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Cosmological constraints on the number of neutrino species
Jan Hamannbased on work in collaboration with:
S. Hannestad, G. Raffelt,I. Tamborra and Y. Wong
INFO 2011Santa Fe
20 July 2011
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Setting the scene:hints for sterile neutrinos?
Observations at odds with standard 3-neutrino interpretation of global oscillation data
LSND anomaly
MiniBooNE antineutrino results
Short-baseline reactor experiments(Bugey, ROVNO, Krasnoyarsk, ILL, Gösgen)
Recent re-evaluation of reactor fluxes
[Aguilar (2001)]
[Aguilar-Arevalo (2010)]
[Mention et al. (2011)]
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Setting the scene:hints for sterile neutrinos?
Observations at odds with standard 3-neutrino interpretation of global oscillation data
LSND anomaly
MiniBooNE antineutrino results
Short-baseline reactor experiments(Bugey, ROVNO, Krasnoyarsk, ILL, Gösgen)
Recent re-evaluation of reactor fluxes
Can possibly resolved with oscillations into sterile
neutrinos with Δm2~eV2
[Aguilar (2001)]
[Aguilar-Arevalo (2010)]
[Mention et al. (2011)]
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Setting the scene:hints for sterile neutrinos?
Results from reactor/global fit:
[Kopp, Maltoni, Schwetz (2011)]
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What is the Universe made of?Assuming the ΛCDM-model:
NASA's cosmic pie
today (z = 0)
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What is the Universe made of?Assuming the ΛCDM-model:
NASA's cosmic pie
today (z = 0)
Neutrinos 0.1 - 2%
Photons 0.006%
INCOMPLETE
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What is the Universe made of?Assuming the ΛCDM-model:
NASA's cosmic pie (2)
at decoupling (z = 1100)
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Radiation content of the Universe
Photons: CMB
Neutrinos: CνB
Other light particle species?
How can we find them?Directly: via scattering
Indirectly: via gravitational effects
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Cosmic Microwave Background
Directly measured by COBE/FIRAS
Blackbody spectrum with
[Mather et al. (1993)]
[Fixsen & Mather (2002)]
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Cosmic Microwave Background
Also affects expansion rate through photon energy density:
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Cosmic Neutrino Background
Neutrinos decouple before e+e--annihilation
extremely low energy
no direct detection to date
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Cosmic Neutrino Background
Neutrino energy density:
LEP: 2.984 ± 0.008
[Dolgov et al. (2002), Wong (2002)]
Large mixing ensures thatdifferent mass/flavour eigenstates typically share a common momentum distribution
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Cosmic Neutrino Background
Neutrino energy density:
For , one would have
Small correction due to νes not being quite completely
decoupled at e+e--annihilation + QED correction
Standard Model expectation:
[Mangano et al. (2005)]
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Radiation content of the Universe
Other light stuff?
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Radiation content of the Universe
Other light stuff?
Putting it all together:
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A few remarks on is not a constant, in general
increase through light decay products of massive particle
decrease when particles go non-relativistic
(in fact, technically ≤ 1 today)
can be < 3.046 at early times if neutrinos out of equilibrium; e.g., low reheating temperature:
[Ichikawa, Kawasaki, Takahashi (2005)]
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Determining from observation
Big Bang NucleosynthesisPrimordial element abundances
DecouplingCosmic Microwave Background anisotropies
Large scale structure
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BBNBoltzmann equation
T
~1 MeV
~0.2 MeV
neutrons and protons in equilibrium
neutrons start decaying
most surviving neutrons end up in 4He
expansion ratenuclear interaction rates
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BBNBoltzmann equation
expansion ratenuclear interaction rate
primordial element abundancesas function of
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BBN
Assume standard BBN with 3 active neutrinos and N
s additional effective ''sterile
neutrino'' species
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BBN
Measure primordial abundances → infer Ns
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BBN
Measure primordial abundances → infer Neff
E.g., Helium:increasing radiation density→ higher expansion rate→ n-p freeze-out at higher T→ n/p = exp[-Δm/T]→ greater Helium abundance
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Primordial abundances: Deuterium
Measure absorption of quasar light in low-metallicity hydrogen clouds at high z
Relatively ''clean'' probe
Deuterium abundance not subject to strong evolution with redshift
From seven measured objects:
[Pettini et al. (2008)]
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Primordial abundances:Helium
Observe Hydrogen and Helium emission lines in H-II regions of metal-poor dwarf galaxies
[Izotov, Thuan (2010)]
Astrophysical systematics
Interstellar reddening
Absorption lines in stellar continuum
Radiative transfer
Collisional corrections
Helium production by Pop III stars → dY/dZ > 0
Y
Metallicity Z
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Primordial abundances: Helium
Reliable treatment of systematics for seven ''high-quality'' systems
Linear regression to zero metallicity, limited to positive slopes
[Aver, Olive, Skillman (2010)]
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Calculating theoretical abundances
Solve Boltzmann equations numerically (e.g., ParthENoPE)
Theoretical uncertainties:
Nuclear rates
negligible for Helium, 1.8% for Deuterium
→ folded into likelihood function
Free neutron lifetime
negligible for Deuterium, 0.6% for Helium
[Pisanti et al. (2008)]
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Free neutron lifetime
No universally agreed upon value:
Averaging would not be reasonable
Re-analysis of older measurements claims bias of roughly +6 s
We consider the two extremal values until the matter is settled
[Particle Data Group (2010)]
[Serebrov et al. (2005)]
[Pichlmaier et al. (2010)]
[Serebrov, Fomin (2010)]
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BBN constraints:Deuterium only
Ns unconstrained from Deuterium alone
Combination with baryon density prior gives upper limit
[JH, Hannestad, Raffelt, Wong (in preparation)]
(90/99)%-credible regionsincluding CMB+LSS prior
on baryon density
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BBN constraints:Helium only
Helium is a much better probe of NS
(90/99)%-credible regionsincluding CMB+LSS prior
on baryon density
effect of going to higherneutron lifetime
→ higher predicted Yp
→ tighter bound on NS
[JH, Hannestad, Raffelt, Wong (in preparation)]
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BBN constraints:Deuterium + Helium
NS < 1.26 (1.24) @95% credibility
Best-fit at NS = 0.86
(90/99)%-credible regionsincluding CMB+LSS prior
on baryon density
[JH, Hannestad, Raffelt, Wong (in preparation)]
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BBN and sterile neutrinos
3+1 scenario slightly preferred over 3+0
3+2 ruled out at high significance ...
[JH, Hannestad, Raffelt, Wong (in preparation)]
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BBN and sterile neutrinos
3+1 scenario slightly preferred over 3+0
3+2 ruled out at high significance ... … unless:
Incomplete thermalisation
→ effective NS is smaller than 2
Non-standard BBN?
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Degenerate BBN
Allow for a neutrino chemical potential ξ
Assume all active species share the same ξ
Two effects:
Additional radiation energy density
Change in initial equilibrium n/p ratio
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BBN constraints:Degenerate BBN
ξ of order 0.1 could save 3+2 (and even 3+3!)
(90/99)%-credible regionsincluding CMB+LSS prior
on baryon density
[JH, Hannestad, Raffelt, Wong (in preparation)]
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and the CMB
[WMAP (2010)]
expand in spherical harmonics
CMB map
CMB angularpower spectrum
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and the CMB
Angular power spectrum is a function of O(10) cosmological parameters (e.g., ω
b, ω
dm, ω
ν, Ω
de, N
eff,...)
1357
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and the CMB
Matter-radiation equality
Sound horizon
Anisotropic stress
Damping tail
1357
Completely degenerate with matter density
Larger → later equality → enhanced early integrated Sachs-Wolfe-effect → higher first peak
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and the CMB
Matter-radiation equality
Sound horizon
Anisotropic stress
Damping tail
1357
Function of radiation, baryon and matter densities
θs = Sound horizon/distance to last scattering surface
determines positions of acoustic peaks
also depends on dark energy density
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and the CMB
Matter-radiation equality
Sound horizon
Anisotropic stress
Damping tail
1357
Free streaming particles → anisotropic stress
Dampens fluctuations during radiation domination
Suppression of power at multipoles > 200
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and the CMB
Matter-radiation equality
Sound horizon
Anisotropic stress
Damping tail
1357
Last scattering surface has finite thickness → exponential damping of fluctuations below damping scale
For fixed peak positions, increasing Neff
enhances damping
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[Millea et al. (2011)]
Damping tail can help break degeneracies with other parameters
and the CMB
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from WMAP+LSS+...
[WMAP: Komatsu et al. (2008)]
lower limit from WMAP alone ( → anisotropic stress)
meaningful upper limit requires combination with other data sets sensitive to matter density and expansion rate ...
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from CMB alone
[Keisler et al. (2011)]
South Pole Telescope Atacama Cosmology Telescope
[Dunkley et al. (2010)]
WMAPWMAP+ACTWMAP+ACT+BAO+H
0
… or measurement of the damping tail of the CMB angular power spectrum
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CMB+X bounds on Precise numbers depend on cosmological model and data sets used
Recent analysis: = 4.47
CMB + SDSS-DR7-BAO + HST ΛCDM + neutrino mass +
95%-credible intervals
-1.74+1.82
[JH, Hannestad, Lesgourgues,Rampf, Wong (2010)]
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Sterile neutrino scenarioTwo qualitatively different
mass hierarchies:
[JH, Hannestad, Raffelt, Tamborra, Wong (2010)]
mν
νa
νs
νa
''3+N'' ''N+3''
N+3
3+N
νs
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Sterile neutrino scenario
3+1, 3+2, 3+3 are fine ...… as long as the steriles are light enough!
Unfortunately, 1 eV appears to be somewhat too heavy
Reminder: we assumed minimal extension of cosmological standard model (ΛCDM+N
eff+m
ν)
[JH, Hannestad, Raffelt, Tamborra, Wong (2010)]
3+N
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Impact on cosmological model
Assume laboratory hints for steriles are real, fix masses to best-fit values in 3+1/3+2
Extend model and allow curvature parameter Ω
k
and dark energy equation of state parameter w to vary
→ w < -1 at more than 95% c.l.
[Kristiansen, Elgarøy (2011)]
3+03+13+2
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Impact on cosmological model
E.g., 1 massive + N massless species
For eV-mass steriles: prefer additional massless species and high matter density
[JH, Hannestad, Raffelt, Wong (in preparation)]
Nm
assl
ess
mS = 0
mS = 1 eVm
S = 2 eV
CMB+BAO+HST+H
0
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PLANCK
Launched 9th May 2009
In orbit around Lagrange point L2
Measures CMB in 9 frequency channels 30-857 GHz
~ 5 arcmin resolution limited by cosmic variance up to multipoles of ~2000
Expected sensitivity to : σ ≈ 0.2[JH, Lesgourgues, Mangano (2007)]
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PLANCK
January: PLANCK early papers (mostly concerning instrument performance and foreground physics)
Cosmology papers: early 2013
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ConclusionsCosmological data show slight preference for additional relativistic degrees of freedom, such as sterile neutrinos
3+2 sterile neutrino interpretation of LSDN/MiniBooNE/ reactor data is problematic if implemented in naïve minimal cosmological model (too many for BBN, too heavy for CMB+LSS)
Incomplete thermalisation or an extension of the cosmological model are required for compatibility
Exciting results from PLANCK soon!