ESO 2014-15 Dark Matter lect3 73 three complementary strategies 2014-15 Dark Matter lect3 74 DIRECT DETECTION EXPERIMENTS 2014-15 Dark Matter lect3 75 Principle of direct detection • Earth moves in WIMP ‘wind’ from halo • Elastic collision of WIMP with nucleus in detector N N • recoil energy Xe ERec = v c2 µ2 mN (1- cosq ) £ 50keV • Velocity of WIMPs ~ velocity of galactic objects v χ ~ 220 km s ~ 10 c 1 2014-15 Dark Matter lect3 3 µ m mN m mN 76 Cross section and event rates • Event rate depends on density of WIMPs in solar system DM Density (GeV cm-3) R N m σ χp ~ 0.3GeV cm3 Rate depends on number N of nuclei in target Distance from centre (kpc) • Rate depends on scattering cross section – present upper limit 44 2 8 Weak σ χp 10 cm 10 pb 2014-15 Dark Matter lect3 interactions! 77 Direct detection challenges R N M p • low rate large detector • very small signal low threshold • large background : protect against cosmic rays, radioactivity, … 2014-15 Dark Matter lect3 78 Annual modulation • Annual modulations due to movement of solar system in galactic WIMP halo • Observed by DAMA/LIBRA – not confirmed by other experiments Earth against the wind in June Maximum rate R N M p R R0 Rm cos t In direction of the wind in December Minimum rate 2014-15 Dark Matter lect3 79 DAMA/LIBRA experiment • In Gran Sasso underground laboratory • Measure scintillation light from nuclear recoil in NaI crystals • Observe modulation of 1 year (full curve) with phase of 152.5 days • If interpreted as SUSY dark matter: M ~ 10-50 GeV/c2 2014-15 Dark Matter lect3 80 RN M From event rate to cross section σ χp Some experiments claim to see a signal at this mass and with this cross section Other experiments see no signal and put upper limits on the cross section Expected cross sections for models with supersymmetry 2014-15 Dark Matter lect3 81 2014-15 Dark Matter lect3 82 Overview • Part 1: Observation of dark matter as gravitational effects – – – – – Rotation curves galaxies, mass/light ratios in galaxies Velocities of galaxies in clusters Gravitational lensing Bullet cluster Alternatives to dark matter • Part 2: Nature of the dark matter : – Baryons and MACHO’s, primordial black holes – Standard neutrinos – Axions • Part 3: Weakly Interacting Massive Particles (WIMPs) • Part 4: Experimental WIMP searches (partly today) • Part 5: Dark energy (next lecture) 2014-15 Dark Matter lect3 83
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