Cosmological probes of neutrino masses (Neutrinos in Cosmology)

Lecture II

Sergio Pastor (IFIC Valencia)

INT. SCHOOL OF PHYSICS ENRICO FERMI, CLXX COURSE

Varenna, June 2008

ν

Exercises: try to calculate…

• The present number density of massive/massless neutrinos nν0 in cm-3

• The present energy density of massive/massless neutrinos Ων0 and find the limits on the total neutrino mass from Ων0

Neutrinos in Cosmology 2nd lecture

Degenerate relic neutrinos (Neutrino asymmetries)

Massive neutrinos as Dark Matter

Effects of neutrino masses on cosmological observables

Neutrino oscillations in the Early Universe

Neutrinos and Primordial Nucleosynthesis

( )

T~MeV t~sec

Prim ordial

Nucleosynthesis

Decoupled neutrinos (Cosmic Neutrino

Background or CNB)

Neutrinos coupled by weak

interactions

Produced elements: D, 3He, 4He, 7Li and

small abundances of others

BBN: Creation of light

elements

Theoretical inputs:

Range of temperatures: from 0.8 to 0.01 MeV

BBN: Creation of light elements

n/p freezing and neutron decay

Phase I: 0.8-0.1 MeV n-p reactions

BBN: Creation of light elements

0.03 MeV

0.07 MeV

Phase II: 0.1-0.01 MeV Formation of light nuclei starting from D

Photodesintegration prevents earlier formation for temperatures closer to nuclear binding energies

BBN: Measurement of Primordial abundances

Difficult task: search in astrophysical systems with chemical evolution as small as possible

Deuterium: destroyed in stars. Any observed abundance of D is lower limit to the primordial abundance. Data from high-z, low

metallicity QSO absorption line systems

Helium-3: produced and destroyed in stars (complicated evolution) Data from solar system and galaxies but not used in BBN analysis

Helium-4: primordial abundance increased by H burning in stars. Data from low metallicity, extragalatic HII regions

Lithium-7: destroyed in stars, produced in cosmic ray reactions. Data from oldest, most metal-poor stars in the Galaxy

Fields & Sarkar PDG 2006

BBN: Predictions vs Observations

2 B10

B 10 h274Ω10

/nnη ≅= − γ

after WMAP5 ΩBh2=0.02265±0.00059

Effect of neutrinos on BBN 1. Neff fixes the expansion rate during BBN

ρ(Neff)>ρ0 → ↑ 4He

Burles, Nollett & Turner 1999

2 p3M

8π H

ρ= 3.4 3.2 3.0

2. Direct effect of electron neutrinos and antineutrinos on the n-p reactions

BBN: allowed ranges for Neff

Mangano et al, JCAP 0703 (2007) 006

Using 4He + D data (95% CL)

1.4 1.2 eff 3.1N

+ −=

2 B10

B 10 h274Ω10

/nnη ≅= − γ

Neutrino oscillations in the Early Universe

Neutrino oscillations are effective when medium effects get small enough

Compare oscillation term with effective potentials

Strumia & Vissani, hep-ph/0606054

Oscillation term prop. to Δm2/2E

First order matter effects prop. to GF[n(e-)-n(e+)]

Second order matter effects prop. to GF(E/MZ2 )[ρ(e-)

+ρ(e+)]

Coupled neutrinos

Flavour neutrino oscillations in the Early Universe

Standard case: all neutrino flavours equally populated oscillations are effective below a few MeV, but have no effect (except for mixing the small distortions δfν) Cosmology is insensitive to neutrino flavour after decoupling!

Non-zero neutrino asymmetries: flavour oscillations lead to (almost) equilibrium for all μν

What if additional, light sterile neutrino species are mixed with the flavour neutrinos?

♣ If oscillations are effective before decoupling: the additional species can be brought into equilibrium: Neff=4

♣ If oscillations are effective after decoupling: Neff=3 but the spectrum of active neutrinos is distorted (direct effect of νe and anti-νe on BBN)

Active-sterile neutrino oscillations

Results depend on the sign of Δm2 (resonant vs non-resonant case)

Active-sterile neutrino oscillations

Dolgov & Villante, NPB 679 (2004) 261

Additional neutrino

fully in eq

Flavour neutrino spectrum depleted

Kirilova, astro-ph/0312569

Active-sterile neutrino oscillations

Dolgov & Villante, NPB 679 (2004) 261

Additional neutrino

fully in eq

Flavour neutrino spectrum depleted

Active-sterile neutrino oscillations

Dolgov & Villante, NPB 679 (2004) 261

Additional neutrino

fully in eq

Degenerate relic neutrinos (relic neutrino asymmetries)

T~MeV t~sec

Prim ordial

Nucleosynthesis

Decoupled neutrinos (Cosmic Neutrino

Background)

Neutrinos coupled by weak

interactions

Equilibrium thermodynami

cs

Particles in equilibrium when T are high and interactions effective

T~1/a(t)

Distribution function of particle momenta in equilibrium

Thermodynamical variables

VARIABLE RELATIVISTIC

NON REL. BOSE FERMI

T~MeV t~sec

Prim ordial

Nucleosynthesis

Neutrinos coupled by weak

interactions

1e 1

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

νµνν µ

ξν=µν /T

Relic neutrino asymmetries

νν nn ≠

[ ]32 3

)3(12 1

νν γ

ν

γ

νν ν ξξπζ

+  

   

 =−=

T T

n nn

L

  



  

   

 +

 

 =∆

42

2 7 15

π ξ

π ξ νν

νN

Raffelt

Fermi-Dirac spectrum with temperature T and

chemical potential µν

More radiation

Degenerate Big Bang Nucleosynthesis

If ξν≠ 0 , for any flavor

  



  

   

 +

 

 =∆

42

2 7 15

π ξ

π ξ νν

νN ρ(ξν)> ρ(0) → ↑ 4He

Plus the direct effect on n↔p if ξ(νe) ≠ 0



 

 −

− −=

 

 e

pn

eq T

mm

p n ξexp ξ e>0 → ↓ 4He

Pairs of values (ξe,∆Nν) that produce the same observed abundances for larger ηBKang & Steigman 1992

Hansen et al 2001 Hannestad 2003

Combined bounds BBN & CMB- LSS

4.2 22.001.0 , ≤≤≤− τµξξe

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

  





  





τττµτ

µτµµµ

τµ

ρρρ ρρρ ρρρ

e

e

eeee

  





  





−−− −−−

132313231223121323122312

132313231223121323122312

1313121312

ccscsscsccss cssssccssccs

scscc

Dominant term: Synchronized Neutrino Oscillations

BB N

Evolution of neutrino asymmetries

07.0 ≤νξ Effective flavor equilibrium (almost) established →

Dolgov et al 2002 Wong 2002 Abazajian et al 2002

07.005.0 ≤≤− ξ Serpico & Raffelt 2005

End of 2nd lecture

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