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Dark Matter and Dark Energy components chapter 7 Lecture 3 See also Dark Matter awareness week December 2010 http://www.sissa.it/ap/dmg/index.html The early universe chapters 5 to 8 Particle Astrophysics , D. Perkins, 2nd edition, Oxford 5. 6 6. 7. 8. The expanding universe Nucleosynthesis and baryogenesis Dark matter and dark energy components Development of structure in early universe excercises Slides + book http://w3 http://w3.iihe.ac.be/ iihe ac be/~cdeclerc/astroparticles cdeclerc/astroparticles Overview • Observation Ob ti off dark d k matter tt as gravitational it ti l effects ff t – – – – – Rotation curves galaxies, mass/light ratios in galaxies V l iti off galaxies Velocities l i iin clusters l t Gavitational lenses Primordial nucleosynthesis Anisotropies in CMB radiation • Nature of dark matter particles: – Baryons and MACHO’s – Neutrinos – Axions • Weakly Interacting Massive Particles (WIMPs) Experimental WIMP searches • Dark energy 2011-12 Dark Matter-Dark Energy 3 Previously t o ρt • Universe is flat k=0 • Dynamics given by Friedman equation 2 ⎛ R ( t ) ⎞ 8π GN 2 = t) H (t ) ≡ ⎜ ( ⎜ R ( t ) ⎟⎟ 3 ⎝ ⎠ • Cosmological redshift • Closure parameter 1+ z = R ( t0 ) z ( t0 ) = 0 R (t ) ρ (t ) Ω (t ) = ρc ( t ) Dark Matter-Dark Energy t0 + Ω r ( t0 )(1 + z ) + 4 Ωk=0 ( ) + Ωk (1 + z ) Λ ( )(1 + z ) 3 Ω t0 2011-12 =H ⎡ ⎣ 2 0 m H (t ) 2 Ω • Energy Ener density densit evolves e ol es with ith time 2 ⎤ ⎦ 4 Dark matter : Why and how much? • Several gravitational observations show that more matter is i in i the h Universe U i than h we can ‘see’ • These particles interact only through weak interactions and gravity • The energy density of Dark Matter todayy is obtained from fitting the ΛCDM model to CMB and other observations luminous 1% dark baryonic 4% Neutrino HDM <1% cold dark matter 18% dark energy 76% Ω rad ( t0 ) ≈ 10−5 Ω matter ( t0 ) ≈ 0.24 0 24 3 4 ⎡ H ( t ) = H Ωm ( t0 )(1+ z) +Ωr ( t0 )(1+ z) +ΩΛ ( t0 )⎤ ⎣ ⎦ 2 2011-12 2 0 Dark Matter-Dark Energy 5 Dark matter nature • The nature of most of the dark matter is still unknown ¾ Is it a particle? Candidates from several models of physics beyond the standard model of particle physics ¾ Is it something else? Modified newtonian dynamics? • the answer will come from experiment 2011-12 Dark Matter-Dark Energy 6 Velocities of galaxies in clusters and M/L ratio G l Galaxy rotation t ti curves Gravitational lensing Bullet Cluster PART 1 GRAVITATIONAL EFFECTS OF DARK MATTER 2011-12 Dark Matter-Dark Energy 7 Evidence for dark matter - 1 • Observations b at different d ff scales l : more matter in the h universe than what is measured as electromagnetic radiation d ((visible bl llight, h radio, d IR, X-rays, g-rays)) • Visible matter = stars, interstellar gas, dust : light & atomic spectra (mainly H) g mass/light / g ratios • Velocities of ggalaxies in clusters Æ high M =1 L M MW ≈ 10 LMW M cluster ≈ 500 Lcluster • Rotation curves of stars in galaxies Æ large missing mass up to large distance from centre 2011-12 Dark Matter-Dark Energy 8 Dark matter in galaxy clusters 1 • Zwicky k (1937): ( ) measured d mass/light /l h ratio in COMA cluster l 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 2011-12 Dark Matter-Dark Energy NASA 9 Dark matter in galaxy clusters • Mass from f velocity l off galaxies l around d centre off mass off cluster using virial theorem 1 KE ( v ) = GPE ( M ) 2 M (velocities) > 1010 M ⎫⎪ ⎛ M ⎞ ⎛M ⎞ ⇒ ≈ × 500 ⎬ ⎜ ⎟ ⎜ ⎟ 7 L L ≈ 10 L ⎝ L ⎠sun ⎪⎭ ⎝ ⎠cluster ⎛M ⎞ ⎜ ⎟ ⎝ L ⎠COMA Missing mass ⎛M ⎞ ⎜ ⎟ ⎝ L ⎠ SUN • P Proposed d explanation: l ti missing i i ‘dark’ ‘d k’ = invisible i i ibl mass • Missing mass has no interaction with electromagnetic radiation 2011-12 Dark Matter-Dark Energy 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 1 v∼ r 2011-12 Dark Matter-Dark Energy 11 NGC 1560 galaxy Optical blue filter HI 21cm line from gas 2011-12 Dark Matter-Dark Energy 12 Universal features • Large number of rotation curves of spiral galaxies measured by Vera Rubin – up to 110kpc from centre • Show a universal behaviour 2011-12 Dark Matter-Dark Energy 13 Milky Way rotation curve Solar system 2011-12 Dark Matter-Dark Energy 14 Dark matter halo Halo of dark matter • G Galaxies l i are embedded b dd d in i dark d k matter halo h l • Halo extends to far outside visible region HALO DISK 2011-12 Dark Matter-Dark Energy 15 Dark matter halo models Milky Way halo models DM M Densitty (GeV V 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 W is Way i modelled d ll d from f measurements of rotation curves of many galaxies Solar system Dark Matter-Dark Energy Distance from centre (kpc) 2011-12 16 Evidence for dark matter -2 • Gavitational lensing by galaxy clusters Æ effect larger than expected from visible matter only 2011-12 Dark Matter-Dark Energy 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 2011-12 Dark Matter-Dark Energy 18 Lens geometries and images 2011-12 Dark Matter-Dark Energy 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 behind Gala ies in Abell cl Galaxies cluster ster 2011-12 Dark Matter-Dark Energy 20 Different lensing effects • Strong lensing: – clearlyy distorted images, g e.g. 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 2011-12 Dark Matter-Dark Energy 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 1E0657-56 2011-12 Dark Matter-Dark Energy 22 Bullet cluster in X-rays • X rays from f h gas and hot d dust d - Chandra Ch d observatory b • mass map contours from weak lensing of many galaxies 2011-12 Dark Matter-Dark Energy 23 Bullet cluster = proof of dark matter • Blue = dark matter mapped 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 d f d Newtonian Dynamics cannot explain l this h 2011-12 Dark Matter-Dark Energy 24 Alternative theories • Newtonian dynamics is different over (inter)-galactic distances • Far away from centre of cluster or galaxy the acceleration of an object becomes small • Explains rotation curves • Does D nott explain l i Bullet B ll t Cl Cluster t 2011-12 Dark Matter-Dark Energy 25 Baryons MACHOs = Massive Compact p Halo Objects j Neutrinos Axions WIMPs = Weakly Interacting Massive Particles →Part 3 PART 2 THE NATURE OF DARK MATTER 2011-12 Dark Matter-Dark Energy 26 What are we looking for? • Particles with mass – interact gravitationally • Particles which are not observed in radio, IR, visible, X-rays, g-rays : neutral and weakly interacting • • • • Candidates: Dark baryonic matter: baryons, MACHOs 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 fi Cold Dark Matter 2011-12 Dark Matter-Dark Energy 27 Total baryon y content Visible baryons Neutral and ionised hydrogen y g – dark baryons y Mini black holes MACHOs BARYONIC MATTER 2011-12 Dark Matter-Dark Energy 28 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 ΩB=.044 He mass fraction D/H abundance NB η= = ( 6.1 ± 0.6 ) × 10−10 Nγ ⇒ Ω B = 0.044 ± 0.005 2011-12 Dark Matter-Dark Energy 29 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 • fi 80% of baryonic mass is dark • Ionised hydrogen H+, MACHOs, mini black holes Ωbaryons ≈ 0.05 Ωlum ≈ 0.01 0 01 • Inter Gallactic Matter = gas of hydrogen in clusters of galaxies • Absorption p of Lya y emission from distant q quasars yyields neutral hydrogen fraction in inter gallactic regions • Most hydrogen is ionised and invisible in absorption spectra fi form dark baryonic matter 2011-12 Dark Matter-Dark Energy 30 Mini black holes • Negligible contribution from mini black holes Ω BH < 10−7 • BHs must have MBH < 105 M • Heavier BH would yield lensing effects which are not observed 2011-12 Dark Matter-Dark Energy 31 Massive Astrophysical p y Compact p Halo Objects j Dark stars in the halo of the Milky Way Observed through g microlensingg of large g number of stars MACHOS 2011-12 Dark Matter-Dark Energy 32 Microlensing • Li Light h off source is i amplified lifi d by b gravitational i i l lens l • When lens is small (star, planet) multiple images of source cannot be distinguished : addition of images = amplification p f effect ff varies with time as lens p passes in • But : amplification front of source - period T • Efficient for observation of e.g. faint stars Period T 2011-12 Dark Matter-Dark Energy 33 Microlensing - MACHOs • Amplification of signal by addition of multiple images of source • Amplification p varies with time off p passage g of lens in front of source ⎛ x2 ⎞ ⎡ x2 ⎤ t A = ⎜1 + ⎟ / ⎢ x 1 + ⎥ 2 ⎠ ⎢⎣ 4 ⎥⎦ ⎝ x∼ T • Typical time T : days to months – depends on distance & velocity • MACHO = dark astronomical object seen in microlensing • M ª 0.001-0.1M 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 2011-12 Dark Matter-Dark Energy 34 Optical depth – experimental challenge • Opticall depth d h t = probability b b l that h source undergoes d gravitational lensing • For r = NLM = Mass density of lenses along line of sight 2 p depth p depends p on • Optical ⎛ DS ⎞ ρ τ = 2π G ⎜ – distance of source DS ⎟ 3 c ⎝ ⎠ – number of lenses −7 τ per source ≈ 10 ( ) • Near periphery of bulge of Milky Way fi Need to record microlensing for millions of stars • Experiments: MACHO, EROS, superMACHO, EROS-2 • EROS-2: 33x106 stars monitored, one candidate MACHO found fi less than 8% of halo mass are MACHOs 2011-12 Dark Matter-Dark Energy 35 Example of microlensing • source = star in Large Magellanic Cloud (LMC, di distance = 50k 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 2011-12 Blue filter red filter Dark Matter-Dark Energy 36 To do • Meebrengen naar examen 2011-12 Dark Matter-Dark Energy 37 STANDARD NEUTRINOS AS DARK MATTER 2011-12 Dark Matter-Dark Energy 38 Standard neutrinos • Standard Model of Particle Physics – measured at LEP N fermion families = 2.984 ± 0.009 → 3 types of light left-handed neutrinos with ith Mν<45GeV/c2 <45G V/ 2 • Fit of observed light element abundances to BBN model (lecture 2) N neutrino t i species i < 3.5 • Neutrinos eut os have a eo onlyy weak ea aand d gravitational interactions 2011-12 Dark Matter-Dark Energy 39 Relic neutrinos • Non-baryonic dark matter = particles – created duringg hot p phase of earlyy universe – 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 γ ↔ e+ + e − ←⎯⎯⎯⎯⎯⎯ →ν i + ν i i = e, μ ,τ • Neutrinos freeze-out duringg radiation dominated era • When interaction rate W << H expansion rate • at kT ~ 3MeV and t > 1s 2011-12 Dark Matter-Dark Energy 40 Cosmic Neutrino Background • Relic neutrino density and temperature today • for given species (ne, nm, nt ) (lecture 2) ⎛3⎞ Nν + Nν = ⎜ ⎟ Nγ = 113 cm-3 ⎝ 11 ⎠ ⎛4 Tν ( 0 ) = ⎜ ⎟ Tγ ( 0 ) = ⎝ 11 ⎠ K 5 9 . 1 1 ⎞ 3 −3 N ≈ 340 cm • Total density for all flavours ν • High Hi h density, densit of order of CMB – but b t difficult diffi lt to detect! dete t! 2011-12 Dark Matter-Dark Energy 41 Neutrino mass • If all critical density today is built up of neutrinos 2 m c ∑ ν = 47 eV ⇒ c V e 6 1 < ν m ρν 1 = Ω = Ων = ρc e , μ ,τ • Measure end of electron energy spectrum in tritium beta decay 3 1 H → 23 He + e − + ν e mν < eV c 2011-12 Dark Matter-Dark Energy 2 42 Neutrino mass Countt rate 3 1 mν = 0.0eV mν < eV c mν = 1.0eV 2011-12 H → 23 He + e − + ν e 2 Electron energy (keV) Dark Matter-Dark Energy 43 Neutrinos as hot dark matter • • • • Relic neutrinos are numerous have very small mass < eV can only be Hot Dark Matter – HDM W Were relativistic l ti i ti when h decoupling d li from f other th matter tt kTª3MeV • Relativistic particles prevent formation of large-scale structures – through free streaming they ‘iron away’ the structures • From simulations of structures: maximum 30% of DM is hot 2011-12 Dark Matter-Dark Energy 44 simulations Hot dark matter 2011-12 warm dark matter Observations 2dF galaxy Dark survey Matter-Dark Energy cold dark matter 45 Postulated to solve ‘strong CP’ problem Could be cold dark matter p particle AXIONS 2011-12 Dark Matter-Dark Energy 46 Strong CP problem • QCD lagrangian l f strong interactions for LQCD = Lquark + Lgauge ( standard ) + Lθ g S2TF a aμν Lθ = θ Fμν F 2 16π • 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. predicted ≈ θ × 10−(15−16) e.cm • Experimental upper limits p e.d .m.experiment < 10−25 e.cm 2011-12 Dark Matter-Dark Energy θ ≤ 10 −10 47 Strong CP problem • Solution l b by Peccei-Quinn : introduce d h h global higher l b l U(1) ( ) symmetry, which is broken at an energy scale fa • This extra term cancels the Lθ term ⎛ ϕ A ⎞ g S2TF a aμν L = ⎜θ − Fμν F ⎟ 2 f A ⎠ 16π ⎝ • With broken symmetry comes a boson field φa = axion with mass 1010 GeV m A ~ 0.6meV fA • Axion is light and weakly interacting • Is a pseudo-scalar with spin 0- ; Behaves like π0 2 3 G m • Decay rate to photons Aγγ A Γ Aγγ = 64π 2011-12 Dark Matter-Dark Energy 48 Axion as cold dark matter • formed boson condensate in very early universe • Therefore candidate as cold dark matter • if mass ª eV its lifetime is larger than the lifetime of universe Æ stable • Production in plasma in Sun or SuperNovae • Searches via decay to 2 photons in magnetic field γ + γ ⎯⎯⎯⎯→ A ⎯⎯⎯ →γ + γ production decay Γ Aγγ = • CAST experiment @ CERN: axions from Sun • If axion densityy = critical densityy todayy then ρa 1 = Ω = Ων = ρc 2011-12 G A2 γγ m3A 64π mA ≈ 10−6 − 10−3 eV c 2 Dark Matter-Dark Energy 49 Axion n-γ coup pling (G GeV-1) Axions were not yet observed Axion model predictions di i Some are excluded by CAST limits Combination of mass and coupling below CAST Axion mass (eV) llimit are stillll allowed ll d by b experiment CAST has best sensitivity 2011-12 Dark Matter-Dark Energy 50 Weaklyy Interactingg Massive Particles PART 3 WIMPS AS DARK MATTER 2011-12 Dark Matter-Dark Energy 51 summary up to now • Standard neutrinos can be Hot DM • Most of baryonic matter is dark dark baryonic 4% luminous 1% cold dark matter 18% • cold dark matter (CDM) is still of unknow type • Need to search for candidates f non-baryonic for b i cold ld dark d k matter in particle physics beyond the SM Neutrino HDM <1% dark energy 76% Ω matter = Ω Baryons + Ων HDM + ΩCDM ≈ 0.05 + 0.01 + 0.18 = 0.24 2011-12 Dark Matter-Dark Energy 52 Non-baryonic CDM candidates • Axions – To reach density of order ρc their mass must be very small −6 −3 mAc ≈ 10 − 10 eV 2 – No experimental p evidence yyet • Most ost popu popular a ca candidate d date for o CDM C : WIMPss • • • • Weakly Interacting Massive Particles present in early hot universe – stable – relics of early universe Cold : Non Non-relativistic relativistic at time of freeze freeze-out out Weakly interacting : conventional weak couplings to standard model p particles - no electromagnetic g or strongg interactions • Massive: gravitational interactions (gravitational lensing …) 2011-12 Dark Matter-Dark Energy 53 WIMP candidates • Massive neutrinos: – standard neutrinos have low masses – contribute to HDM – Massive standard neutrinos up to MZ/2 = 45GeV/c2 are excluded by LEP – Non-standard neutrinos in models beyond standard model • Neutralino χ = Lightest SuperSymmetric Particle (LSP) in R-parity conserving SuperSymmetry (SUSY) ( ) theory h – Lower limit from accelerators ª 50 GeV/c2 – Stable particle – survived from primordial era of universe • Other SUSY candidates: sneutrinos, gravitinos, axinos • Kaluza-Klein states from models with universal extra dimensions • ……. 2011-12 Dark Matter-Dark Energy 54 Expected mass range • Assume WIMP interacts weakly and is non-relativistic at freezeout • Which Whi h mass ranges are allowed? ll d? • Cross section for WIMP annihilation vs mass leads to abundance vs mass → σ ~ s ~ M χ2 2W 2) 4 M χ2 = 2 M M < > s s 1) 4 M χ2 = →σ ~ 1 ~ 1 2 s Mχ 1 Ω χ ( t0 ) ~ σv 2011-12 Dark Matter-Dark Energy 55 Expected mass range: GeV-TeV 2) 4 M χ2 = HDM neutrinos → σ ~ s ~ M χ2 →σ ~ 1 ~ 1 2 s Mχ 1 Ω χ ( t0 ) ~ σv 2011-12 CDM WIMPs 2W 1) 4 4M M χ2 = 2W M M < > s s • Assume WIMP interacts weakly and is non-relativistic at freeze-out freeze out • Which mass ranges are allowed? W • Cross section for WIMP annihilation vs mass leads to abundance vs mass MWIMP (eV) Dark Matter-Dark Energy 56 Cross sections and densities -1 • WIMP with mass M must be non-relativistic at freeze-out Could be neutralino or • gas in thermal equilibrium kT other h weakly kl interacting massive particle Mc 2 → Boltzman gas 3 ⎛ MT ⎞ 2 N (T ) = ⎜ ⎟ e ⎝ 2π ⎠ ⎛ − Mc 2 ⎞ ⎜ ⎟ ⎜ kT ⎟ ⎝ ⎠ number density χ + χ ↔ f + f , ... χ W = N σ Annihilation v • Freeze-out when annihilation rate < expansion rate H ( ≤ H t freeze−out ) χ + χ → f + f , W + + W − , e + + e− ,... • Cross section s depends on model parameters 2011-12 Dark Matter-Dark Energy 57 Cross sections and densities -2 • assume that couplings are of order of weak interactions σ v ∼ GF M 2 • Rewrite R it expansion i rate t H (T ) = • Freeze-out condition W = N σ v ≈ H (TFO ) 1 66 ( g 1.66 ) 1 2 T2 M PL ⎛ − Mc 2 ⎞ ⎡ ⎜ ⎟⎤ 2 ⎜ ⎟ 3 k T T ⎢ 2 2 ⎠⎥ 2 ⎝ ⎡ ⎤⎦ ≈ MT e G M f ) ⎢( ⎥⎣ F M PL ⎢⎣ ⎥⎦ • f = constants t t ≈ 100 • Solve for P = Mcc2/kT at freeze-out 2011-12 * GF = Fermi constant Dark Matter-Dark Energy P ( FO ) = M χ c2 kTFO kT ≈ 25 58 Cross sections and densities - 3 • At freeze-out annihilation rate ≈ expansion rate N (TFO ) σ v ≈ H (TFO ) • WIMP number density today for T0 = 2.73K t0 N R (TFO ) ≈ ) = N (TFO ) 3 R (T0 ) ( 3 (T0 TFO ) × (TFO2 M PL ) 3 σv • Energy density today ρ χ = M χ N ( t0 ) ∼ 6 ×10 ∼ σv σv 3 0 PT M PL −31 GeV s −1 ρ χ 10−25 3 −1 Ω χ ( t0 ) = ∼ cm s ρc σv 2011-12 Dark Matter-Dark Energy P= M χ c2 kTFO ≈ 25 M PL ≈ 1019 GeV 59 N Number densityy Depends p on model Increasing <σAv> today P~25 P=M/T (time ->) 10−25 3 −1 Ω χ ( t0 ) ~ cm s σv 2011-12 Dark Matter-Dark Energy 60 Cross sections and densities - 4 • Relic abundance of WIMPs today 10−25 3 −1 Ω χ ( t0 ) ~ cm s σv • For Ωχ = 1 σ ( χ + χ → X ) ≈ 10 cm ≈ O ( pb ) −35 2 • O(weak interactions) fi 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 Mχv = 2 2 2011-12 ( ) v ~ 3 P c 1 2 ≈ 0.3 Dark Matter-Dark Energy vχ ≈ 0.3 c 61 Neutralino is good candidate for cold dark matter SUSY = extension of standard model at high g energy gy SUPERSYMMETRY 2011-12 Dark Matter-Dark Energy 62 What are we looking for? • Particle with charge = 0 [GeV TeV] domain • With mass in [GeV-TeV] • Only interacting through gravitational and weak interactions • Stable • Decoupled from radiation before BBN era • Has not yet been observed in laboratory = accelerators 2011-12 Dark Matter-Dark Energy 63 Why SuperSymmetry • Gives a unified picture of matter (quarks and leptons) and interactions (gauge bosons and Higgs bosons) • Introduces symmetry between fermions and bosons Q ffermion = boson Q boson = ffermion • Fills the gap between electroweak and Grand Unified Theory scale l M W 102 GeV ≈ 19 = 10−17 M PL 10 GeV • Solves problems of Standard Model, like the hierarchy problem: = divergence of radiative corrections to Higgs mass • Provides P id a dark d k matter tt canndidate did t 2011-12 Dark Matter-Dark Energy 64 SuperSymmetric particles • Need to introduce new particles: supersymmetric particles • Associate to all SM particles a superpartner with spin ±1/2 (fermion ↔ boson) fi sparticles • minimal SUSY: minimal supersymmetric extension of the SM – reasonable assumptions to reduce nb of parameters • Parameters P t = masses, couplings li - mustt be b determined d t i d from f experiment • Searches at colliders: so particles seen yet M > accessible range σ production d i < sensitivity 2011-12 Dark Matter-Dark Energy 65 The new particle table Particle table ((arXiv:hep-ph/0404175v2) pp / ) 2011-12 Dark Matter-Dark Energy 66 Neutralinos as dark matter • Supersymmetric partners of gauge bosons mix to neutralino mass eigenstates • Lightest neutralino χ 01 = χ = N11B + N12W3 + N13 H10 + N14 H 20 R-parity parity quantum number • R 3B + L+ 2 s • baryon number B, lepton number L, spin s R ≡ ( −1) • SM particles: ti l R = 1 and d sparticles: ti l R = -1 1 p+ p→q+g+ X q → q + χ10 g → qq + χ10 • In R R-parity parity conserving models Lightest Supersymmetric Particle (LSP) is stable • LSP = lightest neutralino fi dark matter candidate 2011-12 Dark Matter-Dark Energy 67 Expected abundance vs mass Wch2 • variation of neutralino 2 density as function of Ω χ h mass • Allowed by collider and direct search upper limits on cross sections Predictions of Constrained Minimal Supersymmetric extension of the Standard Model with 7 free parameters W=[.05-0.5] Ω [0.04 Ω= [ – 1.0]] • Expected mass range 50GeV – few TeV 2011-12 ( ) Neutralino N mass (GeV) (G V) Mliχ GeV Dark Matter-Dark Energy 68 The difficult p path to discoveryy WIMP DETECTION 2011-12 Dark Matter-Dark Energy 69 three complementary strategies 2011-12 Dark Matter-Dark Energy 70 Production at accelerators • Controlled production in laboratory: particle accelerators • LHC @ CERN 2011-12 Dark Matter-Dark Energy 71 Example from LHC Probed masses up to ~ TeV So signal was observed H. Bachacou EPS2011 p + p → q + g → jets j t + χ10 + χ10 2011-12 Dark Matter-Dark Energy 72 χ + N → χ + N′ 2011-12 experiment σ ( χ p ) < 10−44 cm 2 = 10−8 pb Dark Matter-Dark Energy 73 WIMPs in the Milky Way halo • Assume galaxy with dark halo gy densityy in ggalactic halo • Energy from rotation curves and simulations ρ χ ~ 0.3GeV cm3 • WIMP velocity in halo O(galactic objects) vχ ~ 270 km s −1 2011-12 Dark Matter-Dark Energy 74 Direct detection challenges R∝N ρχ Mχ σχp • low rate Æ large g detector • very small signal Æ low threshold • large background : protect against cosmic rays, radioactivity, … radioactivity 2011-12 Dark Matter-Dark Energy 75 Annual and diurnal modulation • Annual modulations due to movement of solar system in galactic WIMP halo – 30% effect • Diurnal modulations due to Earth rotation – 2% effect • Observed by DAMA – not confirmed by other experiments 2011-12 Dark Matter-Dark Energy 76 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 152.5 • If interpreted as SUSY dark matter: M ~ 10-50 GeV/c2 2011-12 Dark Matter-Dark Energy 77 Combining different experiments 2011-12 Dark Matter-Dark Energy 78 Noble liquids: XENON100 • 1400m under d mountain in Gran Sasso tunnell ((Italy) l ) : lower l rate of cosmic background • Sensitive core = 100kg liquid Xenon at -106°C • Pure materials – low radioactivityy • Recoil nucleus ionises liquid Xenon • Measure signal from ionisation and scintillation light produced during recoil of nucleon • Double D bl signal i l helps h l against i fake f k events • Started data taking in 2009 2011-12 Dark Matter-Dark Energy 79 2011-12 Dark Matter-Dark Energy 80 XENON100 2011-12 Dark Matter-Dark Energy 81 Combining different experiments 2011-12 Dark Matter-Dark Energy 82 Indirect detection of WIMPs • SSearch h for f signals i l off annihilation ihil i off WIMPs WIMP in i the h Milky Milk Way W halo h l • Detect the produced antiparticles, gamma rays, neutrinos • accumulation near galactic centre or in heavy objects like the Sun due to gravitational attraction 2011-12 Dark Matter-Dark Energy 83 Neutrino signals • Expect WIMPs to accumulate in heavy objects like Sun ρχ χ velocity distribution Earth Sun σcΝ νμ ν int. Gcapture Gannihilation 2011-12 χχ → qq ll W±, Z, H Dark Matter-Dark Energy Detector μ → →νμ 84 Neutrino detection 3km m ice la ayer South Pole station Cherenkov light pattern emitted by the muon is registered by an array of photomultiplier tubes (PMT) Photomultiplier p tubes µ * νμ 2011-12 Dark Matter-Dark Energy 85 Signal and background BG signal A few 10’000 atmospheric neutrinos per year from northern hemisphere Max. a few neutrinos per year from WIMPs ~1010 atmospheric BG muons per year from p southern hemisphere 2011-12 Dark Matter-Dark Energy 86 IceCube search results Sign nal? Num mber off eventss Neutralino 250 GeV to WW Data Background 2011-12 ψ(deg) • Search for neutrinos from WIMP annihilation in the Sun • No significant signal found • Rate is compatible with atmospheric background • Set upper limit on possible flux Dark Matter-Dark Energy 87 Combining the experimental searches σ SD ( χ p ) ⎡⎣cm 2 ⎤⎦ Direct detection experiments 2011-12 IceCube Dark Matter-Dark Energy SUSY models allowed by accelerator results 88 Summary • Observation Ob ti off dark d k matter tt as gravitational it ti l effects ff t – – – – – Rotation curves galaxies, mass/light ratios in galaxies Velocities of galaxies in clusters Gavitational lenses Primordial nucleosynthesis Anisotropies in CMB radiation • Nature of dark matter particles: – Baryons and MACHO’s – Neutrinos – Axions • Weakly Interacting Massive Particles (WIMPs) • Experimental WIMP searches – Accelerators – Direct detection experiments – Indirect detection • Dark energy 2011-12 Dark Matter-Dark Energy 89