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 asymmetry
2014-15
Expanding Universe lect 2
2
Last lecture
• Universe is flat k=0
• Expansion dynamics is described by Friedman-Lemaître
equation
• Cosmological redshift
• Closure parameter
1 z 
R  t0 
z  t0   0
R t 
z t  0  
3H 02
 c  t0  
 5.4 GeV m3
8 GN
• Expansion rate as function of redshift
3
4
2

H  t   H Ωm t 0 1  z   Ωr t 0 1  z   Ω Λ t 0   Ωk t 0 1  z  


2
2014-15
2
0
Expanding Universe lect 2
3
Todays lecture
> TeV
ΩCDM
Part 5
2014-15
Expanding Universe lect 2
© Rubakov
4
Todays lecture
N  B   N  anti  B 
> TeV
Part 5
part 8
2014-15
ΩCDM
Expanding Universe lect 2
© Rubakov
5
Todays lecture
Ωneutrino
Part 5
N  B   N  anti  B 
ΩCDM
part 8
Part 5
2014-15
Expanding Universe lect 2
© Rubakov
6
Todays lecture
Ωbaryons
Part 7
Ωneutrino
Part 5
N  B   N  anti  B 
ΩCDM
part 8
Part 5
2014-15
Expanding Universe lect 2
© Rubakov
7
Ωrad
Todays lecture
Part 4&6
Ωbaryons
Part 7
Ωneutrino
Part 5
N  B   N  anti  B 
ΩCDM
part 8
Part 5
2014-15
Expanding Universe lect 2
© Rubakov
8
Ωrad
Part 4
radiation component - CMB
Physics of the Cosmic Microwave Background
Present day photon density
CMB in Big Bang model
Matter
photons
are released
© Univ Oregon
Baryons/nuclei and
photons in
thermal equilibrium
2014-15
Photons decouple/freeze-out
During expansion they cool
down
Expect to see today a uniform
γ radiation which behaves like a
black body radiation
Expanding Universe lect 2
10
CMB discovery in 1965
• 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
Way
• This could not be explained by stars, radio galaxies etc
• Use Earth based observatory: limited to cm
wavelengths due to absorption of mm waves in
atmosphere
• Observed spectrum was compatible with black body
radiation with T = (3.5 ±1) K
• Obtained the Nobel Prize in 1978 (http://nobelprize.org/)
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Expanding Universe lect 2
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COBE : black body spectrum
• To go down to mm wavelengths : put instruments on satellites
• COBE = COsmic Background Explorer (NASA) satellite observations in
1990s: mm wavelengths
• Large scale dipole anisotropy due to motion of solar system in
universe, with respect to CMB rest frame
v  solar system   300 km
s
• Strong radio emission in galactic plane
• 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)
• Discovered small anisotropies/ripples over angular ranges Δθ=7°
• 2006 Nobel prize to Smoot and Mather for discovery of anisotropies
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Expanding Universe lect 2
12
CMB temperature map
dipole T
small ripples on top of Black Body radiation:
2014-15
Expanding Universe lect 2
T
T
T
 103
 O  mK 
 105
 O  µK 
13
COBE measures black body spectrum
λ=2mm
Intensity Q
0.5mm
• Plancks radiation law for
relativistic photon gas
• Black body with
temperature T emits
radiation with power Q at
frequencies
Q  , T  
Frequency ν (cm-1)
2014-15
3
4 2 c 2

e kT  1
  2
Expanding Universe lect 2
14
COBE measures black body spectrum
λ=2mm
Intensity Q
0.5mm
• CMB has ‘perfect’ black
body spectrum
• Fit of data of different
observatoria to black body
spectrum gives (pdg.lbl.gov,
CMB, 2013)
T  CMB    2.7255  0.0006  K
  max   2mm
• Or
Frequency ν (cm-1)
2014-15
Expanding Universe lect 2
E  kT  0.235 meV
15
CMB number density today 1
• CMB photons have black body spectrum today
• They 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]
 gγ 
p 2 dp
n  p  dp 
gγ = number of


E

  2  photon substates
2 3
k
T
 e
 1


Black body
2014-15
Expanding Universe lect 2
16
CMB number density today 2
n 
N
V
  n  p  dp
gγ=2
1  kT 
n  2.404 2 

 c 
3
T=2.725K
n  t0   411 cm3
2014-15
Expanding Universe lect 2
17
CMB energy density today
 c   E n  p  dp
2
 c   kT 
2
1
4

2

 

3 
c   15 
4
T=2.725K
r c2  t0   0.261 MeV m3
 r  t0    r
2014-15
c
 4.84 105
Expanding Universe lect 2
18
radiation energy density vs time
• In our model the early universe is radiation dominated
• For flat universe → Friedmann equation
• energy density of radiation during expansion
rad  1  z   R 4
4
• Integration yields
2014-15
2
3
c
1
2
rad c  t  
2
32 GN t
Expanding Universe lect 2
19
CMB temperature vs time
æg ö
1
2
4
g
ç
÷
rrad c = p kT ´ ç ÷ ´
2 3 3
2
15
p
hc
è ø
2
3
c
1
2
rad c 
32 GN t 2
1
 2
 45 c 
kT  
  
3
 32 G 
 g
3 5
4
( )
4
1
 4 1
  1
t 2

Trad dom
1.31MeV 1

1
k
t 2
• for t0 = 14Gyr expect TCMB (today) ≈ 10K !!!
• BUT! COBE measures T = 2.7K
• Explanation???
2014-15
Expanding Universe lect 2
20
Summary
R ~ 1/ T
matter
c2
1  z 
3
1

z
 
vacuum
c2
cst
radiation  c
2
4
curvature  c 2
2014-15
Expanding Universe lect 2
1  z 
2
21
Questions?
Part 5
particle physics in the early universe
Radiation dominated universe
From end of inflation to matter-radiation decoupling
From ~ 107 GeV to eV
Physics beyond the Standard Model, SM, nuclear physics
Radiation domination era
Planck era GUT era
kT
• At end of inflation phase
there is a reheating
phase
• Relativistic particles are
created
• Expansion is radiation
dominated
• Hot Big Bang evolution
starts
TeV
t
2014-15
Expanding Universe lect 2
24
Radiation domination era
• At end of inflation phase
there is a reheating
phase
• Relativistic particles are
created
• Expansion is radiation
dominated
• Hot Big Bang evolution
starts
R
Planck era
2014-15
GUT era
Expanding Universe lect 2
t
25
Radiation domination era
Planck era GUT era
kT
TeV
Today’s lecture
t
2014-15
Expanding Universe lect 2
26
Planck mass
Grand
10 TeV-100
~ 1019 GeV Unification
GeV
~ 1015 GeV LHC-LEP
Inflation
period
2014-15
Expanding Universe lect 2
27
Today’s lecture
Planck mass
Grand
10 TeV-100
~ 1019 GeV Unification
GeV
~ 1015 GeV LHC-LEP
Inflation
period
2014-15
Expanding Universe lect 2
28
Relativistic particles
Radiation dominated
kT >> 100 GEV
2014-15
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
• Fermion gas = quarks, leptons n  p  dp 
2
• Fermi-Dirac statistics
(gf = nb of substates)
• boson gas = photons, W and Z bosons …
• Bose Einstein statistics
n  p  dp 
2
(gb = nb of substates)
2014-15
Expanding Universe lect 2
 gf
p 2 dp

E
  2
3
kT
 1
e





 gb 
p 2 dp


E
2
3 
kT  1 

e


30
relativistic particles in early universe
• Bosons and fermions contribute to energy density with
n  p  dp 
2
 gf
p 2 dp

E
 2
3 
kT
 1
e




 c 2   E n  p  dp
*

g
*c 2  t    4  kT 
2 3 3 
15 c  2
4
2014-15
1



Expanding Universe lect 2
7
g   gb   g f
8
*
31
Degrees of freedom for kT > 100 GeV
If we take only the
known particles
bosons
spin per particle
total
W+ WZ
gluons
photon
H-boson
total bosons
fermions
28
spin per particle
total
quarks
antiquarks
e,µ,τ
neutrinos
anti-neutrinos
2014-15
total fermions
Expanding Universe lect 2
90
32
Degrees of freedom for kT > 100 GeV
bosons
spin
per particle
total
W+ W-
1
3
2x3=6
Z
1
3
3
gluons
1
2
8 x 2 = 16
photon
1
2
2
H-boson
0
1
1
total bosons
28
fermions
spin
per particle
total
quarks
½
3 (color) x 2 (spin)
6 x 3 x 2 = 36
antiquarks
2014-15
36
e,µ,τ
½
2
6 x 2 = 12
neutrinos
LH
1
3x1=3
anti-neutrinos
RH
1
3x1=3
total fermions
Expanding Universe lect 2
90
33
Degrees of freedom for kT > 100 GeV
• Assuming only particles from Standard Model of particle
physics
7
g *  28   90  106.75
8
• Energy density in hot universe
*


g
2
4
*c  t     kT 

2 3 3 
15 c  2 
4
1
what happens if there were particles from
theories beyond the Standard Model?
2014-15
Expanding Universe lect 2
34
For instance : SuperSymmetry
•
•
•
•
At LHC energies and higher : possibly SuperSymmetry
Symmetry between fermions and bosons
Consequence is a superpartner for every SM particle
~ Double degrees of freedom g*
2014-15
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
interactions
•
is Lightest Supersymmetric Particle – LSP - in R-parity
conserving scenarios → stable
• Massive : Searches at LEP and Tevatron colliders
Rp=
2014-15
Expanding Universe lect 2
36
Neutralino = Dark Matter ?
• Lightest neutralino may have been created in the early hot
universe when
• Equilibrium interactions
• When kT is too low, neutralinos freeze-out (decouple)
• → are non-relativistic at decoupling = ‘cold’
• survive as independent population till today
• the observed dark matter abundance today puts an upper
limit on the mass (chapter 7)
CDM  1
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Expanding Universe lect 2
37
STATUS AROUND A FEW GEV
2014-15
Expanding Universe lect 2
38
Cool down from > TeV to kT ≈ GeV
• Start from hot plasma of leptons, quarks, gauge bosons,
Higgs, exotic particles
1 1
T
~
• Temperature decreases with time rad dom
2
t
• Production of particles M stops when kT  Mc 2
• For example,
e  e  W   W 
p ptt  X
when
s  2MW  160GeV
when
s  2M top  346GeV
 W , Z   1023 s
• some particles decay: W, Z, t ..
• Run out of heavy particles when kT<<100GeV
2014-15
Expanding Universe lect 2
39
Age of universe at kT ≈ few GeV
• Radiation dominated expansion since Big Bang
Trad dom
1.31MeV 1

1
k
t 2
• Calculate time difference relative to Planck era
•
•
•
•
•
Calculate age of universe at
kT=100 GeV
t=
kT = 1 GeV
t=
kT = 200 MeV
t=
And compare to lifetimes of unstable particles
2014-15
Expanding Universe lect 2
40
Questions?
Free quarks form hadrons
COOLDOWN TO kT ≈ 200 MEV
2014-15
Expanding Universe lect 2
42
A phase transition
Quarks form hadrons
Decay of particles with lifetime < µsec
200 MeV
g*
kT(GeV)
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Expanding Universe lect 2
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Down to kT ≈ 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 around ΛQCD
S    Q
2
2

2
g Strong
4
~

1
b0 ln 
2
Λ QCD
2
 QCD  200 MeV

From fit to data
  E T
When µ ≈ 200 MeV
confinement
Quarks cannot be free at distances
of more than 1fm = 10-15m
2014-15
Expanding Universe lect 2
αs
t
44
Colour confinement
large distances
Expansion of universe
Increases
inter-quark distance
Asymptotic freedom
small distances
2014-15
Expanding Universe lect 2
45
around and below kT ≈ 200 MeV
• free quarks and gluons are gone and hadrons are formed
• Most hadrons are short lived and decay with
  108 s  weak ints. 1023 s strong ints.
• Example
<< 1µs
 1115   uds   p     p     
 n   0  n  e  e
• Leptons : muon and tauon decay weakly
     2 106 s
  e    e

2014-15

Stable or long
lived
    319 1015 s
       
17% 
 .......
Expanding Universe lect 2
46
pauze
QUESTIONS?
Run out of unstable hadrons
Neutrino decoupling/freeze-out
Big bang nucleosynthesis
COOLDOWN TO A FEW MEV
2014-15
Expanding Universe lect 2
48
Cooldown to kT ≈ 10MeV
• After about 1ms all unstable particles have decayed
• Most, but not all, nucleons annihilate with anti-nucleons (chapter 6)
p  p  
106.75
expect
nbaryons
n
~ 1018
43
7
g *  2   10 
 10
4
8
10
g*
3.4
GeV
2014-15
TeV
MeV
kT(GeV) Expanding Universe lect 2
we are left with
γ + e-, νe, νμ, ντ
and their antiparticles
49
Around kT ≈ MeV: Big Bang Nucleosynthesis
• around few MeV: mainly relativistic γ, e,νe, νμ, ντ + antiparticles in thermal equilibrium
e  e   i  i
• + few protons & neutrons
 e  n  e  p
• weak interactions become
 e  p  e  n
very weak
n  p  e  e
• start primordial nucleosynthesis: formation of light nuclei
(chapter 6)
n  p  2 H    2.22 MeV
2
H  n  3H  
H  2 H  4 He  
...........
2
2014-15
Expanding Universe lect 2
50
Around kT ≈ 3MeV : Neutrino freeze out
• Equilibrium between photons and leptons
i  e, , Weak interaction
  e  e  i  i
• remaining photons today : CMB with T=2.75K
n  t0   411 cm
3
rr c 2 (t0 ) = 0.261 MeV m-3
• What about remaining neutrinos?
• Weak interaction cross section decreases with energy
2
G
 ~ Fs
2014-15
6
s  CM energy
Expanding Universe lect 2
GF  1.166 10 5 GeV 2
51
Neutrino freeze-out
e  e   i  i
i  e,  , Weak interaction
• weak collision rate
• e+,
relative
e- number density
(FD statistics) ~ T3
W  n v
interactions/sec
Weak Cross
section
~ s ~ T2
Relative
velocity of e+
and e-
H t   T
• During expansion T decreases W  T
• As soon as W < H neutrinos stop interacting
5
2014-15
Expanding Universe lect 2
2
52
Cosmic Neutrino Background
•
•
•
•
W << H when kT < 3MeV or t > 1s (problem 5.12)
Neutrinos decouple and evolve independently
neutrino freeze-out -> relic neutrinos
Should populate the universe today as Cosmic Neutrino
Background CνB
• what are expected number density and temperature
today?
• Can we detect these neutrinos?
• Could they be dark matter?
2014-15
Expanding Universe lect 2
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Cosmic Neutrino Background
•
•
•
•
At a few MeV   e  e  
i  e, ,
i
i
Number density of neutrinos ≈ number density of photons
But photons are boosted by reaction e+ + e- ® g + g
In the end the photons have a higher
1
æ4ö 3
temperature than the neutrinos with Tn = çè 11 ÷ø Tg
• expected Temperature of neutrinos today
T (t0 )  1.95K E (t0 )  meV
• expected density of relic neutrinos today: for given species
(νe, νμ, ντ )
3
N  N    N  113 cm 3
 11 
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Overview of radiation dominated era
106.75
Quarks confined
in hadrons
Neutrino
Decoupling and
nucleosynthesis
10
g*
3.4
GeV
TeV
2014-15
MeV
Run out of
relativistic
particles
ep recombination
Transition to
matter dominated
universe
kT(GeV)
Expanding Universe lect 2
55
Ωrad
Todays lecture
Part 4&6
Ωbaryons
Part 7
Ωneutrino
Part 5
N  B   N  anti  B 
ΩCDM
part 8
Part 5
2014-15
Expanding Universe lect 2
© Rubakov
56
Questions?
Part 6
matter and radiation decoupling
Recombination of electrons and light nuclei to atoms
Atoms and photons decouple
at Z ~ 1100
Radiation-matter decoupling
• At tdec ≈ 380.000 years, or z ≈1100, or T ≈ 3500K
• matter decouples from radiation and photons can move
freely & remain as today’s CMB radiation
• Matter evolves independently - atoms & molecules are
formed → stars, galaxies, …
• Before tdec universe is ionised
and opaque
• Population consists of
p, H, e, γ + light nuclei + neutrinos
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Protons and neutral hydrogen
 At 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
N
10
Np
~ 10
N p  Ne
• Up to t ≈ 100.000 y thermal equilibrium of p, H, e, γ
e  p  H  
 formation of neutral hydrogen
 ionisation of hydrogen atom
Ne and Np = free e and p
NH = bound H atoms
• When kT < I=13.6 eV e  p 
 H 
2014-15
Expanding Universe lect 2
Tdec?
60
Protons and neutral hydrogen
Ne N p
NH
=
(
Prob electron unbound
(
)
Prob electron bound in H atom
f(T)
)
• number density of free protons Np and of neutral hydrogen
atoms NH as function of T
Np
NH
NH 

NH
 1

 Ne
  2 mkT  2 kTI

 e
2

 h
3
m=electron mass
• At which T will universe run out of ionised hydrogen?
temperature at decoupling
2014-15
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61
Decoupling temperature
• Rewrite in function of fraction x of ionised hydrogen atoms
x
Np
N p  NH

 1
x

1 x  NB
2
Np
NB
  2 mkT  2 kTI

 e
2

 h
3
• strong drop of x between kT ≈ 0.35 - 0.25 eV
• or T between 4000 – 3000 K
•  ionisation stops around T~3500K e  p 
 H 
• period of recombination of e and p to hydrogen atoms
e  p  H 

• Recombination stops when electron density is too small
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Decoupling time
• Reshift at decoupling
• Full calculation
1  z dec
R  t0 
kTdec 3500K



 1270
kT0
2.75K
R  tdec 
5
1

z

1100
t

3.7

10
y
 dec
dec
• When electron density is too small there is no H formation
anymore
• → Photons freeze out as independent population = CMB
• start of matter dominated universe
• We are left with atoms, CMB photons and relic neutrinos
• + possibly relic exotic particles (neutralinos, …)
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Era of matter-radiation equality
• since
baryonic matter
T
3
 photons
T4
• Density of baryons = density of photons when
bar  t  bar  t0  1
1  z  870  1  z dec

1
 phot  t   phot  t0  1  z
• Density of matter (baryons + Dark Matter) = density of
photons + neutrinos when
matter  t 
 m  t0 
1

1
 phot neut  t  1.58   phot  t0  1  z
1  z  3130
• Matter dominates over relativistic particles when Z < 3000
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31 w
  1  z 
z~3000
z~1000
© J. Frieman
2014-15
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Energy per particle
Summary
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T(K)
Time t(s)
Expanding Universe lect 2
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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
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Questions?
Part 7 (chapter 6)
Big Bang Nucleosynthesis
formation of light nuclei when kT ~ MeV
Observation of light element abundances
Baryon/photon ratio
ΩBAR
Overview 1
e , e , ,  e,  , 
• at period of neutrino decoupling
when kT ~ 3 MeV
 , p, n, p, n
• Anti-particles are annihilated – particles remain (part 8)

p  p     N BAR

N
~ 1010
observed
• Fate of baryons? → Big Bang Nucleosynthesis model
• Protons and neutrons in equilibrium due to weak interactions
 e  p  e  n
n  p  e  e
• n and p freeze-out at ~ 1 MeV - Free neutrons decay
• Neutrons are ‘saved’ by binding to protons → deuterons
n  p  D    2.22MeV
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Overview 2
• When kT << I(D)=2.2 MeV dissociation of D stops
• At kT ~ 60 KeV all neutrons are bound in nuclei
• Onset of primordial nucleosynthesis – formation of nuclei
2
H , 3 H , 3He, 4 He, 7 Be, 7 Li
• model of BBN predicts abundances of light elements today
• At recombination (380’000 y) nuclei + e- → atoms + CMB photons
e   p  H   CMB
• Atoms form stars, … → Large Scale Structures (LSS)
 Nbaryon

10  10 

N
photon


10
• Consistency of model:
light element abundances
CMB and LSS observations depend on 10  light elem  10 CMB, LSS 
?
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neutron – proton equilibrium
• When kT ~ 3 MeV neutrinos decouple from e, γ
• particle population consists of
e , e , ,  e,  , 
• Most anti-particles are annihilated
 , p, n, p, n
p  p  
• Tiny fraction of nucleons is left
 e  n  e  p
• Protons and neutrons in equilibrium due to  e  p  e  n
weak interactions with neutrinos
n  p  e  e
And neutron decay τ = (885.7 ± 0.8)s
• Weak interactions stop when W << H →n & p freeze-out
W t   n  v  T 5 H t   T 2
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kT ~ 0.8MeV
72
neutron/proton ratio vs Temperature
• As soon as kT << 1 GeV nucleons are non-relativistic kT  M p c2
• Probablity that proton is in
 M pc2 
E
energy state in [E,E+dE]
Pproton  e kT  exp  


kT 

• During equilibrium between
weak interactions
• at nucleon freeze-out time tFO
kT ~ 0.8MeV
• Free neutrons can decay
with τ = (885.7 ± 0.8)s
2014-15


2
2 

Mc

M

M
c

Nn
n
p


 exp 
 e kT


Np
kT


N n  tFO 
Nn t 
N p t 

Expanding Universe lect 2
N p  tFO 
 0.20
0.20 exp  t  
1.2  0.20 exp  t  
73
Nucleosynthesis onset
• Non-relativistic neutrons form nuclei through fusion:
formation of deuterium
n  p  2 H    2.22MeV
 formation of 2 H
 desintegration of 2 H
• Photodisintegration of 2H stops when kT ≈ 60 KeV <<
I(D)=2.2MeV
• free neutrons are gone
• And deuterons freeze-out
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Nuclear chains
• Chain of fusion reactions
Production of light nuclei
n  p  2 H    2.22 MeV
2
H  n  3H  
2
H  H  3 He  
2
H  2 H  4He  
3
H  2 H  4 He  n
4
He  3 He  7 Be  
7
Be  n  7 Li  p
• ΛCDM model predicts values of relative ratios of light
elements
• We expect the ratios to be constant over time
• Comparison to observed abundances today allows to test the
standard cosmology model
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Observables: He mass fraction
• helium mass fraction
2  Nn N p 
4y
Y


M  He  H   4 y  1 1  N n N p 
M  He 
N He
y
NH
• Is expected to be constant with time – He in stars (formed
long time after BBN) has only small contribution
• model prediction at onset of BBN : kT ~60keV, t~300s
Nn
Np
 0.135
Ypred  0.25
• Observation today in gas clouds … Yobs  0.249  0.009
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Abundances of light elements
• Standard BB nucleosynthesis theory predicts abundances
of light elements today – example Deuterium
• Observations today
DH
D
  2.82  0.21  105
H
10
10
4
BBN
Starts
kT≈80keV
t(s)
• Abundances depend on baryon/photon ratio
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Parameter: baryon/photon ratio
• ratio of baryon and photon number densities
– Baryons = atoms
– Photons = CMB radiation
 N baryon
10  10 
 N photon

10



• In standard model : ratio is constant since BBN era (kT~80
keV, t~20mins)
• Should be identical at recombination time (t~380’000y)
• Observations :
– abundances of light elements, He mass fraction → t~20mins
– CMB anisotropies from WMAP → t~380’000y
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Abundances and baryon density
Observations
Of light elements
Measure η10
ΩBh2
He mass fraction
CMB observations
with WMAP
measure ΩBh2
abundances
Model Predictions
Depend on η10 ΩBh2
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η10 79
CMB analysis
• Baryon-photon ratio
from CMB analysis
• PDG 2013
 B h2  0.02207  0.00027
NB
10 
  6.047  0.074 
N
pdg.lbl.gov
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Light element abundances
• PDG 2013
Yp  0.2465  0.0097
D / H   2.53  0.04  105
Li / H  1.6  0.3 1010
5.7  10  6.7 95%CL 
pdg.lbl.gov
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Questions?
Part 8 (chapter 6)
matter-antimatter asymmetry
Where did the anti-matter go?
What about antimatter ?
• Antiparticles from early universe have disappeared!
• Early universe: expect equal amount of particles &
antiparticles - small CP-violation in weak interactions
• Expect e.g.
N  p  N  p
N  e   N  e 
• primary charged galactic cosmic rays: detect nuclei and no
antinuclei
• Annihilation of matter with antimatter in galaxies would
yield intense X-ray and γ-ray emission – not observed
• 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 =
secundary cosmic rays
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Baryon number conservation
• Violation of baryon number conservation would explain
baryon - anti-baryon asymmetry
• Baryon number conservation = strict law in laboratory
• If no B conservation -> proton decay is allowed p  e 0
• Some theories of Grand Unification allow
p  K 
for quark-lepton transitions
• Search for proton decay in very large underground
detectors, e.g. SuperKamiokande
• No events observed → Lower limit on lifetime
  p   1033 y
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Baryons and antibaryons
• Assume net baryon number = 0 in early universe
• Assume equilibrium between photons, baryons and antibaryons up to ~ 2 GeV p  p    
• Around 10-20 MeV annihilation rate W << H
• A residu of baryons and antibaryons freeze out
Expect
2014-15
NB NB

N
N
1018
Expanding Universe lect 2
oefening
86
Baryons and antibaryons
• Baryons, antibaryons and photons did not evolve since
baryon/anti-baryon freeze-out
• Expect that today N B  N B
NB NB

N
N
• Observe
1018
NB

  6.05  0.07  1010 10 -9
N
NB
 104
NB
Much
too
large!
• Explanation?
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Baryon-antibaryon asymmetry
• Is the model wrong?
• Zacharov criterium : 3 fundamental conditions for
asymmetry in baryon anti-baryon density:
• starting from initial B=0 one would need
– Baryon number violating interactions
– Non-equilibrium situation leading to baryon/anti-baryon asymetry
– CP and C violation: anti-matter has different interactions than
matter
• Search at colliders for violation of C and CP conserving
interactions
• Alpha Magnetic Spectrometer on ISS: search for
antiparticles from space
2014-15
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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
2014-15
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