the$expanding$universe$cmb number density today 1 • cmb$photons$have$black$body$spectrum$today$...
TRANSCRIPT
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 : observaFon data – redshiHs, SN Ia, CMB, LSS, light element abundances -‐ ΛCDM parameter fits
• Part 4: radiaFon density, CMB • Part 5: ParFcle physics in the early universe, neutrino density
• Part 6: maRer-‐radiaFon decoupling • Part 7: Big Bang Nucleosynthesis • Part 8: MaRer -‐ anFmaRer asymmetry
2014-‐15 Expanding Universe lect 2 2
Last lecture
• Universe is flat k=0 • Expansion dynamics is described by Friedman-‐Lemaître equaFon
• Cosmological redshiH
• Closure parameter
• Expansion rate as funcFon of redshiH
2014-‐15 Expanding Universe lect 2 3
( )( )
( ) ( )001 0 0
R tz z t z t
R t+ = = = =∞
Ω t( ) =ρ t( )ρc t( )
H t( )2≡!R t( )R t( )!
"
##
$
%
&&
2
=8πGN3ρ tot t( )−
kc2
R t( )( )2
( )2
300
3 5.48 N
cHt GeV mG
ρπ
= =
( ) ( )( ) ( )( ) ( ) ( )( )3 4 22 1 1 1H t z z z⎡ ⎤= + + + + + +⎣ ⎦0 0 0 020 m r Λ kΩ t Ω t Ω t ΩH t
© Rubakov
ΩCDM Part 5
2014-‐15 4 Expanding Universe lect 2
Todays lecture
> TeV
© Rubakov
ΩCDM Part 5
2014-‐15 5 Expanding Universe lect 2
Todays lecture
> TeV ( ) ( )part 8N B N anti B≠ −
© Rubakov
Ωneutrino Part 5
2014-‐15 6 Expanding Universe lect 2
Todays lecture
ΩCDM Part 5
( ) ( )part 8N B N anti B≠ −
© Rubakov
Ωbaryons Part 7
2014-‐15 7 Expanding Universe lect 2
Todays lecture
Ωneutrino Part 5
ΩCDM Part 5
( ) ( )part 8N B N anti B≠ −
© Rubakov
Ωbaryons Part 7
2014-‐15 8 Expanding Universe lect 2
Todays lecture
Ωneutrino Part 5
ΩCDM Part 5
Ωrad Part 4&6
( ) ( )part 8N B N anti B≠ −
Part 4 radiation component - CMB Physics of the Cosmic Microwave Background
Present day photon density
Ωrad
CMB in Big Bang model
2014-‐15 Expanding Universe lect 2 10
© Univ Oregon
Baryons/nuclei and photons in thermal equilibrium
Ø Photons decouple/freeze-‐out Ø During expansion they cool down Ø Expect to see today a uniform γ radiaFon which behaves like a black body radia2on
photons are released
MaRer
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 absorpFon of mm waves in atmosphere
• Observed spectrum was compaFble with black body radiaFon with T = (3.5 ±1) K
• Obtained the Nobel Prize in 1978 (hRp://nobelprize.org/)
2014-‐15 Expanding Universe lect 2 11
• To go down to mm wavelengths : put instruments on satellites • COBE = COsmic Background Explorer (NASA) satellite observaFons in
1990s: mm wavelengths • Large scale dipole anisotropy due to moFon of solar system in
universe, with respect to CMB rest frame
• Strong radio emission in galacFc plane • AHer subtracFon of dipole and away from galacFc centre: radiaFon
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
COBE : black body spectrum
2014-‐15 Expanding Universe lect 2 12
( )solar system 300 kmv s≈
CMB temperature map
2014-‐15 Expanding Universe lect 2 13
( )3dipole 10T O mKT−Δ ≈ →
( )510T O µKT−Δ ≈ →
small ripples on top of Black Body radiation:
COBE measures black body spectrum
2014-‐15 Expanding Universe lect 2 14
Intensity Q
Frequency ν (cm-‐1)
λ=2mm 0.5mm
( )3
2 2,4
12
kQ
ceωω
π
ω πν
=
−=
hh
TTω
• Plancks radiaFon law for relaFvisFc photon gas
• Black body with temperature T emits radiaFon with power Q at frequencies
COBE measures black body spectrum
2014-‐15 Expanding Universe lect 2 15
Intensity Q
Frequency ν (cm-‐1)
λ=2mm 0.5mm
( ) ( )( )
2.7255 0.0006
max 2
T CMB K
mmλ
= ±
=
0.235E kT meV= =
• CMB has ‘perfect’ black body spectrum
• Fit of data of different observatoria to black body spectrum gives (pdg.lbl.gov, CMB, 2013)
• Or
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 distribu2on : number of photons per unit volume in momentum interval [p,p+dp]
2014-‐15 Expanding Universe lect 2 16
( )2
2 3 1Ek
p dpn p dpeπ
⎛ ⎞= ⎜ ⎟
⎡ ⎤ ⎝ ⎠−⎢ ⎥⎣ ⎦
h T
γg2 gγ = number of
photon substates
Black body
CMB number density today 2
2014-‐15 Expanding Universe lect 2 17
( )N
n n p dpVγ
γ = = ∫
( ) 30 411n t cmγ
−=
gγ=2
T=2.725K
3
2
12.404 kTncγ π
⎛ ⎞= ⎜ ⎟⎝ ⎠h
CMB energy density today
2014-‐15 Expanding Universe lect 2 18
( )2c n p dpρ = ∫E
( )2 30 0.261rc t MeV mρ −=
( )0 54.84 10rr
ct ρ
ρ−Ω = = ×
( )( )
442
32
115
c kTc
πρ
π
⎛ ⎞= ⎜ ⎟
⎝ ⎠hT=2.725K
radiation energy density vs time • In our model the early universe is radiaFon dominated • For flat universe → Friedmann equa2on
• energy density of radiaFon during expansion
• IntegraFon yields
2014-‐15 Expanding Universe lect 2 19
!R2
R2=8πGN3
!
"#
$
%&ρrad
1ρdρdt
= −4!RR= −4
8πGNρrad3
!
"#
$
%&
12
( )2
22
3 132 N
radcc tG
ρπ
=t
( )4 41rad z Rρ −∝ + ∝
CMB temperature vs time
• for t0 = 14Gyr expect TCMB (today) ≈ 10K !!! • BUT! COBE measures T = 2.7K
• Explana2on???
2014-‐15 Expanding Universe lect 2 20
11 43 5 4
132
45 2 132
ckG gγπ
⎛ ⎞⎛ ⎞= × ×⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
hTt
1.31 1rad dom
MeVTk− = 1
2t
22
2
3 132 N
radccG
ρπ
=t
ρradc2 = π 4 kT( )
4×gγ2
!
"##
$
%&&×
115π 2h3c3
Summary
2014-‐15 Expanding Universe lect 2 21
( )
( )
( )
42
32
2
22
1
1
1
radiation c z
matter c z
vacuum c cst
curvature c z
ρ
ρ
ρ
ρ
+
+
+
:
:
:
:
R ~1/T
QuesFons?
Part 5 particle physics in the early universe
RadiaFon dominated universe From end of inflaFon to maRer-‐radiaFon decoupling
From ~ 107 GeV to eV Physics beyond the Standard Model, SM, nuclear physics
Radiation domination era
2014-‐15 Expanding Universe lect 2 24
Planck era GUT era
• At end of inflaFon phase there is a rehea.ng phase
• RelaFvisFc parFcles are created
• Expansion is radiaFon dominated
• Hot Big Bang evoluFon starts
t
kT
TeV
Radiation domination era
2014-‐15 Expanding Universe lect 2 25
Planck era GUT era
• At end of inflaFon phase there is a rehea.ng phase
• RelaFvisFc parFcles are created
• Expansion is radiaFon dominated
• Hot Big Bang evoluFon starts
t
R
Radiation domination era
2014-‐15 Expanding Universe lect 2 26
Planck era GUT era
t
kT
TeV Today’s lecture
2014-‐15 Expanding Universe lect 2 27
Grand UnificaFon ~ 1015 GeV
InflaFon period
Planck mass ~ 1019 GeV
10 TeV-‐100 GeV
LHC-‐LEP
2014-‐15 Expanding Universe lect 2 28
Grand UnificaFon ~ 1015 GeV
InflaFon period
Planck mass ~ 1019 GeV
10 TeV-‐100 GeV
LHC-‐LEP
Today’s lecture
kT >> 100 GEV
RelaFvisFc parFcles RadiaFon dominated
2014-‐15 Expanding Universe lect 2 29
relativistic particles in early universe • In the early hot universe relaFvisFc fermions and bosons contribute to the energy density
• They are in thermal equilibrium at mean temperature T
• Fermion gas = quarks, leptons • Fermi-‐Dirac staFsFcs (gf = nb of substates)
• boson gas = photons, W and Z bosons … • Bose Einstein staFsFcs (gb = nb of substates)
2014-‐15 Expanding Universe lect 2 30
( )2
2 3 21EkT
p dpn p dpeπ
⎛ ⎞= ⎜ ⎟
⎡ ⎤ ⎝ ⎠⎢ ⎥⎣ ⎦
h
bg
−
( )2
2 3 21EkT
p dpn p dpeπ
⎛ ⎞= ⎜ ⎟⎜ ⎟⎡ ⎤ ⎝ ⎠⎢ ⎥⎣ ⎦
h
fg
+
relativistic particles in early universe
• Bosons and fermions contribute to energy density with
2014-‐15 Expanding Universe lect 2 31
n p( )dp = p2dp
π 2!3 eEkT −1
"
#$%
&'
gb2
(
)*
+
,- ( )
2
2 3 21EkT
p dpn p dpeπ
⎛ ⎞= ⎜ ⎟⎜ ⎟⎡ ⎤ ⎝ ⎠
⎢ ⎥⎣ ⎦h
fg
+
( ) ( )42 4* 2 3 3
*1 715 2 8b fc t kT g g
cgρ π
π
⎛ ⎞= = +⎜ ⎟⎜ ⎟
⎝ ⎠∑ ∑h
*g
( )2c n p dpρ = ∫E
Degrees of freedom for kT > 100 GeV
2014-‐15 Expanding Universe lect 2 32
bosons spin per parFcle total W+ W-‐ Z gluons photon H-‐boson total bosons 28 fermions spin per parFcle total quarks anFquarks e,µ,τ neutrinos anF-‐neutrinos total fermions 90
If we take only the known particles
Degrees of freedom for kT > 100 GeV
2014-‐15 Expanding Universe lect 2 33
bosons spin per parFcle total W+ 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 28 fermions spin per parFcle total quarks ½ 3 (color) x 2 (spin) 6 x 3 x 2 = 36 anFquarks 36 e,µ,τ ½ 2 6 x 2 = 12 neutrinos LH 1 3 x 1 = 3 anF-‐neutrinos RH 1 3 x 1 = 3 total fermions 90
Degrees of freedom for kT > 100 GeV
• Assuming only parFcles from Standard Model of parFcle physics
• Energy density in hot universe
2014-‐15 Expanding Universe lect 2 34
* 728 90 106.758
g = + × =
( ) ( )42 4* 2 3 3
115 2
c t kTc
ρ ππ
⎛ ⎞= ⎜ ⎟
⎝ ⎠h
*g
what happens if there were particles from theories beyond the Standard Model?
For instance : SuperSymmetry
• At LHC energies and higher : possibly SuperSymmetry • Symmetry between fermions and bosons • Consequence is a superpartner for every SM parFcle • ~ 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 gravita.onal interac.ons
• is Lightest Supersymmetric ParFcle – LSP -‐ in R-‐parity conserving scenarios → stable
• Massive : Searches at LEP and Tevatron colliders
2014-‐15 Expanding Universe lect 2 36
!χ10
m !χ01( ) > 50GeV c2
Rp =
Neutralino = Dark Matter ?
• Lightest neutralino may have been created in the early hot universe when
• Equilibrium interacFons • When kT is too low, neutralinos freeze-‐out (decouple)
• → are non-‐relaFvisFc at decoupling = ‘cold’ • survive as independent populaFon Fll today • the observed dark maRer abundance today puts an upper limit on the mass (chapter 7)
2014-‐15 Expanding Universe lect 2 37
e+ + e− ↔ !χ01 + !χ0
1
m !χ01( ) < 5TeV c2
kT >>m !χ01( )c2
1CDMΩ <
e+ + e− ← !χ01 + !χ0
1e+ + e− → !χ01 + !χ0
1
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, exoFc parFcles
• Temperature decreases with Fme
• ProducFon of parFcles M stops when • For example,
• some parFcles decay: W, Z, t .. • Run out of heavy par2cles when kT<<100GeV 2014-‐15 Expanding Universe lect 2 39
2kT Mc<<
( ) 23, 10W Z sτ −≈
e e W W+ − + −+ → + 2 160Ws M GeV> =
12
1~rad domTt−
when
p p t t X+ → + + when 2 346tops M GeV> =
Age of universe at kT ≈ few GeV
• RadiaFon dominated expansion since Big Bang
• Calculate Fme difference relaFve to Planck era
• Calculate age of universe at • kT=100 GeV t= • kT = 1 GeV t= • kT = 200 MeV t= • And compare to lifeFmes of unstable parFcles
2014-‐15 Expanding Universe lect 2 40
1.31 1rad dom
MeVTk− = 1
2t
QuesFons?
COOLDOWN TO kT ≈ 200 MEV Free quarks form hadrons
2014-‐15 Expanding Universe lect 2 42
A phase transition
2014-‐15 Expanding Universe lect 2 43
g*
kT(GeV)
200 MeV
Quarks form hadrons Decay of parFcles with lifeFme < µsec
Down to kT ≈ 200 MeV
2014-‐15 Expanding Universe lect 2 44
• Phase transi2on from Quark Gluon Plasma (QGP) to hadrons • Ruled by Quantum Chromo Dynamics (QCD) describing strong interacFons • Strong coupling constant is ‘running’ : energy dependent • From perturbaFve regime to non-‐perturbaFve regime around ΛQCD
confinement Quarks cannot be free at distances
of more than 1fm = 10-‐15m
200QCD MeVΛ =
E Tµ ∝ ∝ From fit to data
( ) ( )2
0
2 222
1~4 lnStrong
Sg
Qb
α µπ µ
= =QCDΛ
When µ ≈ 200 MeV
αs t
2014-‐15 Expanding Universe lect 2 45
Colour confinement large distances
AsymptoFc freedom small distances
Expansion of universe Increases inter-‐quark distance
• free quarks and gluons are gone and hadrons are formed • Most hadrons are short lived and decay with
• Example
• Leptons : muon and tauon decay weakly
around and below kT ≈ 200 MeV
2014-‐15 Expanding Universe lect 2 46
( ) ( )8 2310 weak ints. 10 strong ints.s sτ − −= −
( )( )
15319 10
17%
.......
s
µ τ
τ τ
τ ν νµ
−
− −
→
+
= ×
→ +
( ) ( )0
1115
uds
n
p
n e
p
eµπ
π
νµ−
+
−
−
Λ
+
= → + +
→ + → +
→ +
( ) 62 10
ee
s
µ
τ µ
µ ν ν
−
− − +
×
→ +
=
Stable or long lived
<< 1µs
pauze
QUESTIONS?
COOLDOWN TO A FEW MEV
Run out of unstable hadrons Neutrino decoupling/freeze-‐out Big bang nucleosynthesis
2014-‐15 Expanding Universe lect 2 48
• AHer about 1ms all unstable parFcles have decayed • Most, but not all, nucleons annihilate with anF-‐nucleons (chapter 6)
g*
kT(GeV) TeV
GeV MeV
106.75
10
3.4
Cooldown to kT ≈ 10MeV
2014-‐15 49
* 7 43 10810
42g ⎛ ⎞= + = ≈⎜ ⎟
⎝ ⎠
p p γ γ+ → +
Expanding Universe lect 2
18~10baryonsnnγ
−expect
we are leH with γ + e-, νe, νµ, ντ and their anF-‐parFcles
Around kT ≈ MeV: Big Bang Nucleosynthesis
• around few MeV: mainly relaFvisFc γ, e,νe, νμ, ντ + anF-‐parFcles in thermal equilibrium
• + few protons & neutrons • weak interacFons become very weak
• start primordial nucleosynthesis: formaFon of light nuclei (chapter 6)
2014-‐15 Expanding Universe lect 2 50
2
3
2 2 4
2
2.22
...........
HHHe
n p MeVH nH H
γ
γ
γ
+ ↔ + +
+ → +
+ → +
i i
e
e
e
e e
n e pp e n
n p e
ν ν
ν
ν
ν
+ −
−
+
−
+ ↔ +
+ ↔ +
+ ↔ +
→ + +
Around kT ≈ 3MeV : Neutrino freeze out
• Equilibrium between photons and leptons
• remaining photons today : CMB with T=2.75K
• What about remaining neutrinos? • Weak interacFon cross secFon decreases with energy
2014-‐15 Expanding Universe lect 2 51
( ) , ,i ie e i eν νγ µ τ+ −+↔ ↔ + = Weak interacFon
25 2~ s CM energy 1.166 106
FF
G G GeVσ π− −= = ×s
( ) 30 411n t cmγ
−= ρrc2 t0( ) = 0.261MeV m−3
Neutrino freeze-out
• weak collision rate interacFons/sec
• relaFve
• During expansion T decreases • As soon as W < H neutrinos stop interacFng
2014-‐15 Expanding Universe lect 2 52
W v= σn
e+, e-‐ number density (FD staFsFcs) ~ T3
, ,i ie e i eν ν µ τ+ −+ ↔ + =
Weak Cross secFon ~ s ~ T2
RelaFve velocity of e+
and e-‐
( ) 2 H t T∝5 W T∝
Weak interacFon
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 ma9er?
2014-‐15 Expanding Universe lect 2 53
Cosmic Neutrino Background • At a few MeV • Number density of neutrinos ≈ number density of photons • But photons are boosted by reacFon • In the end the photons have a higher temperature than the neutrinos with
• expected Temperature of neutrinos today
• expected density of relic neutrinos today: for given species (νe, νμ, ντ )
2014-‐15 Expanding Universe lect 2 54
( ) , ,i ie e i eν νγ µ τ+ −+↔ ↔ + =
0( ) 1.95T t Kν = 0( )E t meVν ≈
33 11311
N N cmNν γν−⎛ ⎞= =⎜ ⎟
⎝ ⎠+
e+ + e− → γ +γ
Tν =411!
"#
$
%&
13Tγ
Overview of radiation dominated era
2014-‐15 Expanding Universe lect 2 55
g*
kT(GeV) TeV
GeV MeV
106.75
10
3.4
Neutrino Decoupling and nucleosynthesis
Quarks confined in hadrons
ep recombinaFon TransiFon to maRer dominated universe
Run out of relaFvisFc parFcles
© Rubakov
Ωbaryons Part 7
2014-‐15 56 Expanding Universe lect 2
Todays lecture
Ωneutrino Part 5
ΩCDM Part 5
Ωrad Part 4&6
( ) ( )part 8N B N anti B≠ −
QuesFons?
Part 6 matter and radiation decoupling
RecombinaFon 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 • maRer decouples from radiaFon and photons can move freely & remain as today’s CMB radiaFon
• MaRer evolves independently -‐ atoms & molecules are formed → stars, galaxies, …
• Before tdec universe is ionised and opaque
• PopulaFon consists of p, H, e, γ + light nuclei + neutrinos
2014-‐15 Expanding Universe lect 2 59
Protons and neutral hydrogen
Ø At kT ~ 3 MeV neutrino freeze-‐out and start of BB nucleosynthesis – most p and n bound in light nuclei (part 7)
Ø Photon density much higher than proton density observa.ons
• Up to t ≈ 100.000 y thermal equilibrium of p, H, e, γ
• When kT < I=13.6 eV 2014-‐15 Expanding Universe lect 2 60
formation of neutral hydrogenionisation of hydrogen atom
e p H γ− + ↔ +
→
←
10~10p
NN
γp eN N=
e p− + ←⎯⎯H γ+ Tdec?
Ne and Np = free e and p NH = bound H atoms
Protons and neutral hydrogen
• number density of free protons Np and of neutral hydrogen atoms NH as funcFon of T
• At which T will universe run out of ionised hydrogen? temperature at decoupling
2014-‐15 Expanding Universe lect 2 61
2
321 2H
H
p
H
kN N mk eN N h
π+
−⎛ ⎞⎛ ⎞= = ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠e
TI
NT
m=electron mass
NeN pNH
=Prob electron unbound( )
Prob electron bound in H atom( ) f(T)
Decoupling temperature • Rewrite in funcFon of fracFon x of ionised hydrogen atoms
• strong drop of x between kT ≈ 0.35 -‐ 0.25 eV • or T between 4000 – 3000 K • è ionisaFon stops around T~3500K
• period of recombina.on of e and p to hydrogen atoms
• RecombinaFon stops when electron density is too small
2014-‐15 Expanding Universe lect 2 62
2
2
321 2
1 B
Ikx mk e
x N hπ −⎛ ⎞⎛ ⎞= ⎜ ⎟⎜ ⎟− ⎝ ⎠⎝ ⎠
TTp
p H
p
B
NNx
N N N= =
+
e p H γ− + → +
e p− + ←⎯⎯H γ+
Decoupling time
• ReshiH at decoupling
• Full calculaFon
• When electron density is too small there is no H formaFon anymore
• → Photons freeze out as independent populaFon = CMB
• start of ma9er dominated universe • We are leH with atoms, CMB photons and relic neutrinos • + possibly relic exoFc parFcles (neutralinos, …) 2014-‐15 Expanding Universe lect 2 63
( ) ( )( )
0
0
35001 12702.75
decdec
dec
R t kT KzkT KR t
+ = = = ≈
( )1 1100decz+ = 53.7 10dect y= ×
Era of matter-radiation equality
• since
• Density of baryons = density of photons when
• Density of maRer (baryons + Dark Ma`er) = density of photons + neutrinos when
• MaLer dominates over rela.vis.c par.cles when Z < 3000 2014-‐15 Expanding Universe lect 2 64
3baryonicmatter TΩ : 4
photons TΩ :
( )( )
( )( )0
0
1 11
bar
ph
bar
phot ot
tt
tzt
Ω
Ω
Ω
+Ω= = ( )1 870 1 decz z+ = ≈ +
1 3130z+ ≈( )( )
( )( )
0
0
1 11.58 1
mmatter
pphot neut hot
tt
tzt+
Ω
Ω
Ω= =
Ω × +
2014-‐15 Expanding Universe lect 2 65
( ) ( )311 wzρ+
∝ +
© J. Frieman
z~3000 z~1000
Summary
2014-‐15 Expanding Universe lect 2 66
Energy per parFcle
T(K)
Time 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 : observaFon data – redshiHs, SN Ia, CMB, LSS, light element abundances -‐ ΛCDM parameter fits
• Part 4: radia2on density, CMB • Part 5: Par2cle physics in the early universe, neutrino density
• Part 6: ma`er-‐radia2on decoupling • Part 7: Big Bang Nucleosynthesis • Part 8: MaRer and anFmaRer
2014-‐15 Expanding Universe lect 2 67
QuesFons?
Part 7 (chapter 6) Big Bang Nucleosynthesis formaFon of light nuclei when kT ~ MeV ObservaFon of light element abundances
Baryon/photon raFo ΩBAR
Overview 1 • at period of neutrino decoupling when kT ~ 3 MeV
• AnF-‐parFcles are annihilated – parFcles remain (part 8)
• Fate of baryons? → Big Bang Nucleosynthesis model • Protons and neutrons in equilibrium due to weak interacFons
• n and p freeze-‐out at ~ 1 MeV -‐ Free neutrons decay • Neutrons are ‘saved’ by binding to protons → deuterons
2014-‐15 Expanding Universe lect 2 70
( ),
,, ,
,,,, ,e
ne
p nep
ν ν µ
γ
τ−+
p p γ γ+ → + 10~ 10BARNNγ
−
e nepν ++ ↔ + eepn ν−→ + +
2.22n p D MeVγ+ ↔ + +
observed
Overview 2 • When kT << I(D)=2.2 MeV dissociaFon of D stops • At kT ~ 60 KeV all neutrons are bound in nuclei • Onset of primordial nucleosynthesis – formaFon of nuclei
• model of BBN predicts abundances of light elements today
• At recombina.on (380’000 y) nuclei + e-‐ → atoms + CMB photons
• Atoms form stars, … → Large Scale Structures (LSS)
• Consistency of model: light element abundances CMB and LSS observaFons depend on
2014-‐15 Expanding Universe lect 2 71
2 3 43 77,, , , ,H He HeH Be Li
CMBe p H γ− + → +
1010 10 baryon
photon
NNη ⎛ ⎞≡ ⎜ ⎟
⎝ ⎠
( ) ( )10 10 ,light elem CMB LSSη η=?
neutron – proton equilibrium • When kT ~ 3 MeV neutrinos decouple from e, γ • parFcle populaFon consists of
• Most anF-‐parFcles are annihilated
• Tiny fracFon of nucleons is leH
• Protons and neutrons in equilibrium due to weak interac.ons with neutrinos And neutron decay τ = (885.7 ± 0.8)s
• Weak interacFons stop when W << H →n & p freeze-out
2014-‐15 Expanding Universe lect 2 72
eepn ν−→ + +
e
e
ee
pnp n
ν
ν
−
+
+ ↔ +
+ ↔ +
( ) 2 H t T∝( ) 5 W t n v Tσ= ∝
( ),
,, ,
,,,, ,e
ne
p nep
ν ν µ
γ
τ−+
p p γ γ+ → +
~ 0.8kT MeV
neutron/proton ratio vs Temperature • As soon as kT << 1 GeV nucleons are non-‐rela.vis.c • Probablity that proton is in energy state in [E,E+dE]
• During equilibrium between weak interacFons
• at nucleon freeze-‐out Fme tFO kT ~ 0.8MeV
• Free neutrons can decay with τ = (885.7 ± 0.8)s
2014-‐15 Expanding Universe lect 2 73
( ) 2 2
expMc
n pn kT
p
M M cN eN kT
Δ−⎛ ⎞−⎜ ⎟= − =⎜ ⎟⎝ ⎠
( )( ) 0.20FO
FO
np
N tN t =
2pkT M c<
2
expproton
EpkT M c
P ekT
− ⎛ ⎞∝ = −⎜ ⎟⎜ ⎟
⎝ ⎠
( )( )
( )( )
exp1.2 exp0.200.20
n
p
N t tN t t
τ
τ
−=⎡ ⎤− −⎣ ⎦
Nucleosynthesis onset
• Non-‐relaFvisFc neutrons form nuclei through fusion: formaFon of deuterium
• PhotodisintegraFon of 2H stops when kT ≈ 60 KeV << I(D)=2.2MeV
• free neutrons are gone • And deuterons freeze-‐out
2014-‐15 Expanding Universe lect 2 74
2
2
2
2.22formation of desintegration of
n p H MeVH
H
γ+ ↔ + +
→
←
• Chain of fusion reactions Production of light nuclei
• 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
Nuclear chains
2 3
2
2 2
3 2 4
4 3
7
2
3
7
2.22H
He
B
n p MeVH n HH HH HH H He nHe HeBe n p
e
γ
γ
γ
γ
γ
+ ↔ + +
+ → +
+ → +
+ → +
+ → +
+ → +
+ → +
K
4
7
He
Li
2014-‐15 Expanding Universe lect 2 75
• helium mass fracFon
• Is expected to be constant with Fme – He in stars (formed long Fme aHer BBN) has only small contribuFon
• model predic.on at onset of BBN : kT ~60keV, t~300s • ObservaFon today in gas clouds …
Observables: He mass fraction
2014-‐15 Expanding Universe lect 2 76
( )( ) ( )
( )( )24
4 1 1n p
n p
N NM He yYM He H y N N
= = =+ + +
0.25predY =
He
H
NyN
=
0.249 0.009obsY = ±
0.135np
NN =
Abundances of light elements • Standard BB nucleosynthesis theory predicts abundances of light elements today – example Deuterium
• ObservaFons today
• Abundances depend on baryon/photon raFo 2014-‐15 Expanding Universe lect 2 77
BBN Starts kT≈80keV
410−
t(s)
D H10η
( ) 52.82 0.21 10DH
−= ± ×
Parameter: baryon/photon ratio
• raFo of baryon and photon number densiFes – Baryons = atoms – Photons = CMB radiaFon
• In standard model : raFo is constant since BBN era (kT~80 keV, t~20mins)
• Should be idenFcal at recombinaFon Fme (t~380’000y) • ObservaFons :
– abundances of light elements, He mass fracFon → t~20mins – CMB anisotropies from WMAP → t~380’000y
2014-‐15 Expanding Universe lect 2 78
1010 10 baryon
photon
NN
η⎛ ⎞
≡ ⎜ ⎟⎜ ⎟⎝ ⎠
Abundances and baryon density
2014-‐15 Expanding Universe lect 2 79
He mass fracFon
abundances
ΩBh2
η10
ObservaFons Of light elements Measure
Model PredicFons Depend on η10 ΩBh2
CMB observaFons with WMAP measure ΩBh2
η10
• Baryon-‐photon raFo from CMB analysis
• PDG 2013
2014-‐15 Expanding Universe lect 2 80
CMB analysis
( )
2
10
0.02207 0.00027
6.047 0.074B
BhNNγ
η
Ω = ±
= = ±
pdg.lbl.gov
• PDG 2013
2014-‐15 Expanding Universe lect 2 81
Light element abundances
( )( )
5
10
0.2465 0.0097
/ 2.53 0.04 10
/ 1.6 0.3 10
pY
D H
Li H
−
−
= ±
= ± ×
= ± ×
( )105.7 6.7 95%CLη< <
pdg.lbl.gov
QuesFons?
Part 8 (chapter 6) matter-antimatter asymmetry
Where did the anF-‐maRer go?
What about antimatter ? • An.par.cles from early universe have disappeared! • Early universe: expect equal amount of parFcles & anFparFcles -‐ small CP-‐violaFon in weak interacFons
• Expect e.g.
• primary charged galacFc cosmic rays: detect nuclei and no anFnuclei
• AnnihilaFon of maRer with anFmaRer in galaxies would yield intense X-‐ray and γ-‐ray emission – not observed
• Few positrons and an.protons fall in on Earth atmosphere : in agreement with pair creaFon in inter-‐stellar maRer
• An.par.cles produced in showers in Earth atmosphere = secundary cosmic rays
2014-‐15 Expanding Universe lect 2 84
( ) ( )N e N e+ −= ( ) ( )N p N p=
Baryon number conservation
• ViolaFon of baryon number conservaFon would explain baryon -‐ anF-‐baryon asymmetry
• Baryon number conserva.on = strict law in laboratory • If no B conservaFon -‐> proton decay is allowed • Some theories of Grand UnificaFon allow for quark-‐lepton transiFons
• Search for proton decay in very large underground detectors, e.g. SuperKamiokande
• No events observed → Lower limit on lifeFme
2014-‐15 Expanding Universe lect 2 85
0p ep K
π
ν
+
+
→
→
( ) 3310p yτ >
Baryons and antibaryons • Assume net baryon number = 0 in early universe • Assume equilibrium between photons, baryons and anF-‐baryons up to ~ 2 GeV
• Around 10-‐20 MeV annihilaFon rate W << H • A residu of baryons and anFbaryons freeze out
Expect
2014-‐15 Expanding Universe lect 2 86
p p γ γ+ ↔ +
1810B BNNN Nγ γ
−= :oefening
Baryons and antibaryons • Baryons, anFbaryons and photons did not evolve since baryon/anF-‐baryon freeze-‐out
• Expect that today
• Observe
• ExplanaFon?
2014-‐15 Expanding Universe lect 2 87
1810
B B
B B
N NNN
N Nγ γ
−
=
= :
( ) 10
4
6.05 0.07 10
10
B
B
B
NN
NN
γ
η −
−
= = ± ×
<
: -910Much too large!
Baryon-antibaryon asymmetry • Is the model wrong? • Zacharov criterium : 3 fundamental condi.ons for asymmetry in baryon an.-‐baryon density:
• starFng from iniFal B=0 one would need – Baryon number violaFng interacFons – Non-‐equilibrium situaFon leading to baryon/anF-‐baryon asymetry – CP and C violaFon: anF-‐maRer has different interacFons than maRer
• Search at colliders for violaFon of C and CP conserving interacFons
• Alpha MagneFc Spectrometer on ISS: search for anFparFcles from space
2014-‐15 Expanding Universe lect 2 88
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 : observaFon data – redshiHs, SN Ia, CMB, LSS, light element abundances -‐ ΛCDM parameter fits
• Part 4: radiaFon density, CMB • Part 5: ParFcle physics in the early universe, neutrino density
• Part 6: maRer-‐radiaFon decoupling • Part 7: Big Bang Nucleosynthesis • Part 8: MaRer and anFmaRer
2014-‐15 Expanding Universe lect 2 89