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Transcript of Cosmological probes of neutrino masses (Neutrinos in ... · PDF file Neutrino oscillations in...

  • 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

    Slide 1 Slide 2 Slide 3 Slide 4 Slide 5 Slide 6 Slide 7 Slide 8 Slide 9 Slide 10 Slide 11 Slide 12 Slide 13 Slide 14 Slide 15 Slide 16 Slide 17 Slide 18 Slide 19 Slide 20 Slide 21 Slide 22 Slide 23 Slide 24 Slide 25 Slide 26 Slide 27