The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 :...
Transcript of The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 :...
The expanding universe
Lecture 2
Expanding universe : content• part 1 : ΛCDM model ingredients: Hubble flow, cosmological principle, geometry of universe
• part 2 : ΛCDM model ingredients: dynamics of expansion, energy density components in universe
• Part 3 : observation data – redshifts, SN Ia, CMB, LSS, light element abundances ‐ ΛCDM parameter fits
• Part 4: radiation density, CMB• Part 5: Particle physics in the early universe, neutrino density
• Part 6: matter‐radiation decoupling• Part 7: Big Bang Nucleosynthesis• Part 8: Matter ‐ antimatter asymmetryy y
2013‐14 Expanding Universe lect 2 2
Last lecture• Universe is flat k=0
• Expansion dynamics is described by Friedman‐LemaîtreExpansion dynamics is described by Friedman Lemaître equation
( ) ( )( ) ( )
( )( )
22
22
83
NR t G cR t R t
π⎛ ⎞= −⎜ ⎟⎜ ⎟
⎝ ⎠H t k
≡ totρ t
• Cosmological redshift ( )( ) ( ) ( )0
01 0 0R t
z z t z tR t
+ = = = = ∞
( ) ( )( )R t⎝ ⎠
• Closure parameter
( ) ( ) ( )R t
( ) ( )tΩ =
ρ t( )
2303 5 4Ht GeV mρ
• Expansion rate as function of redshift
( ) ( )ct
tρΩ = ( ) 0
0 5.48 N
c t GeV mG
ρπ
= =
• Expansion rate as function of redshift
( ) ( )( ) ( )( ) ( ) ( )( )3 4 22 1 1 1H t z z z⎡ ⎤= + + + + + +⎣ ⎦0 0 0 02
0 m r Λ kΩ t Ω t Ω t ΩH t
2013‐14 Expanding Universe lect 2 3
⎣ ⎦
reslectur
Todays
ΩCDM
T
> TeV CDMPart 5
© Rubakov2013‐14 4Expanding Universe lect 2
reslectur
Todays
ΩCDM
T
> TeV( ) ( )N B N anti B≠ − CDMPart 5
( ) ( )part 8
© Rubakov2013‐14 5Expanding Universe lect 2
reslectur
ΩneutrinoPart 5
Todays
T
ΩCDM( ) ( )N B N anti B≠ − CDMPart 5
( ) ( )part 8
© Rubakov2013‐14 6Expanding Universe lect 2
re
ΩbaryonsPart 7s
lectur
Todays
ΩneutrinoPart 5T Part 5
ΩCDM( ) ( )N B N anti B≠ − CDMPart 5
( ) ( )part 8
© Rubakov2013‐14 7Expanding Universe lect 2
Ω
re
ΩradPart 4&6
ΩbaryonsPart 7s
lectur
Todays
ΩneutrinoPart 5T Part 5
ΩCDM( ) ( )N B N anti B≠ − CDMPart 5
( ) ( )part 8
© Rubakov2013‐14 8Expanding Universe lect 2
Part 4Part 4radiation component - CMBpPhysics of the Cosmic Microwave Backgroundy g
Present day photon density
CMB in Big Bang model
Matter
photonsare released
© U i O
are released
© Univ Oregon
Baryons/nuclei and Photons decouple/freeze‐outBaryons/nuclei and photons in thermal equilibrium
Photons decouple/freeze outDuring expansion they cool
downExpect to see today a uniform
γ radiation which behaves like a bl k b d di ti
2013‐14 Expanding Universe lect 2 10
black body radiation
CMB discovery in 1965di d i 1965 b P i d Wil (B ll l b )• discovered in 1965 by Penzias and Wilson (Bell labs) when searching for radio emission from Milky Way
• Observed a uniform radio noise from outside the Milky• Observed a uniform radio noise from outside the MilkyWay
• This could not be explained by stars radio galaxies etc• This could not be explained by stars, radio galaxies etc
• Use Earth based observatory: limited to cm wavelengths due to absorption of mm waves inwavelengths due to absorption of mm waves in atmosphere
• Observed spectrum was compatible with black body p p yradiation with T = (3.5 ±1) K
• Obtained the Nobel Prize in 1978 (http://nobelprize.org/)
2013‐14 Expanding Universe lect 2 11
T d l h i lli
COBE : black body spectrum• To go down to mm wavelengths : put instruments on satellites
• COBE = COsmic Background Explorer (NASA) satellite observations in 1990s: mm wavelengths1990s: mm wavelengths
• Large scale dipole anisotropy due to motion of solar system in universe with respect to CMB rest frameuniverse, with respect to CMB rest frame
( )solar system 300 kmv s≈
• Strong radio emission in galactic plane
• After subtraction of dipole and away from galactic centre: radiation• After subtraction of dipole and away from galactic centre: radiation was uniform up to 0.005%
• Has perfect black body spectrum with T = 2 735±0 06 K (COBE 1990)• Has perfect black body spectrum with T = 2.735±0.06 K (COBE 1990)• Discovered small anisotropies/ripples over angular ranges Dq=7°• 2006 Nobel prize to Smoot and Mather for discovery of anisotropies• 2006 Nobel prize to Smoot and Mather for discovery of anisotropies
2013‐14 Expanding Universe lect 2 12
CMB temperature map
( )3dipole 10T O mKT−Δ ≈ →
ll i l t f Bl k B d di ti( )510T O µKT
−Δ ≈ →small ripples on top of Black Body radiation:
2013‐14 Expanding Universe lect 2 13
COBE measures black body spectrum
I t it Ql=2mm 0.5mm
• Plancks radiation law for relativistic photon gas
Intensity Q• Black body withtemperature T emitstemperature T emitsradiation with power Q atfrequencies w
3
frequencies w
( )3
2 2,4
kQ
c ωω
π=
TTω
Frequency n (cm‐1)
12
keω πν
−=
T
2013‐14 Expanding Universe lect 2 14
q y ( )
COBE measures black body spectrum
I t it Ql=2mm 0.5mm
• CMB has ‘perfect’ black body spectrum
Intensity Q• Fit of data of differentobservatoria to black bodyobservatoria to black body spectrum gives (pdg.lbl.gov, CMB)
( ) ( )( )
2.7255 0.0006
2
T CMB K
λ
= ±
CMB)
( )max 2mmλ =
Frequency n (cm‐1)0.235E kT meV= =
• Or
2013‐14 Expanding Universe lect 2 15
q y ( )
radiation energy density vs time • In our model the early universe is radiation dominated
• For flat universe→ Friedmann equationq2
2
83
Nrad
GRR
π ρ⎛ ⎞= ⎜ ⎟⎝ ⎠
• energy density of radiation during expansion
3R ⎝ ⎠
1281 4 4 N radGd R π ρρ ⎛ ⎞
= − = − ⎜ ⎟( )4 41rad z Rρ −∝ + ∝
• Integration yields
3Rρ ⎜ ⎟⎝ ⎠dt
23 1
( )
• Integration yields( )
22
2
3 132 N
radcc tG
ρπ
=t
2013‐14 Expanding Universe lect 2 16
CMB number density today 1• CMB photons have black body spectrum today
• They also had black body spectrum when CMB was createdThey also had black body spectrum when CMB was created
• But ! Temperature T in past was higher than today
• CMB = photon gas in thermal equilibrium
• → Bose‐Einstein distribution : number of photons per unit volume in momentum interval [p,p+dp]
( )2
Ep dpn p dp
⎛ ⎞= ⎜ ⎟⎡ ⎤ ⎝ ⎠
γg2
gγ = number of 2 3 1
Ekeπ
⎡ ⎤ ⎝ ⎠−⎢ ⎥⎣ ⎦
T 2 photon substates
2013‐14 Expanding Universe lect 2 17
Black body
CMB number density today 2
( )N
n n p dpVγ
γ = = ∫ ( )Vγ ∫
gγ=2
31 kT⎛ ⎞2
12.404 kTncγ π
⎛ ⎞= ⎜ ⎟⎝ ⎠
T=2.725K
( ) 3411n t cm−
2013‐14 Expanding Universe lect 2 18
( )0 411n t cmγ =
CMB energy density today
( )2c n p dpρ = ∫ E
( )( )
442
32
115
c kT πρ⎛ ⎞
= ⎜ ⎟⎝ ⎠
( )( )32 15c
ρπ
⎜ ⎟⎝ ⎠
T 2 725K
( )2 30 261t M V −
T=2.725K
( )2 30 0.261rc t MeV mρ =
( )054.84 10r
r t ρρ
−Ω = = ×
2013‐14 Expanding Universe lect 2 19
cρ
CMB temperature vs time 2
22
3 132rad
ccG
ρπ
=t ( )42 4
2 3 3
12 15radg
c kc
γρ ππ
⎛ ⎞= × ×⎜ ⎟
⎝ ⎠T
11 43 5 445 2 1⎛ ⎞⎛ ⎞ 1 31 1MeV
32 NGπ t 2 15 cπ⎝ ⎠
43 5 4
132
45 2 132
ckG gγπ
⎛ ⎞⎛ ⎞= × ×⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
Tt
1.31 1rad dom
MeVTk− = 1
2t
• for t0 = 14Gyr expect TCMB (today) ª 10K !!! for t0 14Gyr expect TCMB (today) 10K !!!
• BUT! COBE measures T = 2.7K
• Explanation???
2013‐14 Expanding Universe lect 2 20
Summary
( )42 1radiation c zρ +∼ ( )( )32
2
1matter c z
t
ρ +∼
( )
2
22 1
vacuum c cst
curvature c z
ρ
ρ +
∼
∼
2013‐14 Expanding Universe lect1 21
Questions?
Part 5Part 5particle physics in the early universep p y y
Radiation dominated universe
From end of inflation to matter‐radiation decoupling
From ~ 107 GeV to eVFrom 107 GeV to eV
Physics beyond the Standard Model, SM, nuclear physics
Radiation domination eraPlanck era GUT eraPlanck era GUT era
kT• At end of inflation phase
there is a reheatingh
TeVphase
• Relativistic particles are t dcreated
• Expansion is radiation dominateddominated
• Hot Big Bang evolutionstartsstarts
2013‐14 Expanding Universe lect 2 24
t
Radiation domination era
• At end of inflation phase there is a reheatinghphase
• Relativistic particles are t dcreated
• Expansion is radiation dominateddominated
• Hot Big Bang evolutionstartsstarts
R
2013‐14 Expanding Universe lect 2 25
Planck era GUT era t
Radiation domination eraPlanck era GUT eraPlanck era GUT era
kT
TeVToday’s lecture
2013‐14 Expanding Universe lect 2 26
t
Grand Planck mass 1 TeV‐100 Unification~ 1015 GeV
~ 1019 GeV GeVLHC‐LEP
Inflation periodperiod
2013‐14 Expanding Universe lect 2 27
Today’s lecture
Grand Planck mass 1 TeV‐100
Today s lecture
Unification~ 1015 GeV
~ 1019 GeV GeVLHC‐LEP
Inflation periodperiod
2013‐14 Expanding Universe lect 2 28
Relativistic particles
Radiation dominated
kT >> 100 GEV
2013‐14 Expanding Universe lect 2 29
relativistic particles in early universe• In the early hot universe relativistic fermions and bosons contribute to the energy density
• They are in thermal equilibrium at mean temperature T
2d ⎛ ⎞g• Fermion gas = quarks, leptons• Fermi‐Dirac statistics
( )2
2 3 21E
kT
p dpn p dpeπ
⎛ ⎞= ⎜ ⎟⎜ ⎟⎡ ⎤ ⎝ ⎠⎢ ⎥⎣ ⎦
fg
+Fermi Dirac statistics(gf = nb of substates)
⎢ ⎥⎣ ⎦
• boson gas = photons, W and Z bosons … • Bose Einstein statisti s ( )
2p dpd⎛ ⎞⎜ ⎟bg• Bose Einstein statistics
(gb = nb of substates)( )
2 3 21E
kT
p pn p dpeπ
= ⎜ ⎟⎡ ⎤ ⎝ ⎠⎢ ⎥⎣ ⎦
bg
−
2013‐14 Expanding Universe lect 2 30
⎣ ⎦
relativistic particles in early universe• Bosons and fermions contribute to energy density with
2p dp ⎛ ⎞g 2d ⎛ ⎞g( )2 3 21
EkT
p dpn p dpeπ
⎛ ⎞= ⎜ ⎟⎡ ⎤ ⎝ ⎠
⎢ ⎥⎣ ⎦
bg
−( )
2
2 3 21E
kT
p dpn p dpeπ
⎛ ⎞= ⎜ ⎟⎜ ⎟⎡ ⎤ ⎝ ⎠
⎢ ⎥⎣ ⎦
fg
+⎢ ⎥⎣ ⎦ ⎢ ⎥⎣ ⎦
( )2c n p dpρ = ∫ E ( )c n p dpρ = ∫ E
( ) ( )42 4* 2 3 3
*1 715 2 8b fc t kT g ggρ π
⎛ ⎞= = +⎜ ⎟⎜ ⎟
⎝ ⎠∑ ∑
*g( ) ( ) 2 3 315 2 8b fcπ ⎜ ⎟⎝ ⎠
∑ ∑
2013‐14 Expanding Universe lect 2 31
Degrees of freedom for kT > 100 GeVb i ti l t t lbosons spin per particle total
W+ W‐
If we take only the known particles
Z
gluons
photonphotonH‐boson
total bosons 28
fermions spin per particle total
quarksantiquarksantiquarks
e,µ,τneutrinos
2013‐14 Expanding Universe lect 2 32
anti‐neutrinos
total fermions 90
Degrees of freedom for kT > 100 GeVbosons spin per particle total
W+W 1 3 2 x 3 = 6W+ W‐ 1 3 2 x 3 = 6
Z 1 3 3
gluons 1 2 8 x 2 = 16
photon 1 2 2
H‐boson 0 1 1
total bosons 28total bosons 28
fermions spin per particle total
quarks ½ 3 (color) x 2 (spin) 6 x 3 x 2 = 36
antiquarks 36antiquarks 36
e,µ,τ ½ 2 6 x 2 = 12
neutrinos LH 1 3 x 1 = 3
2013‐14 Expanding Universe lect 2 33
anti‐neutrinos RH 1 3 x 1 = 3
total fermions 90
Degrees of freedom for kT > 100 GeV• Assuming only particles from Standard Model of particlephysics
* 728 90 106.758
g = + × =
• Energy density in hot universe
⎛ ⎞*
( ) ( )42 4* 2 3 3
115 2
c t kTc
ρ ππ
⎛ ⎞= ⎜ ⎟
⎝ ⎠
*g⎝ ⎠
what happens if there were particles fromtheories beyond the Standard Model?
2013‐14 Expanding Universe lect 2 34
For instance : SuperSymmetry• At LHC energies and higher : possibly SuperSymmetry
• Symmetry between fermions and bosonsSymmetry between fermions and bosons
• Consequence is a superpartner for every SM particle
~ D bl d f f d *• ~ Double degrees of freedom g*
2013‐14 Expanding Universe lect 2 35
Neutralino = Dark Matter ?• Neutral gaugino and higgsino fields mix to form 4 mass eigenstates
→ 4 neutralinos• no charge no colour only weak and gravitational• no charge, no colour, only weak and gravitationalinteractions
i Li ht t S t i P ti l LSP i R it0• is Lightest Supersymmetric Particle – LSP ‐ in R‐parityconserving scenarios → stable
01χ
• Massive : Searches at LEP and Tevatron colliders
( )1 20 50m GeV cχ >( )0 50m GeV cχ >
2013‐14 Expanding Universe lect 2 36
Neutralino = Dark Matter ?• Lightest neutralino may have been created in the early hot universe when ( )1 2
0kT m cχ>>
• Equilibrium interactions 1 1e e χ χ+ −+ ↔ +
( )0kT m cχ>>
• Equilibrium interactions
• When kT is too low, neutralinos freeze‐out (decouple) 0 0e e χ χ+ ↔ +
1 1+1 1+
• → are non‐relativistic at decoupling = ‘cold’
1 10 0e e χ χ+ −+ ← +1 1
0 0e e χ χ+ −+ → +
• survive as independent population till today
• the observed dark matter abundance today puts an upper• the observed dark matter abundance today puts an upperlimit on the mass (chapter 7)
( )1 25m TeV cχ <1Ω <
2013‐14 Expanding Universe lect 2 37
( )0 5m TeV cχ <1CDMΩ <
Questions?
COOLDOWN TO A FEW GEV
2013‐14 Expanding Universe lect 2 39
Cool down from > TeV to kT ª GeV• Start from hot plasma of leptons, quarks, gauge bosons, Higgs, exotic particles
• Temperature decreases with time 12
1~rad domTt−
• Production of particles M stops when 2kT Mc<<• For example,
e e W W+ − + −+ → + 2 160Ws M GeV> =when
p p t t X+ → + + when 2 346tops M GeV> =
• some particles decay: W, Z, t .. ( ) 23, 10W Z sτ −≈
• Run out of heavy particles when kT<<100GeV2013‐14 Expanding Universe lect 2 40
Age of universe at kT ≈ few GeV• Radiation dominated expansion since Big Bang
1 31 1M V1.31 1rad dom
MeVTk− = 1
2t
• Calculate time difference relative to Planck era
2013‐14 Expanding Universe lect 2 41
Quarks form hadrons
COOLDOWN TO kT ≈ 200 MEVQ
2013‐14 Expanding Universe lect 2 42
A phase transition
200 MeV
Quarks form hadronsDecay of particles with lifetime < µsec
g*
kT(G V)2013‐14 Expanding Universe lect 2 43
kT(GeV)
Down to kT ª 200 MeV• Phase transition from Quark Gluon Plasma (QGP) to hadrons
• Ruled by Quantum Chromo Dynamics (QCD) describing strong interactions
• Strong coupling constant is ‘running’ : energy dependent
• From perturbative regime to non‐perturbative regime aroundΛQCD
200QCD MeVΛ =( ) ( )2
0
2 222
1~4 lnStrong
Sg
Qb
α μπ μ
= =QCDΛ
E Tμ ∝ ∝ From fit to data( )0 lnb μ QCDΛ
confinement
When µ ≈ 200 MeV
αQuarks cannot be free at distances
of more than 1fm = 10‐15m
αst
2013‐14 Expanding Universe lect 2 44
Colour confinementlarge distancesg
Asymptotic freedom
2013‐14 Expanding Universe lect 2 45
small distances
around and below kT ª 200 MeV• free quarks and gluons are gone and hadrons are formed
• Most hadrons are short lived and decay withy
( ) ( )8 2310 weak ints. 10 strong ints.s sτ − −= − << 1µs
• Example ( ) ( )1115 uds pp μπ νμ− −Λ = → + +→ +
• Leptons : muon and tauon decay weakly
0 n n eeπ + −+→ + → +
Stable or longLeptons : muon and tauon decay weakly
( ) 15319 10 sτ τ −= ×( ) 6
Stable or long lived
( )( )
319 10
17%
s
μ τ
τ τ
τ ν νμ− − +
= ×
→ +( ) 62 10
ee
s
μ
τ μ
μ ν ν
−
− − +
×
→ +
=
2013‐14 Expanding Universe lect 2 46
.......→ee μμ ν ν+→ +
pauze
QUESTIONS?Q
Run out of unstable hadrons
Neutrino decoupling/freeze‐outp g/
Big bang nucleosynthesis
COOLDOWN TO A FEW MEV
2013‐14 Expanding Universe lect 2 48
Cooldown to kT ª 10MeV• After about 1ms all unstable particles have decayed
• Most, but not all, nucleons annihilate with anti‐nucleons (chapter 6)
p p γ γ+ → + 18~ 10baryonsnn
−expect
106.75* 7 43 10102g ⎛ ⎞= + = ≈⎜ ⎟
nγ
108
104
2g = + = ≈⎜ ⎟⎝ ⎠
g*10
3 4
we are left withg + e-, ne, nm, nt
GeV MeV
3.4 g , e, m, tand their anti‐particles
kT(GeV)TeV2013‐14 49Expanding Universe lect 2
Around kT ≈ MeV: Big Bang Nucleosynthesis• around few MeV: mainly relativistic g, e,ne, nm, nt + anti‐particles in thermal equilibrium
• + few protons & neutrons
• weak interactions becomei ie e
n e p
ν ν
ν
+ −
−
+ ↔ +
+ ↔ +• weak interactions become
very weake
e
n e p
p e n
ν
ν +
+ ↔ +
+ ↔ +
• start primordial nucleosynthesis: formation of light nucleien p e ν−→ + +
(chapter 6) 2
32
2.22HH
n p MeVH n
γ
γ
+ ↔ + +
+ → +2 2 4
HHe
H nH H
γ
γ
+ → +
+ → +
2013‐14 Expanding Universe lect 2 50
...........
Around kT ≈ 3MeV : Neutrino freeze out• Equilibrium between photons and leptons
( ) , ,i ie e i eν νγ μ τ+ −+↔ ↔ + = Weak interaction
• Weak interaction cross section decreases with energy
( ) , ,i iγ μ
225 2~ s CM energy 1.166 106
FF
G G GeVσ π− −= = ×s
2013‐14 Expanding Universe lect 2 51
Neutrino freeze-out at t ≈ 1s
• weak collision rate interactions/secW v= σn
, ,i ie e i eν ν μ τ+ −+ ↔ + = Weak interaction
weak collision rate interactions/sec
l ti
W v= σn
b d it C ti R l ti• relativee+, e‐ number density(FD statistics) ~ T3
Cross section ~ s ~ T2
Relative velocity
• During expansion T decreases ( ) 2H t T∝5W T∝During expansion T decreases
• when W << H or kT < 3MeV or t > 1s
Ne trinos no longer intera t
( )tW T∝
→ Neutrinos no longer interact• Neutrinos decouple and evolve independently
• neutrino freeze‐out Æ relic neutrinos2013‐14 Expanding Universe lect 2 52
Cosmic Neutrino Background• Relic neutrinos are oldest relic of early universe –decoupled at about 1s – before CMB photons
• Should be most abundant particles in sky with CMB photonsphotons
• Should populate universe today as Cosmic Neutrino Background CνB or cosmogenic neutrinosBackground CνB or cosmogenic neutrinos
• what are expected number density and temperaturetoday?
• Can we detect these neutirnos?oefening
2013‐14 Expanding Universe lect 2 53
Cosmic Neutrino Background• At few MeV there was thermal equilibrium betweenphotons and leptons
( )• Number density neutrinos ª number density photons
( ) , ,i ie e i eν νγ μ τ+ −+↔ ↔ + =
• expected Temperature of neutrinos today0( ) 1.95T t Kν = 0( )E t meVν ≈
• expected density of relic neutrinos today: for given species(ne, nm, nt ) 3⎛ ⎞e m t
33 11311
N N cmNν γν−⎛ ⎞= =⎜ ⎟
⎝ ⎠+
• CνB could explain part of Dark Matter : weakly interacting, massive, stable – is Hot DM (chapter 7)massive, stable is Hot DM (chapter 7)
2013‐14 Expanding Universe lect 2 54
Overview of radiation dominated era
Quarks confined106.75
Neutrino
Qin hadrons
Run out of
10
Decoupling andnucleosynthesis
relativisticparticles
g*3.4
ep recombinationTransition to
GeV MeV matter dominateduniverse
kT(GeV)TeV
2013‐14 Expanding Universe lect 2 55
Ω
re
ΩradPart 4&6
ΩbaryonsPart 7s
lectur
Todays
ΩneutrinoPart 5T Part 5
ΩCDM( ) ( )N B N anti B≠ − CDMPart 5
( ) ( )part 8
© Rubakov2013‐14 56Expanding Universe lect 2
Questions?
Part 6Part 6 matter and radiation decouplingp g
Recombination of electrons and light nuclei to atomsg
Atoms and photons decouple
at Z ~ 1100at Z 1100
Radiation-matter decoupling• At tdecª 380.000 years, or z ª1100, or T ª 3500K
• matter decouples from radiation and photons can movematter decouples from radiation and photons can move freely & remain as today’s CMB radiation
• Matter evolves independently ‐ atoms & molecules are• Matter evolves independently ‐ atoms & molecules are formed→ stars, galaxies, …
• Before tdec universe is ionisedand opaque
• Population consists of p, H, e, g + light nuclei + neutrinos
2013‐14 Expanding Universe lect 2 59
Protons and neutral hydrogenAt kT ~ 3 MeV neutrino freeze‐out and start of BB nucleosynthesis – most p and n bound in light nuclei (part 7)
Photon density much higher than proton density
observations Nobservations 10~ 10p
NN
γp eN N=
• Up to tª 100.000 y thermal equilibrium of p, H, e, ge p H γ− + ↔ + Depends on densities
formation of neutral hydrogenionisation of hydrogen atom
→←
Depends on densitiesof free e and pNe and Np
• When kT < I=13.6 eV
y g e p
e p− + ←⎯⎯ H γ+ Td ?
2013‐14 Expanding Universe lect 2 60
Tdec?
Protons and neutral hydrogen• Calculate ( )
( )Prob
Prob &
electron bound in H atom
electron unbound relativisticf(T)
b d it f f t N d f t l h d
( )Prob &electron unbound relativistic
• number density of free protons Np and of neutral hydrogenatoms NH as function of T
N d i f f
2
321 2Hp kN N mk e
N N hπ+
−⎛ ⎞⎛ ⎞= = ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠
TI
NT
Ne = density of free electronsm=electron mass
• At which T will universe run out of ionised hydrogen?
HHN N h⎝ ⎠⎝ ⎠eN m=electron mass
• At which T will universe run out of ionised hydrogen?
temperature at decoupling
2013‐14 Expanding Universe lect 2 61
Decoupling temperature• Rewrite in function of fraction x of ionised hydrogen atoms
2 321 2 Ix mkπ −⎛ ⎞⎛ ⎞TNN
2
21 21 B
kx mk ex N h
π⎛ ⎞⎛ ⎞= ⎜ ⎟⎜ ⎟− ⎝ ⎠⎝ ⎠TTp
p H
p
B
NNx
N N N= =
+
• strong drop of x between kT ª 0.35 ‐ 0.25 eV• or T between 4000 – 3000 K• fi ionisation stops around T~3500K e p− + ←⎯⎯ H γ+
• period of recombination of e and p to hydrogen atoms
• Recombination stops when electron density is too small
e p H γ− + → +p y
2013‐14 Expanding Universe lect 2 62
Decoupling time• Reshift at decoupling
( ) ( )( )
0
0
35001 12702.75
decdec
dec
R t kT KzkT KR t
+ = = = ≈
• Full calculation
( ) 0dec
( )1 1100decz+ = 53.7 10dect y= ×
• When electron density is too small there is no H formation anymore
• → Photons freeze out as independent population = CMB
• start of matter dominated universe• start of matter dominated universe
• We are left with atoms, CMB photons and relic neutrinos
• + possibly exotic particles (neutralinos, …)2013‐14 Expanding Universe lect 2 63
Era of matter-radiation equality• since 3
baryonic matter TΩ ∼ 4photons TΩ ∼
• Density of baryons = density of photons when( ) ( ) 1t tΩ Ω( )( )
( )( )
0
0
1 11
bar
ph
bar
phot ot
tt
tzt
ΩΩ
Ω+Ω
= = ( )1 870 1 decz z+ = ≈ +
• Density of matter (baryons + Dark Matter) = density of photons + neutrinos when
1 3130z+ ≈( )( )
( )( )
0 1 11 58 1
mmatter tt
tt
ΩΩ
Ω= =
Ω ( ) ( )01.58 1pphot neut hott zt+ ΩΩ × +
• Matter dominates over relativistic particles when Z < 30002013‐14 Expanding Universe lect 2 64
( ) ( )3 11 wzρ +∝ +
~1000z~3000 z~1000
2013‐14 Expanding Universe lect1 65
© J. Frieman
Summary
cle
er partic T(K)
ergy
peEne
2013‐14 Expanding Universe lect 2 66Time t(s)
Expanding universe : content• part 1 : ΛCDM model ingredients: Hubble flow, cosmological principle, geometry of universe
• part 2 : ΛCDM model ingredients: dynamics of expansion, energy density components in universe
• Part 3 : observation data – redshifts, SN Ia, CMB, LSS, light element abundances ‐ ΛCDM parameter fits
• Part 4: radiation density, CMB• Part 5: Particle physics in the early universe, neutrino density
• Part 6: matter‐radiation decoupling• Part 7: Big Bang Nucleosynthesis• Part 8: Matter and antimatter
2013‐14 Expanding Universe lect 2 67
Questions?
Part 7 (chapter 6)Part 7 (chapter 6)Big Bang Nucleosynthesisg g yformation of light nuclei when kT ~ MeVObservation of light element abundances
Baryon/photon ratioy /p
ΩBAR
Overview 1 ( )• at period of neutrino decoupling
when kT ~ 3 MeV
( ),
,, ,
,,,
, ,en
ep n
ep
ν ν μ
γ
τ−+
• Anti‐particles are annihilated – particles remain (part 8),, , , ppγ
p p γ γ+ → + 1010BARNp p γ γ+ → + 10~ 10BARNNγ
−
observed
• Fate of baryons? → Big Bang Nucleosynthesis model• Protons and neutrons in equilibrium due to weak interactionsq
• n and p freeze‐out at ~ 1 MeV ‐ Free neutrons decaye nepν ++ ↔ + eepn ν−→ + +
p y
• Neutrons are ‘saved’ by binding to protons → deuterons
2 22n p D MeVγ+ ↔ + +
2013‐14 Expanding Universe lect 2 70
2.22n p D MeVγ+ ↔ + +
Overview 2Wh kT I(D) 2 2 M V di i ti f D t• When kT << I(D)=2.2 MeV dissociation of D stops
• At kT ~ 60 KeV all neutrons are bound in nuclei
O f i di l l h i f i f l i• Onset of primordial nucleosynthesis – formation of nuclei
l f b f l h l
2 3 43 77,, , , ,H He HeH Be Li• model of BBN predicts abundances of light elements today
• At recombination (380’000 y) nuclei + e‐→ atoms + CMB photons
CMBe p H γ− + → +• Atoms form stars, … → Large Scale Structures (LSS)
1010 baryonN⎛ ⎞⎜ ⎟• Consistency of model:
light element abundances
1010 10 baryon
photonNη ⎛ ⎞≡ ⎜ ⎟⎝ ⎠
( ) ( )li ht l CMB LSS?CMB and LSS observations depend on 2013‐14 Expanding Universe lect 2 71
( ) ( )10 10 ,light elem CMB LSSη η=?
neutron – proton equilibrium• When kT ~ 3 MeV neutrinos decouple from e, γ• particle population consists of ( ), ,, , ,ee e ν ν μ τ−+
• Most anti‐particles are annihilated
( ),, , ,n p npγ
• Tiny fraction of nucleons is left−
p p γ γ+ → +
• Protons and neutrons in equilibrium due to
e
e
e
e
pn
p n
ν
ν
−
+
+ ↔ +
+ ↔ +weak interactions with neutrinos
And neutron decay t = (885.7 ± 0.8)seepn ν−→ + +
• Weak interactions stop whenW << H →n & p freeze-out
( ) 2H t T∝( ) 5W t n v Tσ= ∝ ~ 0 8kT MeV2013‐14 Expanding Universe lect 2 72
( )H t T∝( ) W t n v Tσ= ∝ ~ 0.8kT MeV
neutron/proton ratio vs Temperature• As soon as kT << 1 GeV nucleons are non‐relativistic
• Probablity that proton is in
2pkT M c<
2E M c− ⎛ ⎞energy state in [E,E+dE] expproton
pkT M cP e
kT⎛ ⎞
∝ = −⎜ ⎟⎜ ⎟⎝ ⎠
• During equilibrium between
weak interactions( ) 2 2
expMc
n pn kT
p
M M cN eN kT
Δ−⎛ ⎞−⎜ ⎟= − =⎜ ⎟⎝ ⎠
• at nucleon freeze‐out time tFO
p ⎜ ⎟⎝ ⎠
( ) 0 20FOnN tkT ~ 0.8MeV
( )( ) 0.20FO
FO
npN t =
( ) ( )0 20N• Free neutrons can decay
with t = (885.7 ± 0.8)s
( )( )
( )( )
exp1.2 exp
0.200.20
n
p
N t tN t t
ττ
−=⎡ ⎤− −⎣ ⎦
2013‐14 Expanding Universe lect 2 73
T(keV)Free neutrons and protons
weak interactions in equilibriumin equilibrium
( )nN t0.8MeV
n,p freeze‐out 60 KeV( )( )
n
pN t,p 60 KeV
D freeze‐outNuclear reactionsNuclear reactions
dominate
1s 1min
2013‐14 Expanding Universe lect 2 74t(s) t(s)©Steigman 2007 300 s
Nucleosynthesis onset• Non‐relativistic neutrons form nuclei through fusion: formation of
deuterium 2 2 22n p H MeVγ+ ↔ + +2
2
2.22formation of d i i f
n p H MeVH
H
γ+ ↔ + +
→
• Photodisintegration of 2H stops when kT ≈ 60 KeV << I(D)=2.2MeV
2desintegration of H←
• free neutrons are gone
• And deuterons freeze‐out
nNFree N =0
pN Free Nn=0
2013‐14 Expanding Universe lect 2 75
Nuclear chains• Chain of fusion reactions
Production of light nuclei 2 3
2 2.22Hn p MeVH n H
γ
γ
+ ↔ + +
+ → +g2
2 2
3HeH n HH HH H
γ
γ
+ → +
+ → +4He2 2
3 2 4
4 3 7
H HH H He n
γ+ → +
+ → + …
4He
4 3
7
7BHe HeBe n p
e γ+ → +
+ → +7Li
• ΛCDM model predicts values of relative ratios of light elements• We expect the ratios to be constant over timeWe expect the ratios to be constant over time• Comparison to observed abundances today allows to test the
standard cosmology modelstandard cosmology model
2013‐14 Expanding Universe lect 2 76
Observables: He mass fraction• helium mass fraction
( ) ( )24 N NM H( )( ) ( )
( )( )24
4 1 1n p
n p
N NM He yYM He H y N N
= = =+ + +
He
H
NyN
=
• Is expected to be constant with time – He in stars (formedlong time after BBN) has only small contribution
• model prediction at onset of BBN : kT ~60keV, t~300s
0.25predY =0.135np
NN =
• Observation today in gas clouds … 0.249 0.009obsY = ±
pN
2013‐14 Expanding Universe lect 2 77
Abundances of light elements• Standard BB nucleosynthesis theory predicts abundancesof light elements today – example Deuterium
• Observations today
D H( ) 52 82 0 21 10D −± × D H
10η( )2.82 0.21 10
H= ± ×
BBN StartskT 80keV
410−
kTª80keV
/t(s)
• Abundances depend on baryon/photon ratio2013‐14 Expanding Universe lect 2 78
Parameter: baryon/photon ratio• ratio of baryon and photon number densities
– Baryons = atoms 1010 baryonNη
⎛ ⎞⎜ ⎟
y
– Photons = CMB radiation
• In standard model : ratio is constant since BBN era (kT~80
1010 10 y
photonNη ≡ ⎜ ⎟⎜ ⎟
⎝ ⎠In standard model : ratio is constant since BBN era (kT 80 keV, t~20mins)
• Should be identical at recombination time (t~380’000y)• Should be identical at recombination time (t 380 000y)
• Observations : – abundances of light elements, He mass fraction → t~20mins
– CMB anisotropies fromWMAP→ t~380’000y
2013‐14 Expanding Universe lect 2 79
Abundances and baryon densityWBh2
He mass fraction
B
Observations Of li h lOf light elementsMeasure η10
abundancesCMB observations with WMAPwith WMAP measure WBh2
Model PredictionsModel PredictionsDepend on η10 WBh2
2013‐14 Expanding Universe lect 2 80η10
CMB analysis• Baryon‐photon ratio from CMB analysis
• PDG 2013
( )
2 0.02207 0.00027
6 047 0 074B
BhNη
Ω = ±
±( )10 6.047 0.074B
Nγη = = ±
pdg.lbl.gov
2013‐14 Expanding Universe lect 2 81
p g g
Light element abundances• PDG 2013
( ) 5
0.2465 0.0097
/ 2.53 0.04 10pY
D H −
= ±
= ± ×( )( ) 10/ 1.6 0.3 10Li H −= ± ×
( )5 7 6 7 95%CLη< < ( )105.7 6.7 95%CLη< <
pdg.lbl.gov
2013‐14 Expanding Universe lect 2 82
p g g
Questions?
Part 8 (chapter 6)Part 8 (chapter 6)matter-antimatter asymmetryy y
Where did the anti‐matter go?g
What about antimatter ?• Antiparticles from early universe have disappeared!• Early universe: expect equal amount of particles & y p q pantiparticles ‐ small CP‐violation in weak interactions
• Expect e.g. ( ) ( )N e N e+ −= ( ) ( )N p N p=p g
• primary charged galactic cosmic rays: detect nuclei and no
( ) ( )N e N e= ( ) ( )N p N p
primary charged galactic cosmic rays: detect nuclei and no antinuclei
• Annihilation of matter with antimatter in galaxies wouldAnnihilation of matter with antimatter in galaxies wouldyield intense X‐ray and g‐ray emission – not observed
• Few positrons and antiprotons fall in on Earth atmosphere :Few positrons and antiprotons fall in on Earth atmosphere : in agreement with pair creation in inter‐stellar matter
• Antiparticles produced in showers in Earth atmosphere =Antiparticles produced in showers in Earth atmosphere secundary cosmic rays
2013‐14 Expanding Universe lect 2 85
Baryon number conservation• Violation of baryon number conservation would explainbaryon ‐ anti‐baryon asymmetry
• Baryon number conservation = strict law in laboratory
• If no B conservationÆ proton decay is allowed 0p e π+→• If no B conservation Æ proton decay is allowed
• Some theories of Grand Unification allowp ep K
π
ν+→
→
for quark‐lepton transitions
• Search for proton decay in very large underground detectors, e.g. SuperKamiokande
• No events observed→ Lower limit on lifetimeNo events observed Lower limit on lifetime
( ) 3310p yτ >
2013‐14 Expanding Universe lect 2 86
Baryons and antibaryonsb b l• Assume net baryon number = 0 in early universe
• Assume equilibrium between photons, baryons and anti‐b t ~ 2 G Vbaryons up to ~ 2 GeV
A d 10 20 M V ihil ti t W H
p p γ γ+ ↔ +
• Around 10‐20 MeV annihilation rate W << H• A residu of baryons and antibaryons freeze out
Expect 1810B BNNN Nγ γ
−= ∼To do!γ γ
• Uitwerking meebrengen op examen2013‐14 Expanding Universe lect 2 87
Baryons and antibaryons• Baryons, antibaryons and photons did not evolve sincebaryon/anti‐baryon freeze‐out
• Expect that today
18
B B
B B
N NNN
=
1810B BNNN Nγ γ
−= ∼
• Observe ( ) 106.05 0.07 10BNNγ
η −= = ± × ∼ -910Much tool !
410B
B
NN
γ
−<large!
• Explanation?
B
2013‐14 Expanding Universe lect 2 88
Baryon-antibaryon asymmetryh d l ?• Is the model wrong?
• Zacharov criterium : 3 fundamental conditions for asymmetry in baryon anti‐baryon density:
• starting from initial B=0 one would needg– Baryon number violating interactions
– Non‐equilibrium situation leading to baryon/anti‐baryon asymetryNon equilibrium situation leading to baryon/anti baryon asymetry
– CP and C violation: anti‐matter has different interactions thanmatter
• Search at colliders for violation of C and CP conservinginteractionsinteractions
• Alpha Magnetic Spectrometer on ISS: search for antiparticles from spaceantiparticles from space
2013‐14 Expanding Universe lect 2 89
Expanding universe : content• part 1 : ΛCDM model ingredients: Hubble flow, cosmological principle, geometry of universe
• part 2 : ΛCDM model ingredients: dynamics of expansion, energy density components in universe
• Part 3 : observation data – redshifts, SN Ia, CMB, LSS, light element abundances ‐ ΛCDM parameter fits
• Part 4: radiation density, CMB• Part 5: Particle physics in the early universe, neutrino density
• Part 6: matter‐radiation decoupling• Part 7: Big Bang Nucleosynthesis• Part 8: Matter and antimatter
2013‐14 Expanding Universe lect 2 90