The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 :...

90
The expanding universe Lecture 2

Transcript of The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 :...

Page 1: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

The expanding universe

Lecture 2

Page 2: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 3: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

⎣ ⎦

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reslectur

Todays

ΩCDM

T

> TeV CDMPart 5

© Rubakov2013‐14 4Expanding Universe lect 2

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reslectur

Todays

ΩCDM

T

> TeV( ) ( )N B N anti B≠ − CDMPart 5

( ) ( )part 8

© Rubakov2013‐14 5Expanding Universe lect 2

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reslectur

ΩneutrinoPart 5

Todays

T

ΩCDM( ) ( )N B N anti B≠ − CDMPart 5

( ) ( )part 8

© Rubakov2013‐14 6Expanding Universe lect 2

Page 7: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 8: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 9: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

Part 4Part 4radiation component - CMBpPhysics of the Cosmic Microwave Backgroundy g

Present day photon density

Page 10: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 11: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 12: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 13: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 14: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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 ( )

Page 15: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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 ( )

Page 16: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 17: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 18: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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 =

Page 19: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 20: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 21: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 22: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

Questions?

Page 23: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 24: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 25: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 26: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

Radiation domination eraPlanck era GUT eraPlanck era GUT era

kT

TeVToday’s lecture

2013‐14 Expanding Universe lect 2 26

t

Page 27: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

Grand Planck mass 1 TeV‐100 Unification~ 1015 GeV

~ 1019 GeV GeVLHC‐LEP

Inflation periodperiod

2013‐14 Expanding Universe lect 2 27

Page 28: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 29: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

Relativistic particles

Radiation dominated

kT >> 100 GEV

2013‐14 Expanding Universe lect 2 29

Page 30: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

⎣ ⎦

Page 31: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 32: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 33: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 34: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 35: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 36: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 37: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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 <

Page 38: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

Questions?

Page 39: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

COOLDOWN TO A FEW GEV

2013‐14 Expanding Universe lect 2 39

Page 40: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 41: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 42: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

Quarks form hadrons

COOLDOWN TO kT ≈ 200 MEVQ

2013‐14 Expanding Universe lect 2 42

Page 43: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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)

Page 44: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

Page 45: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

Colour confinementlarge distancesg

Asymptotic freedom

2013‐14 Expanding Universe lect 2 45

small distances

Page 46: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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+→ +

Page 47: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

pauze

QUESTIONS?Q

Page 48: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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

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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 ⎛ ⎞= + = ≈⎜ ⎟

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

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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

...........

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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

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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

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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

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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

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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

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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

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Questions?

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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

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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

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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?

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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

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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

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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

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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

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( ) ( )3 11 wzρ +∝ +

~1000z~3000 z~1000

2013‐14 Expanding Universe lect1 65

© J. Frieman

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Summary

cle

er partic T(K)

ergy

peEne

2013‐14 Expanding Universe lect 2 66Time t(s)

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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

2013‐14 Expanding Universe lect 2 67

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Questions?

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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

Page 70: The expanding universe - iihe.ac.be · 2014-02-28 · Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmologicalprinciple, geometryof universe •

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+ ↔ + +

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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=?

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Questions?

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Part 8 (chapter 6)Part 8 (chapter 6)matter-antimatter asymmetryy y

Where did the anti‐matter go?g

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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

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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

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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

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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

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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

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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

2013‐14 Expanding Universe lect 2 90