C. W. Kim

KIAS

The Johns Hopkins

Neutrinos in Cosmology

October 27, 2008

It is truly remarkable that we should have come so far in determining, from the passive collection of a small fraction of the photons that chance to come our way, the properties of neutrinos better than nuclear/particle physics has ever attempted in many decades. (Charles Bennett in Nature in 2006) 1

Pauli to his friend Baade:1930

“Today I did something a physicist should never do. I predicted something which will never be observed experimentally…”

Neutrino : Pauli’particle

2

Fundamental Building Blocks

Quarks u c t

d s b (3 Colors )

Leptons

e μ τ

ν ν νe μ τ Neutrinos

3

4

Important Issues

1. Mass

2. Mixing

3. Number of flavors

4. CP violation

Oscillations

Lepto-genesis

5

From present evidences of oscillations from experiments measuring

atmospheric, solar, reactor and accelerator neutrinos

We know that flavour neutrino oscillations exist

Weak e.s.Mass e.s.

6

Neutrinos are mixed.

Production and detection

via Weak eigenstates

Propagation (Equ. Of motion)

via Mass eigenstates

νν

νµ

e

τ

=

U U Ue1 e2 e3

U U Uµ1 µ2 µ3

U U Uτ1 τ2 τ3

•

νν

ν2

1

3

(( They are massive. )

7

Mixing Matrix : Nuclear/Particle Physics

3

√

√2 2

2 22

sin θ13 ei δ

U≈

θ θθ ≈ ≈ < 35 4512 23 13

13o oo

Bi-large mixing with U =0, θ = θ , θ = θ = π /6e3 ATM23 12 SOL

√21

1

√2

√3 1

√22√21

√2

√3 1

2

8

• Tritium beta decay: measurements of endpoint energy

m(νe) < 2.2 eV (95% CL) Mainz

Future experiments (KATRIN) m(νe) ~ 0.2-0.3 eV

• Neutrinoless double beta decay: if Majorana neutrinos

experiments with 76Ge and other isotopes: ImeeI < 0.4hN eV

Laboratory mass measurement experiments

e -33 eHe H

-2e2)Z(A, Z)(A,

9

m ( ν ) < 0.17 Mev (95%CL)

from π → μ + ν

m ( ν ) < 18.2 MeV (95%CL)

from τ → 3 π + 2 π + ν

μ

μ

τ

+τ

Particle Physics

10

11

If ∑ m j < 8 x 10 eV, the inverted hierarchy is ruled out !!

There are at least two neutrinos which are heavier than 8 X 10 eV .

-2

-3

No lower bound for the lightest neutrino !! 12

Tritium β

decay< 2.2 eV

2/1

22

iiei mUm

e

Neutrinoless

double betadecay<0.4-1.6 eV

i

ieiee mUm 2

<0.3-1.5 eV Cosmology

iim~

Absolute Mass Searches

13

T < eVT ~ MeV

Formation of Large Scale Structures

LSS

Cosmic Microwave Background

CMB

PrimordialNucleosynthesis

BBN

No flavour sensitivity Neff & mννevs νμ,τ Neff

Relic neutrinos influence several cosmological epochs

14

15

photons

neutrinos

cdm

baryons

Λ

Evolution of the background densities

m3=0.05 eV

m2=0.009 eV

m1≈ 0 eV

16

Number of Neutrino Flavors

17

Number of Neutrino flavors(in the Universe)

Decay of Z : data) (LEP 008.0984.2 N

N influences H :

Slow expansion ⇒ less He. Fast expansion ⇒ more He

+ 1.4- 1.2

4

4

(Particles such as sterile neutrinos are not included. m < 45 GeV).

BBN : N = 3.1 95% CL ( He + D data)

(Neutron life time = 14.76 minutes)

eff

eff

N = 3 ⇒ N = 3.046 (standard value)

(SM and neutrino oscillations : ν v.s. ν )

4

ν ν

e μ,τ

*

( Not relic!)*

18

N

inv

( Z → l l )

= 2.9840 ± 0.0082

This is valid for m < 45 GeV.

Particle Physics

Γ = Nν Γ( Z → ν ν )

= νinvΓ

ν

( Z → )ΓΓ ν ν

l l( Z → )

Z boson:

SM

19

Number of Neutrino flavors(in the Universe)

Decay of Z : data) (LEP 008.0984.2 N

N influences H :

Slow expansion ⇒ less He. Fast expansion ⇒ more He

+ 1.4- 1.2

4

4

(Particles such as sterile neutrinos are not included. m < 45 GeV).

BBN : N = 3.1 95% CL ( He + D data)

(Neutron life time = 14.76 minutes)

eff

eff

N = 3 ⇒ N = 3.046 (standard value)

(SM and neutrino oscillations : ν v.s. ν )

4

ν ν

e μ,τ

*

( Not relic!)*

20

T ( ) ~ 2 MeV : CC & NC

T ( ) ~ 3 MeV : NC only

No μ & τ in plasma

dec

dec νe

νμ ,τ

Neutrino Oscillations in plasma before decoupling

21

311

4

8

71

158

73

15

3/44

24

2

r TT

Ω Ω Ω Ω = 1 Λ m γ ν+ + +

*

To be determined22

1/3

411

T

T

ν

γ

23

311

4

8

71

158

73

15

3/44

24

2

r TT

Ω Ω Ω Ω = 1 Λ m γ ν+ + +

*

To be determined 24

Effect of Neff at later epochsNeff modifies the radiation content: Changes the epoch of matter-radiation equivalence

Galaxy Mass SpectrumAnisotropy Spectrum

25

WMAP 3b

26

↑

m

WMAP 5

27

Results: WMAP 5-year data

N eff = 4.4 + 1.5 (68%C.L.)_

1.9 < N < 7.8 (95%C.L.)eff

even after breaking degeneracy using

BAO, SN and HST28

Neutrino Mass Values

29

eV 93.2

mh Ω i

i2

ν

eV 15 m 0.3Ω Ω

eV 46 m 1 Ω eV 93.2

mhΩ

iimν

iiν

ii

2ν

MpceV 30

m 41

-1

ν

Neutrino Free Streaming

Φ

b, cdm

ν

30

30

mν

32

33

5

34

Parameter degeneracy: Neutrino mass and wIn cosmological models with more parameters the neutrino mass bounds can be relaxed.

Ex: quintessence-like dark energy with ρDE=w pDE

WMAP Coll, astro-ph/0603449

Λ

35

WMAP 5 year Data

WMAP -5

WMAP5 plus

BAO + SN

36

Neutrino Mass from Cosmology

1. CMB alone: Σm < 1.5 eV (95% CL)

2. With BAO and SN:

Σm < 0.61 eV (95% CL) with w = 1

Σm

ν

ν

ν < 0.66 eV (95% CL) without w = 1

( Remember that Σm and H are degenerate for CMB

but no degeneracy between w and Σ m )

ν o

3. To go beyond, we need SDSS, Lyman-α, … But bias, …

ν

37

Neutrinos as HDM

● As long as HDM is relativistic, HDM perturbations within the horizon

are erased by “ Free – Streaming”.

● Free-streaming stops when HDM becomes

non-relativistic at Zn-r .→ If HDM dominates, top-down structure

formation but, observation → bottom-up.

→ limit on Σ m j j

P(k)ΔP(k)

~ (1 eV

Σ m j j) (

ΩM h2 )0.10● _

Reduces small scale amplitude of Mass Fluctuations38

Horizon distance at matter = radiationEnters in matter dominated era

Enters in rad. Dominated era

Σ m = 1 eVi

39

13

40

Neutrino Mass from Cosmology

1. CMB alone: Σm < 1.5 eV (95% CL)

2. With BAO and SN:

Σm < 0.61 eV (95% CL) with w = 1

Σm

ν

ν

ν < 0.66 eV (95% CL) without w = 1

( Remember that Σm and H are degenerate for CMB but

no degeneracy between w and Σ m )ν o

3. To go beyond, we need SDSS, Lyman-α, sdFGRs … But galaxy bias, … :Non-linear effects

ν

Let’s pull it down to 0.08 eV

(Two ν are heavier than this value)

Star Gazer

m ν

WMAP

Lyman-α forest data

Absorption lines in the spectrum of distant quasars due to intermediate H clouds which absorb Lyman-α lines at

λα = 1215.67 Ao

Lyman-α forest data

Absorption lines in the spectrum of distant quasars due to intermediate H clouds which absorb Lyman-α lines at

λα = 1215.67 Ao

Layers of H Clouds ⇒ forest

Lyman-α forest spectrum from Q2139-4434 (z= 3.23)

Lyman-α forest data

Absorption lines in the spectrum of distant quasars due to intermediate H clouds which absorb Lyman-α lines at

λα = 1215.67 Ao

Layers of H Clouds ⇒ forest

Absorption lines ⇒ Study of change of power spectrum of δρ/ρ for small λ

But this is very difficult and model dependent ( bias ).

ΔP(k)/P(k) ~ -10 Ω / Ω : a factor of 2 suppression for Σm = 1 eV(7% of CDM)

νo

Mo

j

WMAP3

* m < 0.7 eV (95% CL)

*H and m degeneracy

νO

Unknown m ⇒ one of the largest systematic errors for estimating cosmological parameters from CMB

* m > 0.3 eV favors smaller Hubble constant.

ν

( Clean and Robustν

ν

*To improve the limit, need data other than WMAP !

SDSS, 2dFGRS, Lyman-α forest, Gravitational lensing,…

But inherent systematic errors need to be understood.

Conclusions

even with WMAP1 alone)