The$expanding$universe$cdeclerc/astroparticles/2014-15/...CMB in Big Bang model 201415 $...

92
The expanding universe Lecture 2

Transcript of The$expanding$universe$cdeclerc/astroparticles/2014-15/...CMB in Big Bang model 201415 $...

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The  expanding  universe  

Lecture  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  :  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  

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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

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© Rubakov  

ΩCDM  Part 5

2014-­‐15   4  Expanding  Universe  lect  2  

Todays  lecture  

>  TeV  

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© Rubakov  

ΩCDM  Part 5

2014-­‐15   5  Expanding  Universe  lect  2  

Todays  lecture  

>  TeV  ( ) ( )part 8N B N anti B≠ −

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© Rubakov  

Ωneutrino Part 5  

2014-­‐15   6  Expanding  Universe  lect  2  

Todays  lecture  

ΩCDM  Part 5

( ) ( )part 8N B N anti B≠ −

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© 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≠ −

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© 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≠ −

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Part 4 radiation component - CMB  Physics  of  the  Cosmic  Microwave  Background  

Present  day  photon  density  

Ωrad

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CMB in Big Bang model

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© 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    

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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/)  

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•  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

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( )solar system 300 kmv s≈

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CMB temperature map

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( )3dipole 10T O mKT−Δ ≈ →

( )510T O µKT−Δ ≈ →

small ripples on top of Black Body radiation:

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COBE measures black body spectrum

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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    

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COBE measures black body spectrum

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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    

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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]  

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( )2

2 3 1Ek

p dpn p dpeπ

⎛ ⎞= ⎜ ⎟

⎡ ⎤ ⎝ ⎠−⎢ ⎥⎣ ⎦

h T

γg2 gγ  =  number  of  

photon  substates  

Black  body  

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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

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CMB energy density today

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( )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  

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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  

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!R2

R2=8πGN3

!

"#

$

%&ρrad

1ρdρdt

= −4!RR= −4

8πGNρrad3

!

"#

$

%&

12

( )2

22

3 132 N

radcc tG

ρπ

=t

( )4 41rad z Rρ −∝ + ∝

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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

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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

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2014-­‐15   Expanding  Universe  lect  2   22  

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QuesFons?  

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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  

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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  

kT  

TeV  

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Radiation domination era

2014-­‐15   Expanding  Universe  lect  2   26  

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  

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Radiation domination era

2014-­‐15   Expanding  Universe  lect  2   27  

Planck  era   GUT  era  

t  

kT  

TeV  Today’s  lecture  

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2014-­‐15   Expanding  Universe  lect  2   28  

Grand  UnificaFon  ~  1015  GeV  

 InflaFon  period  

Planck  mass  ~  1019  GeV  

10  TeV-­‐100  GeV  

LHC-­‐LEP  

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2014-­‐15   Expanding  Universe  lect  2   29  

Grand  UnificaFon  ~  1015  GeV  

 InflaFon  period  

Planck  mass  ~  1019  GeV  

10  TeV-­‐100  GeV  

LHC-­‐LEP  

Today’s  lecture  

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kT  >>  100  GEV  

RelaFvisFc  parFcles  RadiaFon  dominated  

2014-­‐15   Expanding  Universe  lect  2   30  

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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   31  

( )2

2 3 21EkT

p dpn p dpeπ

⎛ ⎞= ⎜ ⎟

⎡ ⎤ ⎝ ⎠⎢ ⎥⎣ ⎦

h

bg

( )2

2 3 21EkT

p dpn p dpeπ

⎛ ⎞= ⎜ ⎟⎜ ⎟⎡ ⎤ ⎝ ⎠⎢ ⎥⎣ ⎦

h

fg

+

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relativistic particles in early universe

•  Bosons  and  fermions  contribute  to  energy  density  with    

2014-­‐15   Expanding  Universe  lect  2   32  

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

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Degrees of freedom for kT > 100 GeV

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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

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2014-­‐15   Expanding  Universe  lect  2   34  

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Degrees of freedom for kT > 100 GeV

2014-­‐15   Expanding  Universe  lect  2   35  

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  

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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   36  

* 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?

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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   37  

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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   38  

!χ10

m !χ01( ) > 50GeV c2

Rp =

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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   39  

e+ + e− ↔ !χ01 + !χ0

1

m !χ01( ) < 5TeV c2

kT >>m !χ01( )c2

1CDMΩ <

e+ + e− ← !χ01 + !χ0

1e+ + e− → !χ01 + !χ0

1

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STATUS  AROUND  A  FEW  GEV  

2014-­‐15   Expanding  Universe  lect  2   40  

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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   41  

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> =

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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   42  

1.31 1rad dom

MeVTk− = 1

2t

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2014-­‐15   Expanding  Universe  lect  2   43  

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QuesFons?  

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COOLDOWN  TO  kT  ≈ 200  MEV  Free  quarks  form  hadrons  

2014-­‐15   Expanding  Universe  lect  2   45  

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A phase transition

2014-­‐15   Expanding  Universe  lect  2   46  

g*  

kT(GeV)  

200  MeV  

Quarks  form  hadrons  Decay  of  parFcles  with  lifeFme  <  µsec  

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Down to kT ≈ 200 MeV

2014-­‐15   Expanding  Universe  lect  2   47  

•  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  

     

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2014-­‐15   Expanding  Universe  lect  2   48  

Colour  confinement  large  distances  

AsymptoFc  freedom  small  distances  

Expansion  of  universe  Increases    inter-­‐quark  distance  

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•  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   49  

( ) ( )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  

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pauze  

QUESTIONS?  

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COOLDOWN  TO  A  FEW  MEV  

Run  out  of  unstable  hadrons  Neutrino  decoupling/freeze-­‐out  Big  bang  nucleosynthesis    

2014-­‐15   Expanding  Universe  lect  2   51  

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•  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   52  

* 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  

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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   53  

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

+ −

+

+ ↔ +

+ ↔ +

+ ↔ +

→ + +

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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   54  

( ) , ,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

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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   55  

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  

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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   56  

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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   57  

( ) , ,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

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Overview of radiation dominated era

2014-­‐15   Expanding  Universe  lect  2   58  

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  

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© Rubakov  

Ωbaryons Part 7  

2014-­‐15   59  Expanding  Universe  lect  2  

Todays  lecture  

Ωneutrino Part 5  

ΩCDM  Part 5

Ωrad Part 4&6  

( ) ( )part 8N B N anti B≠ −

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QuesFons?  

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Part 6 matter and radiation decoupling  

RecombinaFon  of  electrons  and  light  nuclei  to  atoms    Atoms  and  photons  decouple  

at  Z  ~  1100  

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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   62  

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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   63  

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  

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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   64  

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)  

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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   65  

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+

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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   66  

( ) ( )( )

0

0

35001 12702.75

decdec

dec

R t kT KzkT KR t

+ = = = ≈

( )1 1100decz+ = 53.7 10dect y= ×

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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   67  

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 × +

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2014-­‐15   Expanding  Universe  lect  2   68  

( ) ( )311 wzρ+

∝ +

© J.  Frieman  

z~3000   z~1000  

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Summary

2014-­‐15   Expanding  Universe  lect  2   69  

Energy  per  parFcle  

T(K)  

Time  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  :  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   70  

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QuesFons?  

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Part 7 (chapter 6) Big Bang Nucleosynthesis  formaFon  of  light  nuclei  when  kT  ~  MeV  ObservaFon  of  light  element  abundances    

Baryon/photon  raFo  ΩBAR  

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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   73  

( ),

,, ,

,,,, ,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  

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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   74  

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=?  

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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   75  

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

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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   76  

( ) 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

−=⎡ ⎤− −⎣ ⎦

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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   77  

2

2

2

2.22formation of desintegration of

n p H MeVH

H

γ+ ↔ + +

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•  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   78  

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•  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   79  

( )( ) ( )

( )( )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 =

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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   80  

BBN    Starts  kT≈80keV  

410−

t(s)  

D H10η

( ) 52.82 0.21 10DH

−= ± ×

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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   81  

1010 10 baryon

photon

NN

η⎛ ⎞

≡ ⎜ ⎟⎜ ⎟⎝ ⎠

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Abundances and baryon density

2014-­‐15   Expanding  Universe  lect  2   82  

He  mass  fracFon  

abundances  

ΩBh2  

η10  

ObservaFons    Of  light  elements  Measure    

Model  PredicFons  Depend  on     η10   ΩBh2  

CMB  observaFons  with  WMAP  measure     ΩBh2  

η10  

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•  Baryon-­‐photon  raFo  from  CMB  analysis  

•  PDG  2013  

2014-­‐15   Expanding  Universe  lect  2   83  

CMB analysis

( )

2

10

0.02207 0.00027

6.047 0.074B

BhNNγ

η

Ω = ±

= = ±

pdg.lbl.gov  

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•  PDG  2013  

2014-­‐15   Expanding  Universe  lect  2   84  

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  

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QuesFons?  

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Part 8 (chapter 6) matter-antimatter asymmetry  

Where  did  the  anF-­‐maRer  go?  

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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   87  

( ) ( )N e N e+ −= ( ) ( )N p N p=

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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   88  

0p ep K

π

ν

+

+

( ) 3310p yτ >

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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   89  

p p γ γ+ ↔ +

1810B BNNN Nγ γ

−= :oefening  

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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   90  

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!  

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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  

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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  :  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    

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