"From neutrinos....". DK&ER, lecture12 1 Cosmology and Relic Neutrinos Expanding Universe Big Bang...

"From neutrinos ....". DK&ER, lecture12

1

Cosmology and Relic Neutrinos

Expanding Universe Big Bang Nucleosynthesis Cosmic Microwave Background measurements Relic neutrinos Informations about neutrino mass Leptogenesis

Galaxies


2Photograph courtesy NASA, ESA, and the Hubble Heritage Team (STScI/AURA)-ESA/Hubble Collaboration

Antennae galaxiesAntennae galaxies

Andromeda galaxyAndromeda galaxy

Galaxy Evolution Explorer

Galaxies


3


4

Expanding Universe

In 1929 Hubble observed redshifts of spectral lines from distant gallaxies and ascribed them to velocities:

v =Hr where r is distance to a gallaxy

0,2z

Hubble constant

' 1(1 )

1z z


5

Expanding Universe

Expansion of the Universe depends on time. If R(t) is a universal distance scale then:

0

0

( ) ( )

v( ) ( )

r t R t r

t R t r

R

HR

H is time-dependent but today:

0 0

0,040 0,03

19

km100

s×Mpc

0,73

1 Mpc=3,09 10 km

H h

h

Universe expansion is described by the solution of Einstein equations:2 2

22

8

3 3NGR kc

HR R

gravit constant.

energy density

cosmological constant

NG

Friedmann equation

0,1 90 0,2

0

113,7 10 latt

H


6

Critical density

2 22

2

8

3 3NGR kc

HR R

0k

1k

1k

For k==0 and nonrelat. constant M one gets:

20

2 3

3 GeV5,6

8 c mc

N

H

G

gravit constant.

energy density

cosmological constant

NG

critical density

It is then convenient to define:

1 2

9 3 32 NR G M t

302 6 NH G

3

2

R t

R 10

00

210 lat

3t

H

0,1 90 0,2

0

113,7 10 latt

H More precisely:

Age of the UniverseAge of the Universe


7

Cosmological Parameters

stala grawit.

gęstosc energii

stala kosmologiczna

NG

0k

1k

1k i.e. for k=0 Ω=1 independent on t

For various k and Λ=0 one can define:

Ωtot =

c

k

R2=H 2 Ωtot −1( )then

dla Ωtot <1 k=-1

dla Ωtot >1 k=+1

Ω


8

Cosmological Parameters

stala grawit.

gęstosc energii

stala kosmologiczna

NG

0k

1k

1k

For various k and Λ=0 one can define:

Ωtot =

c

k

R2=H 2 Ωtot −1( )then

It is often convenient to separate a contribution from relat. particles Ωγ and from pressureless matter Ωm and introduce :

Ω =

3H 2

Then

k

R2=H 2 Ωm+Ωr +Ω −1( )

Ω


9

Radiation dominance in early Universe

How various densities evolve with time?3

m R Matter density:

Radiation energy density: because:4

r R

1ch h R

= photon density x photon energy

because wavelength changes with scale R

3R

Therefore while now matter dominates the early Universe was dominated by radiative energy.

From Friedmann equation and Stefan-Boltzmann law. one gets :

temperature:

1 MeV

t sekkT

i.e. at the beginning the Universewas very hot: Big Bang


10

Big BangThe earliest moment: 43 32 1910 s 10 K 10 GeV

Planck mass We would need quantum gravity (which we do not know) for

earlier moments.

Probably sometimes at this epoch cosmic inflation happened.

In one of the models: early enough the cosmological constant dominates Friedmann equation: giving:

2

3

R

R

2 13

2 1

t tR R e

341 30

322

10 s10

10 s

R

R

Next we’ll describe how the Universe cooled down. We assume, that particles for which: are in thermal equilibrium in comparable abundances and reactions can proceed in both directions eg:

2kT Mcp p

Cosmic Inflation is necessary in the Big Bang theory to explain the large scale uniformity of the Universe today.


11

Big Bang – whole picture

http://outreach.web.cern.ch/outreach/public/CERN/PicturePacks/BigBang.html


12

Breaking of the symmetry of interactions

1019 GeV 1014 GeV 100 GeV 1 GeV 10 meV

D. Kiełczewska, wykład 14

Big Bang (1)

• Wielka Unifikacja – wszystkie oddz. nierozróżnialne• bozonów X, Y tyle co np. kwarków• leptony kwarki {(B-L)=0}

• Plazma kwarkowo-gluonowa• Bozony X, Y znikają• Prawd. pojawia się nadmiar materii nad antymaterią wskutek rozpadów ciężkich neutrin N??

e

1910 GeV

1410 GeV


14

• gamma energy drops enough to allow formation of hadrons • neutrinos do not have enough energy for

they decouple from matter and move freely

Big Bang (2)

• elmgt and weak forces separate • all W’s and Z’s decayed not enough energy to produce them

Relic neutrinos

e

e

100 GeV

1 MeV

e e


15

Big Bang (3)

• not enough energy to create e+ e- pairs

• positrons disappear• light nuclei are bound Nucleosynthesis

• electrons bound into atoms• photons interact much moreslowly („decouple” from matter) and move freely

Relic gammas orcosmic microwave bkg

e

e

0,1 MeV

2 eV

e e


16


17

Nucleosynthesis

Let’s take Universe ~1 sec old By now most of heavier particles annihilated with their antiparticles What is left is: 109 times more and than baryons The following processes take place:

e+nÉ e−+ p

e+ pÉ e+ +n n→ e−+ p+e

But: 2 1,3 MeVn pQ M M c

exp 0,23n

p

N Q

N kT

Moreover neutrons decay with 896 s Effectively after 400 sec one gets: 0,14n

p

N

N

Also a part of neutrons is bound in

nuclei and they don’t

decay anymore.


18

Nucleosynthesis

Nuclei are produced in elmgt processes:Atoms appear only 300 000 years later.

n+ pÉ 2H +n+ 2H→ 3H +p+ 3H→ 4He+p+ 2H→ 3He+n+ 3He→ 4He+

Production of various nuclei strongly depends on the relative density of baryons to photons. It appears, that observed abundances of various isotopes agree with expectations if:

105,5 10BN

N

Experimental confirmation of

BB


19

Number of neutrino species in BB nucleosynthesis

Expansion rate depends on energy density, which in turn depends on the number of neutrino flavors: N

For faster expansion less neutrons manage to decay and more helium nuclei can be bound.

range acceptable for other nuclei

3N consistent wit LEPmeasurements


20

Cosmic microwave background CMB

Another observation consistent with BB model.

Remnant of the hot cosmic plasma

1 MeV

t sekkT According to:

we may expect that today the temperature of CMB is a few K.

CMB photon energy spectrum agrees with the black body frequency distribution.

In 1965 r Penzias i Wilsondiscovered CMB.Its temp.:

2,725 0,001 KT

COBE satellite (1999)


21

CMB anisotropy measured by WMAP

Satellite experiment „Wilkinson Microwave Anisotropy Probe.” has collected data since 2001. It studies temp. fluctuations with precision of 10-5. Images Universe 300 000 years old.

Fluctuations may come from inflation era. If eg. inflation was when:34

-26

14

10 s

=10 m

10 GeV

t

ct

kT

then according to Heisenberg principle we may expect „quantum fluctuations”

10

4

10 GeV

10

ckT

ctkT

kT

Quantum fluctuations could give rise to matter condensation seeds, from which gallaxies evolved


22

Cosmic Microwave Background- anisotropy measurements (WMAP)

WMAP & 2dfGRS,astro-ph/0302209

Autocorrelation function:

measures temp. fluctuations around a mean temp. T0

in the directions m and n.For small angles:

2

2

2

1( ) (2 1) (cos )

4 l ll

l l

C a l P

C a

curve: CDM model

( ) ( ) ( ) , cosC T m T n m n

By fitting the model to the data a surprising number ofparameters can be determined.

Models fitted to the data


23

• Springs represent photon pressure and balls represent the effective mass of the fluid.

• Regions of compression (maxima) represent hot regions and rarefaction (minima) cold regions

A baryon-photon liquid in a gravitation potential well.

Radiative pressure of photons competes with the gravitation which compresses the liquid.

Acoustic oscillations appear in liquid..

WMAP measures maxima and minima of acoustic oscillations and consequently properties of the liquid as well as the potential well.

Baryon-photon ratio in the CMB


24

Baryons increase the effective mass of the fluid. This changes the balance between pressure and gravity in the fluid. Gravitational infall now leads to greater compression of the fluid in the potential well.

This increases the amplitude of the oscillation.Thus the relative heights of the peaks present one way of measuring the baryon content of the universe.

Ωb

Curvature of the Universe


25

A spatial temperature fluctuation on the last scattering surface appears to us as an anisotropy on the sky. The conversion from physical scale into angular scale depends on the curvature of the universe and the distance to the last scattering surface.

Photons free stream to the observer on geodesics analogous to lines of longitude to the pole. Thus the same angular scale represents a smaller physical scale in a closed universe.

E.g. in the case of positive curvatureE.g. in the case of positive curvature

Curvature and cosmol. constant


26

The spacing between the peaks provides the most robust test of the curvature.

k =0Ω ≅0.7

From WMAP measurements:From WMAP measurements:

Summary of recent measurements


27

http://pdg.lbl.gov/2008/ Particle Data Group

http://pdg.lbl.gov/2008/

Summary of recent results (PDG2008)


28

Ω < 0.04

Measurements of distant supernovae


29

Supernovae Ia have known luminosity as a function of time so they may serve as

„standard candles”.

Comparing the expected luminosity with the observed one can determine the SN distance.

Measurement of the „redshift” allows to determine the recession velocity

Supernova measurements

(SNIa)

Strong indication of Dark Energy

Cosmological parameters


31PDG 2008PDG 2008

Ω ≅0.7

Ωmatter ≅ 0.3

k = 0

However we do not understand the nature of energy represented by Λ

However we do not understand the nature of energy represented by Λ

We call it Dark EnergyWe call it Dark Energy

Matter density slows down expansion

Flat geometryFlat geometry

History of the Universe

http://map.gsfc.nasa.gov/m_mm.html


34

Neutrino and photon decoupling

/1.4T T

Then both temperatures decrease with the increasingscale of the Universe as 1/R so eventually now:

2.725 0.001 K (0.23 meV)

1.949 0.001 K (0.17 meV)

T

T

2

3

8( )

2 exp( ) 1

spinn E dEn E dE

EhkT

For nonrelativistic case:

kinE E

Maxwell distribution

At decoupling the neutrino temperature is slightly lower than that of photons

+1 for neutrinos-1 for photons

Because of an effect of „reheating” when slow electr.annihilate

2e e


35

What do we know about ?c

Ω

0,040,060,76

Ω

0,0030,0050,042b

Ω

0,020,040,20DM m b

Ω Ω Ω

Ωvis = 4,6±0,5( )⋅10−5

0,030,040,24m

Ω

„Visible” matter i.e. stars, gas etc:

Baryons visible or invisible calculated from nucleosynthesis:

Total matter deduced from gravitational potential energy of gallaxies and gal. clusters:

Dark matter:

Ciemna energia

1,02 0,02totΩ

„flat geometry” k=0


36

The most recent WMAP results

(04/2008)Energiy balance of the Universe

Today

380 000 years after BB

Ω =

3H 2

Dark energy contribution rises with time

Dark energy contribution rises with time


37

Relic neutrinos

3

3

10

410 cm

3340 cm

11

10 baryon

n

n N n

n n

Number density from thermodynamic equilibrium

293.8eV

i i i

crit

m n m

h

Ω Neutrino Dark Matter:

Ω- neutrino fraction of thetotal energy of theUniverse

for 3 flavors

0.040.030.71h


38

Weighing Neutrinos with Galaxy Surveys

Recent results from experiments:

Large scale cluster formation is prevented by relativistic neutrinos which stream out of the clusters.This sets a limit on a fraction of energy carried by neutrinos.

Ω < 0.04 PDG2008

The line is for ΛCDM model


39

Neutrino contribution to the Universe energy

3

1

0.05ii

m eV

With that one can calculate the neutrino contribution to the total energy in the Universe:

32

1

/ 93 0.0011ii

m h

Ω which is much more than all the visible matter:

3

16.6ii

m eV

From ΛCDM cosmology:

0.26Ω On the other hand we have the limit (from tritium decays):

From oscillations:

54,6 0,5 10

mi

i∑ <1.9 eV

Ω < 0.04

0.05 eV < m3 < 0.6 eVwhich gives for a heaviest state:


40

Current bounds on neutrino masses

from cosmol.

Ω < 0.04


41

Matter-antimatter asymmetry

We therefore expect that some processes violating CP symmetry gave rise to this matter excess. The observed CP violation in quark sector isnot enough to explain the above ratio.

A question: maybe CP violation in lepton sector may explain this excess?

One would expect that BB produced the same amount of matter and antimatter. However one observes an excess of matter over antimatter

105,5 10BN

N


42

Because: so the following decays are possible:

Leptogenesis

The most attractive explanation of matter-antimatter asymmetry is by Leptogenesis

If neutrinos are Majorana particles, then an elegant way to get their masses is via interactions with Higgs of both: known light LH neutrinos as well as very heavy RH neutrinos N with masses of 10(9-15) GeV. N should be produced in the very early moments of BB.N N

....

....

N l

N l

where l+, l- are charged leptons

If: then:CP ... ...N l N l

we get excess of leptons over antileptons” Leptogenesis.Then a baryon excess can be obtained via so called sphalerons.


43

CP violation for Majorana neutrinos

One can ask: if then what is the difference between:

L eL

e

So the clue to understand matter asymmetry is to look for differences in oscillations: and

The difference is that in + decays neutrinos are mostly LH and consequently after oscillations they produce e-:

L .....eL N e

R

e

R eR .....eR N e

If Leptogenesis hypothesis is true then we all come from heavy neutrinos.

while the opposite happens for decays:

Summary

D. Kiełczewska, wykład 14

Cosmology and particle physcics are closely connected Cosmology has become an experimental science Big Bang Model confirmed by:

• measurements of cosmic microwave background CMB• abundances of light nuclei in Universe

BUTBUT

We don’t know what constitutes more than 90% of Universe energy

• Dark Matter ?• Dark Energy ?

We don’t understand how the matter-antimatter symmetry has been broken during the Universe

"From neutrinos....". DK&ER, lecture12 1 Cosmology and Relic Neutrinos Expanding Universe Big Bang...

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