Particle Cosmology. V.A. Rubakov. Institute for Nuclear Research of the Russian Academy of Sciences, Moscow and Moscow State University

Transcription

1 Particle Cosmology V.A. Rubakov Institute for Nuclear Research of the Russian Academy of Sciences, Moscow and Moscow State University

2 Topics Basics of Hot Big Bang cosmology Dark matter: WIMPs Axions Warm dark matter, gravitinos Baryon asymmetry Electroweak mechanism Leptogenesis

3 Lecture 1

4 Outline of Lecture 1 Basics of Hot Big Bang cosmology Dark matter: evidence WIMPs

5 Basics of Hot Big Bang cosmology The Universe at large is homogeneous, isotropic and expanding. 3d space is Euclidean (observational fact!) All this is encoded in space-time metric ds 2 = dt 2 a 2 (t)dx 2 x : comoving coordinates, label distant galaxies. a(t)dx : physical distances. a(t): scale factor, grows in time; a 0 : present value (matter of convention) z(t)= a 0 a(t) 1 : redshift Light of wavelength λ emitted at time t has now wavelength λ 0 = a 0 a(t) λ =(1+z)λ. H(t)= ȧ a : Hubble parameter, expansion rate

6 Present value H 0 =(70.4±1.4) km/s Mpc =( yrs) 1 1 Mpc= light yrs= cm Hubble law (valid at z 1) z=h 0 r The Universe is warm: CMB temperature today T 0 = K Fig. It was denser and warmer at early times. Fig.

7 Hubble diagram for SNe1a 20 m 0 V (mag) z mag=5log 10 r+const

8 CMB spectrum T = K

9 Present number density of photons Present entropy density n γ = #T 3 = cm 3 s=2 2π2 45 T neutrino contribution=3000 cm 3 In early Universe s= 2π2 45 g T 3 g : number of relativistic degrees of freedom with m T; fermions contribute with factor 7/8. Entropy density scales exactly as a 3 Temperature scales approximately as a 1.

10 Friedmann equation: expansion rate of the Universe vs total energy density ρ (M Pl = G 1/2 = GeV): (ȧ ) 2 H 2 = 8π a 3M 2 Pl Einstein equations of General Relativity specified to homogeneous isotropic space-time with zero spatial curvature. Present energy density ρ 0 =ρ c = 3M2 Pl 8π H2 6 GeV 0 = 5 10 cm 3 ρ

11 Present composition of the Universe Ω i = ρ i,0 ρ c present fractional energy density of i-th type of matter. Ω i = 1 i Dark energy: Ω Λ = 0.72 ρ Λ stays (almost?) constant in time Non-relativistic matter: Ω M = 0.28 ρ M = mn(t) scales as ( a0 a(t) ) 3 Dark matter: Ω DM = 0.23 Usual matter (baryons): Ω B = Relativistic matter (radiation): Ω rad = (for massless neutrinos) ( ) 4 ρ rad = ω(t)n(t) scales as a0 a(t)

12 Friedmann equation H 2 (t)= 8π 3MPl 2 [ρ Λ + ρ M (t)+ρ rad (t)]= H0 2 [ Ω Λ + Ω M ( a0 a(t) ) 3 + Ω rad ( ) ] 4 a0 a(t)... = Radiation domination= Matter domination= Λ domination z eq = 3200 now T eq = 8700 K=0.75 ev t eq = yrs

13 Dark energy domination 2.7 К Today 13.7 billion years z 0.7: accelerated expansion begins matter domination 8700 K radiation-matter equality 57 thousand years radiation domination s: Inflation???

14 Expansion at radiation domination Friedmann equation: (ȧ a ) 2 H 2 = 8π 3M Pl ρ Radiation energy density: Stefan Boltzmann ρ = π2 30 g T 4 g : number of relativistic degrees of freedom (about 100 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

15 Expansion law: H 2 = 8π 3MPl 2 ρ = ȧ2 a 2 = const a 4 Solution: t = 0: Big Bang singularity Decelerated expansion: ä<0. NB: Λ-domination a(t)=const t H = ȧ a = 1 2t, ρ 1 t 2 ȧ 2 a 2 = 8π 3MPl 2 ρ Λ = const= a(t)=e H Λt accelerated expansion.

16 Cornerstones of thermal history Big Bang Nucleosynthesis, epoch of thermonuclear reactions p+n 2 H 2 H+p 3 He 3 He+n 4 He up to 7 Li Abundances of light elements: measurements vs theory T = K, t = s Earliest time in thermal history probed so far Fig. Recombination, transition from plasma to gas. z=1090, T = 3000 K, t = years Last scattering of CMB photons Neutrino decoupling: T = 2 3 MeV K, t 0.1 1s Generation of dark matter Generation of matter-antimatter asymmetry Fig. may have happend before the hot Big Bang epoch

17 Y p D H He. Baryon density Ω b h D/H p BBN CMB He/H p Li/H p Baryon-to-photon ratio η η 10 = η = baryon-to-photon ratio. Consistent with CMB determination of η

18 T = K, δt T WMAP

19 Dark energy domination 2.7 К Today 13.7 billion years z 0.7: accelerated expansion begins 3000 K last scattering of CMB photons 370 thousand years 8700 K radiation-matter equality 57 thousand years 10 9 K nucleosynthesis s Generaion of dark matter Generation of matter-antimatter asymmetry Inflation???

20 Unknowns 4.6% ordinary matter, no antimatter 0.5% stars 0.3 1% neutrino 72% 23% dark energy dark matter

21 Dark matter Astrophysical evidence: measurements of gravitational potentials in galaxies and clusters of galaxies Velocity curves of galaxies Fig. Backup slide 1 Velocities of galaxies in clusters Original Zwicky s argument, 1930 s v 2 = G M(r) r Temperature of gas in X-ray clusters of galaxies Gravitational lensing of clusters Fig. Backup slide 2 Etc.

22 Outcome Ω M ρ M ρ c = Assuming mass-to-light ratio everywhere the same as in clusters NB: only 10 % of galaxies sit in clusters Nucleosynthesis, CMB: Ω B = The rest is non-baryonic, Ω DM Physical parameter: mass-to-entropy ratio. Stays constant in time. Its value ( ρdm s ) 0 = Ω DMρ c s 0 = GeV cm cm 3 = GeV

23 Cosmological evidence: growth of structure CMB anisotropies: baryon density perturbations at recombination photon last scattering, T = 3000 K, z = 1100: δ B ( ) δρb ρ B z=1100 ( δt T ) CMB 10 4 In matter dominated Universe, matter perturbations grow as δρ ρ (t) a(t) Perturbations in baryonic matter grow after recombination only If not for dark matter, ( ) δρ = ρ today No galaxies, no stars... Perturbations in dark matter start to grow much earlier (already at radiation-dominated stage)

24 Growth of perturbations (linear regime) Radiation domination Matter domination Λ domination δ DM δ γ δ B Φ t eq t rec t Λ t

25 NB: Need dark matter particles non-relativistic early on. Neutrinos are not considerable part of dark matter (way to set cosmological bound on neutrino mass, m ν < 0.2 ev for every type of neutrino) If thermal relic: UNKNOWN DARK MATTER PARTICLES ARE CRUCIAL FOR OUR EXISTENCE Cold dark matter, CDM m DM 100 kev Warm dark matter m DM 1 30 kev

26 WIMPs Simple but very suggestive scenario Assume there is a new heavy stable particle X Interacts with SM particles via pair annihilation (and crossing processes) X+ X q q,etc Parameters: mass M X ; annihilation cross section at non-relativistic velocity σ(v) Assume that maximum temperature in the Universe was high, T M X Calculate present mass density (somewhat oversimplified) Recall H(T)= T 2 M Pl with M Pl = M Pl/(1.66 g ) GeV at T 100 GeV

27 Number density of X-particles in equilibrium at T < M X : Maxwell Boltzmann n X = g X d 3 p (2π) 3e M 2 X +p2 T = g X ( MX T 2π ) 3/2 e M X T Mean free time wrt annihilation: travel distance τ ann v, meet one X particle to annihilate with in volume στ ann v = στ ann vn X = 1 = τ ann = 1 n X σv Freeze-out: τ 1 ann(t f ) H(T f ) = n X (T f ) σv T 2 f /M Pl = T f M X ln(m X M Pl σv ) NB: large log T f M X /20 Define σv σ 0 (constant for s-wave annihilation)

28 Number density at freeze-out n X (T f )= T 2 f σ 0 M Pl Number-to-entropy ratio at freeze-out and later on n X (T f ) s(t f ) where #=45/(2π 2 ). Mass-to-enropy ratio = # n X(T f ) g T 3 f = # ln(m XM Pl σ 0) M X σ 0 g M Pl Confirmed by honest calculation, backup slides 3-5 M X n X s = # ln(m XM Pl σ 0) σ 0 g (T f )M Pl Most relevant parameter: annihilation cross section σ 0 σv at freeze-out

29 M X n X s = # ln(m XM Pl σ 0) σ 0 g (T f )M Pl Correct value, mass-to-entropy= GeV, for σ 0 σv =(1 1.3) cm 2 =(1 1.3) pb Weak scale cross section. Gravitational physics and EW scale physics combine into mass-to-entropy 1 M Pl ( ) TeV GeV α W Mass M X should not be much higher than 100 GeV Weakly interacting massive particles, WIMPs. Cold dark matter candidates, T f M X /20, and in kinetic equilibrium long after.

30 WIMP candidates SUSY: neutralinos, X = χ But situation is often tense: annihilation cross section is often too low Important supperssion factor: σv v 2 T/M χ because of p-wave annihilation in case χχ Z f f: Relativistic f f = total angular momentum J = 1 χχ: identical fermions = L=0, parallel spins impossible = p-wave

31 Example: Higgs portal Many other possibilities Just to have a WIMP, introduce scalar singlet S. Renormalizable interaction with Higgs only. Impose symmetry S S = stable S. L S = 1 ( µ 2 ( µs) 2 2 s 2 S2 + λ SH 4 S2 H H+ λ ) S 4 S4 In vacuo H = v/ 2+h/ 2: vertices λ SH 4 vhs2 + λ SH 8 h2 S 2

32 Light S, m S m H /2. Fairly popular a year ago No longer viable: main annihilation channel SS b b. Cross section suppressed by y 2 b m2 b S b λ HS v H y b = m b v S b σv =1 pb = quite large λ SH = Invisible Higgs decay H SS by far dominant. H λ HS v S S Nice excersize: calculate σv and Γ(H SS)

33 Degeneracy: m s just below m H /2. Pole enhanced σv = not so large λ SH = + threshold suppression of invisible Higgs decay H SS = viable and interesting. Signature: invisible Higgs decay. Relatively heavy S: m s > m W. Main annihilation channels SS WW,ZZ,HH. Interesting for direct dark matter detection experiments and LHC at m S 150 GeV. Signature pp H +jet jet+ss; jet + missing E T Sumary of direct detection limits: backup slide 6

34 TeV SCALE PHYSICS MAY WELL BE RESPONSIBLE FOR GENERATION OF DARK MATTER Is this guaranteed? By no means. Another good DM candidate: axion. Plus a lot of exotica... Crucial impact of LHC to cosmology, direct and indirect dark matter searches

35 Backup slides

36 1. Rotation curves

37 2. Gravitational lensing

38 3. Honest calculation of WIMP abundance Boltzmann equation for =n X /s (accounts for expansion): d dt = σv s( 2 2 eq) First term in r.h.s.: annihilation; second term: creation Creation terminates when d lnn X,eq dt σv n X,eq Recall n X,eq = g X ( MX T 2π ) 3/2 e M X T Then d lnn eq dt (m X /T)H = m X T/MPl, so creation terminates at T = T such that n X,eq (T ) m XT M Pl σv

39 4. This again gives (although exact result is slightly different from main lecture, e.g., by argument of log not shown) T M X ln(m X M Pl σv ) Since t, WIMPs annihilate, In terms of T this reads This integrates to d dt = σv s 2 d dt = 2π2 45 g M Pl σv 2 1 (T) 1 (T )= 2π2 45 g M Pl σv (T T)

40 5 At late times (low temperatures) we finally have 1 = # T σ 0 g MPl = # ln(m XM Pl σ 0) M X σ 0 g M Pl which is precisely the same result as in main lecture, except for precise argument of log (not shown). Note that this value of is much smaller than (T ) 1 s(t ) m X T M Pl σv = #m X T 1 T σ 0 g M Pl So, it indeed makes sense to talk about two-stage process: termination of creation and then wash-out by annihilation.

41 6.Direct detection ] 2 WIMP-Nucleon Cross Section [cm DAMA/Na CoGeNT XENON10 (2011) DAMA/I CRESST-II (2012) EDELWEISS (2011/12) XENON100 (2012) observed limit (90% CL) Expected limit of this run: ± 1 σ expected ± 2 σ expected SIMPLE (2012) CDMS (2010/11) COUPP (2012) ZEPLIN-III (2012) XENON100 (2011) WIMP Mass [GeV/c ]