Cosmological Aspects of Neutrino Physics (II) Sergio Pastor (IFIC) 61st SUSSP St Andrews, August...

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03/17/22 Cosmological Aspects of Neutrino Physics (II) Sergio Pastor (IFIC) 61st SUSSP St Andrews, August 2006 ν

Transcript of Cosmological Aspects of Neutrino Physics (II) Sergio Pastor (IFIC) 61st SUSSP St Andrews, August...

04/19/23

Cosmological Aspects of Neutrino Physics (II)

Sergio Pastor (IFIC)61st SUSSP

St Andrews, August 2006

ν

Cosmological Aspects of Neutrino Physics

2nd lecture

Degenerate relic neutrinos (Neutrino asymmetries)

Massive neutrinos as Dark Matter

Effects of neutrino masses on cosmological observables

T~MeVt~sec

Primordial

Nucleosynthesis

Decoupled neutrinos(Cosmic Neutrino

Background)

Neutrinos coupled by weak

interactions

Equilibrium thermodynami

cs

Particles in equilibriumwhen T are high and interactions effective

T~1/a(t)

Distribution function of particle momenta in equilibrium

Thermodynamical variables

VARIABLERELATIVISTIC

NON REL.BOSE FERMI

T~MeVt~sec

Primordial

Nucleosynthesis

Neutrinos coupled by weak

interactions

1e1

T),(p,f )/T-(p

/T

Relic neutrino asymmetries

nn

32

3

)3(12

1

T

T

n

nnL

42

27

15

N

Raffelt

Fermi-Dirac spectrum with temperature T and

chemical potential

More radiation

Degenerate Big Bang Nucleosynthesis

If 0 , for any flavor

42

27

15

N ()>(0) 4He

Plus the direct effect on np if (e)0

e

pn

eqT

mm

p

n exp e>0 4He

Pairs (e,N) that produce the same observed abundances for larger B Kang & Steigman 1992

Hansen et al 2001 Hannestad 2003

Combined bounds BBN & CMB-LSS

4.2 22.001.0 , e

In the presence of flavor oscillations ?

Degeneracy direction (arbitrary ξe)

Flavor neutrino oscillations in the Early Universe

• Density matrix

• Mixing matrix

• Expansion of the Universe• Charged lepton background (2nd order contribution)• Collisions (damping)• Neutrino background: diagonal and off-diagonal potentials

e

e

eeee

132313231223121323122312

132313231223121323122312

1313121312

ccscsscsccss

cssssccssccs

scscc

Dominant term: Synchronized Neutrino Oscillations

BBN

Evolution of neutrino asymmetries

07.0 Effective flavor equilibrium (almost) established

Dolgov et al 2002Abazajian et al 2002Wong 2002Lunardini & Smirnov 2001

07.005.0 Serpico & Raffelt 2005

Massive Neutrinos and Cosmology

04/19/23

Relic neutrinos influence several cosmological epochs

T < eVT ~ MeV

Formation of Large Scale Structures

LSS

Cosmic Microwave Background

CMB

Primordial

Nucleosynthesis

BBN

No flavour sensitivity Neff & mννevs νμ,τ Neff

We know that flavour neutrino oscillations exist

From present evidences of oscillations from experiments measuring atmospheric, solar, reactor and accelerator neutrinos

Evidence of Particle Physics beyond the Standard Model !

),,(),(e, 321 ννντμ

Mixing Parameters...From present evidences of oscillations from experiments measuring

atmospheric, solar, reactor and accelerator neutrinos

Mixing matrix U

Maltoni, Schwetz, Tórtola, Valle, NJP 6 (2004) 122

Mixing Parameters...From present evidences of oscillations from experiments measuring

atmospheric, solar, reactor and accelerator neutrinos

Mixing matrix U

Maltoni, Schwetz, Tórtola, Valle, NJP 6 (2004) 122

Mixing Parameters...From present evidences of oscillations from experiments measuring

atmospheric, solar, reactor and accelerator neutrinos

Maltoni, Schwetz, Tórtola, Valle, NJP 6 (2004) 122

... and neutrino masses

Data on flavour oscillations do not fix the absolute scale of neutrino masses

eV

atmatm

solar

solar

eV 0.009 Δm

eV 0.05Δm

2sun

2atm

NO

RM

AL

INV

ER

TE

D

eV

m0

What is the value of m0 ?

Direct laboratory bounds on mν

Searching for non-zero neutrino mass in laboratory experiments

• 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

e -33 eHe H

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

Absolute mass scale searches

Neutrinoless double beta decay

< 0.4-1.6 eV

Tritium β decay < 2.2 eV

2/1

22

iiei mUm

e

< 0.3-2.0 eVCosmology i

im~

i

ieiee mUm 2

04/19/23

Evolution of the background densities: 1 MeV → now

photons

neutrinos

cdm

baryons

Λ

m3=0.05 eV

m2=0.009 eV

m1≈ 0 eV

Ωi= ρi/ρcrit

The Cosmic Neutrino Background

• Number density

• Energy density

323

3

11

3(6

11

3

2 CMBγννν Tπ

)ζn)(p,Tf

π)(

pdn

nm

T

)(p,Tfπ)(

pdmp

i

ii

CMB

νν

43/42

3

322

11

4

120

7

2

Massless

Massive

mν>>T

Neutrinos decoupled at T~MeV, keeping a spectrum as that of a relativistic species 1e

1T)(p,f p/T

At present 112 per flavour cm )( -3

Contribution to the energy density of the Universe

eV 93.2

mh Ω i

i2

ν

52 101.7h Ω ν

Neutrinos as Dark Matter

• Neutrinos are natural DM candidates

• They stream freely until non-relativistic (collisionless phase mixing) Neutrinos are HOT Dark Matter

• First structures to be formed when Universe became matter -dominated

• Ruled out by structure formation CDM

MpceV 30

m 41

-1

ν

Neutrino Free Streaming

Φ

b, cdm

ν

eV 15 m 0.3Ω Ω

eV 46 m 1 Ω eV 93.2

mhΩ

iimν

iiν

ii

Neutrinos as Dark Matter

• Neutrinos are natural DM candidates

• They stream freely until non-relativistic (collisionless phase mixing) Neutrinos are HOT Dark Matter

• First structures to be formed when Universe became matter -dominated

• Ruled out by structure formation CDM

MpceV 30

m 41

-1

ν

eV 15 m 0.3Ω Ω

eV 46 m 1 Ω eV 93.2

mhΩ

iimν

iiν

ii

Neutrinos as Hot Dark MatterEffect of Massive Neutrinos: suppression of Power at small scales

RAFFELT

Neutrinos as Hot Dark MatterEffect of Massive Neutrinos: suppression of Power at small scales

RAFFELT

Neutrinos as Hot Dark Matter

Massive Neutrinos can still be subdominant DM: limits on mν from Structure Formation (combined with other cosmological data)

Cosmological observables

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inflation radiation matière énergie noire

acceleration

acceleration

slow deceleration

fast deceleration

??

inflation RD (radiation domination) MD (matter domination) dark energy domination

Power Spectrum of density fluctuations

Matter power spectrum is the Fourier transform of the

two-point correlation function

Field of density Fluctuations

)(

)(x

x

Galaxy Redshift Surveys

SDSS

2dFGRS

~ 1300 M

pc

Cosmological observables: LSS

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inflation radiation matière énergie noire

acceleration

acceleration

slow deceleration

fast deceleration

??

inflation RD (radiation domination) MD (matter domination) dark energy domination

0<z<0.20<z<0.2

matter power spectrum P(k) galaxy redshift surveys

linear non-linear δρ/ρ<1 δρ/ρ ~ 1

60 Mpc

bias uncertainty

Distribution of large-scale

structures at low z

Power spectrum of density fluctuations

Bias b2(k)=Pg(k)/Pm(k)

kmax

SDSS2dFGRS

Non-linearity

Cosmological observables : LSS

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inflation radiation matière énergie noire

acceleration

acceleration

slow deceleration

fast deceleration

??

inflation RD (radiation domination) MD (matter domination) dark energy domination

2<z<32<z<3

Lyman-α forests in quasar spectra matter power spectrum P(k)

various systematics Distribution of large-scale structures at

medium z

Neutrinos as Hot Dark Matter

• Effect of Massive Neutrinos: suppression of Power at small scales

Massive Neutrinos can still be subdominant DM: limits on mν from Structure Formation (combined with other cosmological data)

ffν

Structure formation after equality

baryons and CDM

experiencegravitational

clustering

Structure formation after equality

baryons and CDM

experiencegravitational

clustering

growth of /(k,t) fixed by

« gravity vs. expansion » balance

a

Structure formation after equality

baryons and CDM

experiencegravitational

clustering

neutrinosexperience

free-streamingwith

v = c or <p>/m

Structure formation after equality

baryons and CDM

experiencegravitational

clustering

neutrinos cannot cluster below a diffusion length

= ∫ v dt < ∫ c dt

Structure formation after equality

baryon and CDM

experiencegravitational

clustering

baryons and CDM

experiencegravitational

clustering

neutrinosexperience

free-streamingwith

v = c or <p>/m

o neutrinos cannot cluster below a diffusion length

= ∫ v dt < ∫ c dt

for (2/k) < ,free-streaming supresses growth of structures during MD

a1-3/5 f with f = /m ≈ (m)/(15 eV)

Structure formation after equality

baryon and CDM

experiencegravitational

clustering

baryons and CDM

experiencegravitational

clustering

neutrinosexperience

free-streamingwith

v = c or <p>/m

J.Lesgourgues & SP, Phys Rep 429 (2006) 307 [astro-ph/0603494]

Structure formation after equality

cdm

b

metric

a

Massless neutrinos

J.Lesgourgues & SP, Phys Rep 429 (2006) 307 [astro-ph/0603494]

Structure formation after equality

cdm

b

metric

a

1-3/5fa

Massive neutrinos

fν=0.1

Effect of massive neutrinos on P(k)

Observable signature of the total mass on Observable signature of the total mass on P(k) :P(k) :P(k) massiveP(k) massive

P(k) masslessP(k) massless

variousvariousffν

Lesgourgues & SP, Phys. Rep. 429 (2006) 307

Cosmological observables: CMB

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inflation radiation matière énergie noire

acceleration

acceleration

slow deceleration

fast deceleration

??

inflation RD (radiation domination) MD (matter domination) dark energy domination

z≈1100z≈1100

photon power spectra CMB temperature/polarization anisotropies

Anisotropies of the Cosmic

Microwave Background

CMB TT DATA

Multipole Expansion

Map of CMBR temperature Fluctuations

T

T-),T(),Δ(

Angular Power Spectrum

CMB TT DATA

Multipole Expansion

Map of CMBR temperature Fluctuations

T

T-),T(),Δ(

Angular Power Spectrum

CMB Polarizatio

n DATA

TT

TE

EE

BB

WMAP 3

Effect of massive neutrinos on the CMB spectra

1) Direct effect of sub-eV massive neutrinos on the evolution of the baryon-photon coupling is very small

2) Impact on CMB spectra is indirect: non-zero Ων today implies a change in the spatial curvature or other Ωi . The background evolution is modified

Ex: in a flat universe,

keep ΩΛ+Ωcdm+Ωb+Ων=1

constant

Effect of massive neutrinos on the CMB spectra

Problem with parameter degeneracies: change in other cosmological parameters can mimic the effect of nu masses

Effect of massive neutrinos on the CMB and Matter Power

Spectra

Max Tegmark

www.hep.upenn.edu/~max/

End of 2nd lecture