Cosmology. Expanding Universe. Outline of Lecture 1. Expanding Universe Dark matter: evidence WIMPs Warm dark matter: gravitinos?

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1 Comology V.A. Rubakov Outline of Lecture 1 Expanding Univere Dark matter: evidence WIMP Warm dark matter: gravitino? Intitute for Nuclear Reearch of the Ruian Academy of Science, Mocow Expanding Univere The Univere at large i homogeneou, iotropic and expanding. 3d pace i Euclidean (obervational fact!) All thi i encoded in pace-time metric d 2 = dt 2 a 2 (t)dx 2 x :comovingcoordinate,labelditantgalaxie. a(t)dx :phyicalditance. a(t): cale factor, grow in time; a 0 : preent value (matter of convention) z(t)= a 0 a(t) 1: redhift Light of wavelength! emitted at time t ha now wavelength! 0 = a 0 a(t)! = (1 + z)!. Preent value H 0 =(71.0 ± 2.5) km/ Mpc =( yr) 1 1 Mpc = light yr = cm Hubble law (valid at z 1) z = H 0 r The Univere i warm: CMBtemperaturetoday T 0 = K H(t)= ȧ a : Hubble parameter, expanion rate It wa dener and warmer at early time.

2 Hubble diagram for SNe1a CMB pectrum 20 m 0 V (mag) z T = K mag = 5log 10 r + cont Preent number denity of photon Preent entropy denity = 2 2#2 45 T 0 3 In early Univere n " = #T 3 = cm 3 + neutrino contribution = cm 3 = 2#2 45 g T 3 g :numberofrelativiticdegreeoffreedomwithm T ; fermion contribute with factor 7/8. Friedmann equation: expanion rate of the Univere v total energy denity $ (M Pl = G 1/2 = GeV): (ȧ ) 2 H 2 = 8# a 3MPl 2 $ Eintein equation of General Relativity pecified to homogeneou iotropic pace-time with zero patial curvature. Preent energy denity $ 0 =$ c = 3M2 Pl 8# H2 6 GeV 0 = 5 10 cm 3 Entropy denity cale exactly a a 3 Temperature cale approximately a a 1.

3 Preent compoition of the Univere % i = $ i,0 $ c preent fractional energy denity of i-th type of matter. &% i = 1 i Dark energy: % ' = 0.72 $ ' tay (almot?) contant in time Non-relativitic matter: % M = 0.28 $ M = mn(t) cale a ( ) 3 a0 a(t) Dark matter: % DM = 0.23 Uual matter (baryon): % B = Relativitic matter (radiation): % rad = (for male neutrino) ( ) 4 $ rad = ((t)n(t) cale a a0 a(t) Dark energy domination 2.7 К Today 13.7 billion year z 0.7: acceleratedexpanionbegin matter domination 8700 K radiation-matter equality 57 thouand year radiation domination : Inflation??? Friedmann equation [ H 2 (t)= 8# ( ) 3 ( ) ] 4 3MPl 2 [$ ' + $ M (t)+$ rad (t)]= H0 2 a0 a0 % ' + % M + % rad a(t) a(t)...= Radiation domination= Matter domination= ' domination z eq = 3200 now T eq = 8700 K = 0.75 ev t eq = yr Expanion at radiation domination Friedmann equation: (ȧ a ) 2 H 2 = 8# 3M Pl $ Radiation energy denity: Stefan Boltzmann $ = #2 30 g T 4 g :numberofrelativiticdegreeoffreedom(about100 in SM at T 100 GeV). Hence H(T)= T 2 M Pl with M Pl = M Pl/(1.66 g ) GeV at T 100 GeV

4 Expanion law: Solution: t = 0: BigBangingularity Decelerated expanion: ä < 0. NB: '-domination H 2 = 8# 3MPl 2 $ = ȧ2 a 2 = cont a 4 a(t)=cont t H = ȧ a = 1 2t, $ ) 1 t 2 ȧ 2 a 2 = 8# 3MPl 2 $ ' = cont= a(t)=e H 't accelerated expanion. Caual tructure of pace-time in hot Big Bang theory Comological (particle) horizon Light travel along d 2 = dt 2 a 2 (t)dx 2 = 0 = dx = dt/a(t). If emitted at t = 0, travelfinitecoordinateditance t * = 0 dt a(t ) ) t at radiation domination * ) t = viible Univere increae in time Phyical ize of caually connected region at time t (horizon ize) t l H,t = a(t) 0 dt a(t ) = 2t at radiation domination In hot Big Bang theory at both radiation and matter domination l H,t t H 1 (t) Today l H,t0 15 Gpc = cm Cornertone of thermal hitory Big Bang Nucleoynthei, epoch of thermonuclear reaction p + n 2 H 2 H + p 3 He 3 He+ n 4 He up to 7 Li We ee many region that were caually diconnected by time t r. Why are they all the ame? Abundance of light element: meaurement v theory T = K, t = Earliet time in thermal hitory probed o far Recombination, tranitionfromplamatoga. z = 1090, T = 3000 K, t = year Lat cattering of CMB photon Neutrino decoupling: T = 2 3 MeV K, t Generation of dark matter Generation of matter-antimatter aymmetry may have happend before the hot Big Bang epoch

5 Y D 0.23 H He. Baryon denity % b h T = K,,T T He H D/H p CMB 3 He/H p Li/H p Baryon-to-photon ratio * 10 * 10 = * = baryon-to-photon ratio. Conitent with CMB determination of* WMAP Dark energy domination 2.7 К Today 13.7 billion year z 0.7: acceleratedexpanionbegin Unknown 4.6% ordinary matter, no antimatter 0.5% tar 0.3 1% neutrino 3000 K lat cattering of CMB photon 370 thouand year 8700 K radiation-matter equality 57 thouand year 72% 23% 10 9 K nucleoynthei Generaion of dark matter Generation of matter-antimatter aymmetry Inflation??? dark energy dark matter

6 Dark matter Rotation curve Atrophyical evidence: meaurement of gravitational potential in galaxie and cluter of galaxie Velocity curve of galaxie Velocitie of galaxie in cluter Original Zwicky argument, 1930 v 2 = G M(r) r Temperature of ga in X-ray cluter of galaxie Gravitational lening of cluter Etc. Gravitational lening Outcome % M $ M $ c = Auming ma-to-light ratio everywhere the ame a in cluter NB: only 10 % of galaxie it in cluter Nucleoynthei, CMB: % B = The ret i non-baryonic, % DM Phyical parameter: ma-to-entropy ratio. Stay contant in time. It value ( $DM ) 0 = % DM$ c 0 = GeV cm cm 3 = GeV

7 Comological evidence: growth of tructure CMB aniotropie: baryon denity perturbation at recombination photon lat cattering, T = 3000 K, z = 1100: ( ),$B, B $ B z=1100 (,T T ) CMB 10 4 Growth of perturbation (linear regime) Radiation domination Matter domination ' domination In matter dominated Univere, matter perturbation grow a,$ (t) ) a(t) $, ", DM, B Perturbation in baryonic matter grow after recombination only If not for dark matter, ( ),$ = $ today No galaxie, no tar... Perturbation in dark matter tart to grow much earlier (already at radiation-dominated tage) t eq t rec - t ' t WIMP NB: Need dark matter particle non-relativitic early on. Neutrino are not coniderable part of dark matter (way to et comological bound on neutrino ma, m. < 0.2 ev for every type of neutrino) If thermal relic: UNKNOWN DARK MATTER PARTICLES ARE CRUCIAL FOR OUR EXISTENCE Cold dark matter, CDM Warm dark matter m DM 100 kev m DM 1 30 kev Simple but very uggetive cenario Aume there i a new heavy table particle X Interact with SM particle via pair annihilation (and croing procee) X + X q q,etc Parameter: ma M X ;annihilationcroectionat non-relativitic velocity /(v) Aume that maximum temperature in the Univere wa high, T M X Calculate preent ma denity Recall H(T)= T 2 M Pl with M Pl = M Pl/(1.66 g ) GeV at T 100 GeV

8 Number denity of X-particle in equilibrium at T < M X : Maxwell Boltzmann n X = g X d 3 p (2#) 3 e M 2 X +p2 T = g X ( MX T 2# ) 3/2 e M X T Mean free time wrt annihilation: travel ditance 0 ann v,meet one X particle to annihilate with in volume /0 ann v = /0 ann vn X = 1 = 0 ann = 1 n X /v Freeze-out: 0 1 ann(t f ) H(T f ) = n X (T f ) /v T 2 f /M Pl = T f NB: large log T f M X /30 M X ln(m X M Pl /v ) Define /v / 0 (contant for -wave annihilation) Number denity at freeze-out T 2 f n X (T f )= / 0 MPl Number-to-entropy ratio at freeze-out and later on n X (T f ) (T f ) where # = 45/(2# 2 ). Ma-to-enropy ratio M X n X = # n X(T f ) g T 3 f = # ln(m XM Pl / 0) / 0 g (T f )M Pl = # ln(m XM Pl / 0) M X / 0 g M Pl Mot relevant parameter: annihilation cro ection / 0 /v at freeze-out M X n X = # ln(m XM Pl / 0) / 0 g (T f )M Pl Correct value, ma-to-entropy= GeV, for / 0 /v =(1 2) cm 2 Weak cale cro ection. Gravitational phyic and EW cale phyic combine into ma-to-entropy 1 M Pl ( ) TeV GeV 1 W SUSY: neutralino, X = 2 But ituation i rather tene already: annihilation cro ection i often too low Important upperion factor: /v ) v 2 ) T /M 2 becaue of p-wave annihilation in cae 22 Z f f : Relativitic f f = total angular momentum J = 1 22:identicalfermion= L = 0, parallelpinimpoible= p-wave Ma M X hould not be much higher than 100 GeV Weakly interacting maive particle, WIMP. Cold dark matter candidate

9 msugra at fairly low tan3 Larger tan3 i better 5000 tan 3 = 10, µ > tan 3 = 50, µ > m 0 (GeV) 3000 m 0 (GeV) 1000 m h = 114 GeV 2000 m h = 114 GeV m 1/2 (GeV) m 1/2 (GeV) Warm dark matter: gravitino? Cloud over CDM Numerical imulation of tructure formation with CDM how Too many dwarf galaxie Afewhundredatelliteofagalaxylikeour But only dozen oberved o far Too high denity in galactic center ( cup ) Not crii yet But what if one really need to uppre mall tructure? Warm dark matter Decouple when relativitic, T f m. Remain relativitic until T m (auming thermal ditribution). Doe not feel gravitational potential before that. Perturbation of wavelength horter than horizon ize at that time get meared out = mall ize object do not form ( free treaming ) Horizon ize at T m Preent ize of thi region l(t ) = H(T m) 1 = M Pl T 2 = M Pl m 2 High initial momenta of DM particle = Warm dark matter (modulo g factor). l c = T T 0 l(t)= M Pl mt 0 Object of initial comoving ize maller than l c are le abundant

10 Gravitino Initial ize of dwarf galaxy l dwar f 100 kpc cm Require l c M Pl mt 0 l dwarf = obtain ma of DM particle M Pl m 3 kev T 0 l dwar f (M Pl = GeV, T 1 0 = 0.1 cm). Particle of mae in 1 10 kev range are good warm dark matter candidate Ma m 3/2 F/M Pl F = SUSY breaking cale. = Gravitino light for low SUSY breaking cale. E.g. gauge mediation Light gravitino = LSP = Stable Decay width of uperpartner into gravitino + SM particle 4 S M5 S F 2 M S = ma of uperpartner S M5 S m 2 3/2 M2 Pl Gravitino production in decay of uperpartner d(n 3/2 /) dt = n S 4 S n S / = cont g 1 for T M S,whilen S ) e M S /T for T M S = production mot efficient at T M S (low comological expanion with unuppreed n S ) n 3/2 Ma-to-entropy ratio 4 S g H(T M S ) M Pl g M 2 S m 3/2 n 3/2 M3 S m 3/2 1 g 3/2 M Pl M 5 S m 2 3/2 M2 Pl m 3/2 n 3/2 & S M 3 S m 3/2 1 g 3/2 M Pl For m 3/2 = afewkev,ma-to-entropy= GeV M S GeV Need light uperpartner and low maximum temperature in the Univere, T max 1 TeV to avoid overproduction in colliion of uperpartner (and in decay of quark and gluino if they are heavy) Rather contrived cenario, but generating warm dark matter i alway contrived NB: 4 NLSP M5 S m 2 3/2 M2 Pl = c0 NLSP = afew mm afew 100 m for m 3/2 = 1 10 kev, M S = GeV Longer lifetime for heavier gravitino (CDM candidate)

11 TeV SCALE PHYSICS MAY WELL BE RESPONSIBLE FOR GENERATION OF DARK MATTER I thi guaranteed? By no mean. Another good DM candidate: axion. Plu a lot of exotica... Crucial impact of LHC to comology, direct and indirect dark matter earche WIMP, ignal at LHC: Stronget poible motivation for direct and indirect detection Inferred interaction with baryon = trategy for direct detection AhandleontheUnivereat T =(afew) 10 GeV (a few) 100 GeV t = cf. T = 1 MeV, t = 1 at nucleoynthei Gravitino-like AlotofworktomakeurethatitiindeedDMparticle Hard time for direct and indirect earche No ignal at LHC Need luck to figure out who i dark matter particle Need more hint from comology and atrophyic Outline of Lecture 2 Baryon aymmetry of the Univere. What the problem? Electroweak baryogenei. Electroweak baryon number violation Electroweak tranition What can make electroweak mechanim work? Dark energy