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Neutrinos in cosmology
Yvonne Y. Y. WongRWTH Aachen
INSS 2012, Blacksburg VA, July 10 – 21, 2012
-
BBN
Structureformation
Last scatteringsurface (CMB)
Inflation: seedsfor structureformation?
-
BBN
Structureformation
Last scatteringsurface (CMB)
Inflation: seedsfor structureformation?
Why study neutrinos??
Big bang neutrinos are the second most abundant known particle species by number density.
Light neutrinos (m < eV) behave as:● Radiation at early times (BBN).● Matter at late times (structure formation).
-
● Lecture 1: Neutrinos and homogeneous cosmology
– Homogeneous and isotropic universe
– Particles in cosmology: the hot universe
– Evidence for relic neutrinos
– Prospects for direct detection
● Lecture 2: Neutrinos in the inhomogeneous universe
Plan...
-
● J. Lesgourgues and S. Pastor, Massive neutrinos and cosmology, Phys. Rep. 429 (2006) 307 [astro-ph/0603494].
● S. Hannestad, Primordial neutrinos, Ann. Rev. Nucl. Part. Sci. 56 (2006) 137 [hep-ph/0602058].
● Y. Y. Y. Wong, Neutrino mass in cosmology: status and prospects, Ann. Rev. Nucl. Part. Sci. 61 (2011) 69 [arXiv:1111.1436].
● A. D. Dolgov, Neutrinos in cosmology, Phys. Rept. 370 (2002) 333 [hep-ph/0202122].
Useful references...
-
1. Neutrinos and homogeneous cosmology...
-
1.1 Homogeneous and isotropic universe...
-
● Modern cosmology is based on the hypothesis that our universe is homogeneous and isotropic on sufficiently large length scales.
– Homogeneous → same everywhere
– Isotropic → same in all directions
– Sufficiently large scales → > O(100 Mpc)
● I pc = 1 parsec = 3.0856 x 1018 cm
– Distance from Sun to Galactic centre ~ 10 kpc
– Distance to the Virgo cluster ~ 20 Mpc
– Size of the visible universe ~ O(10 Gpc)
Friedmann-Lemaître-Robertson-Walker universe...
-
● Homogeneity and isotropy imply maximally symmetric 3-spaces (3 translational and 3 rotational symmetries).
– A spacetime metric that satisfies these requirements:
Friedmann-Lemaître-Robertson-Walker universe...
ds2=−dt 2+a2(t)[ dr21−K r2+r2(d θ2+sin2θd ϕ2)] FLRW metrica(t) = Scale factor
Spatial geometryK = -1 (hyperbolic), 0 (flat), +1 (spherical)
-
● Test particles moving on geodesics in a FRLW universe suffer cosmological redshift:
● For photons:
● In a FRLW universe, there is a one-to-one correspondence between t, a, and z → We use them interchangeably as a measure of time.
Kinematics: cosmological redshift...
∣⃗p∣∝a−1Proper momentum of a point particle measuredby a comoving observer
λ0λe=E eE0=a ( t0)a (te)
≡1+zz = Redshift parameter
Wavelength measured by comoving observer
Wavelength emittedby comoving emitter
t0= today
-
● Matter/energy content is encoded in the stress-energy tensor Tμν.
● Homogeneity and isotropy imply only one viable form:
– Fluids at rest with respect to the FLRW coordinates (or comoving frame)
Matter/energy content...
T̄ (α)μ ν=(−ρ̄α(t) ḡ 00 00 P̄α(t) ḡ ij)
ρα = Energy density of fluid α in the fluid's rest frame
Pα = Pressure of fluid αin the fluid's rest frame
-
● Relativistic (at least for a significant part of their evolution history
– Photons (mainly the CMB)– Relic neutrinos (analogous to the CMB)– Gravitational waves??
● Nonrelativistic matter– Atoms (or constituents thereof)– Dark matter (does not emit light but feels gravity)
● Other funny things
– Vacuum energy/dark energy– ??
Matter/energy content: what is out there?
-
● Local conservation of energy-momentum:● In a FLRW universe:
● A general fluid can be specified by an equation of state parameter:
– Nonrelativistic matter (wm ~ 0):
– Radiation (wr = 1/3):
– Vacuum energy (wΛ = -1):
Matter/energy content: conservation laws...
∇μT (α)μν=0
d ρ̄αdt +3
ȧa (ρ̄α+P̄α)=0
Continuity equation;one equation per fluid α
ρ̄m∝a−3
ρ̄r∝a−4
ρ̄Λ∝constant
wα( t )≡ P̄α( t )/ρ̄α(t)
-
log(ρ)
log(a)
ρ̄r∝a−4
ρ̄Λ=const
ρ̄m∝a−3
Radiation domination Matter domination Λ domination
Matter-radiationequality
Matter-Λequality
-
log(ρ)
log(a)-3 0
ρ̄r∝a−4
ρ̄Λ=const
-9 -6
ρ̄m∝a−3
Radiation domination Matter domination Λ domination
Matter-radiationequality
Matter-Λequality
Today
a0=1 By convention
-
log(ρ)
log(a)-3 0
ρ̄r∝a−4
ρ̄Λ=const
-9 -6
ρ̄m∝a−3
Radiation domination Matter domination Λ domination
Matter-radiationequality
Matter-Λequality
Today
a0=1 By convention
Structure formation
Last scattering Surface (CMB)
Big bangnucleosynthesis
-
13.4 billion years ago(at photon decoupling)
Composition today
● Different evolution for different forms of energy densities means that radiation dominated in the early universe, while dark energy was relatively unimportant.
MasslessNeutrinos(3 families)
-
● Derived from the Einstein equation:
● The Friedmann equation is an evolution equation for the scale factor a(t):
● Friedmann+continuity equations → specify the whole system.
Friedmann equation...
H 2(t)≡( ȧa )2
=8πG3 ∑α ρ̄α−K
Friedmann equation
Rμν−12gμνR=8πGT μν
H(t) = Hubble parameter
-
● You may also have seen the Friedmann equation in this form:
● Current observations:
Friedmann equation: critical density...
H 2(t)=H 2(t 0)[Ωma−3+Ωra−4+ΩΛ+ΩK a−2 ]
Ωα=ρ̄α(t 0)ρcrit( t0)
, ρcrit(t )≡3H 2(t )8πG , ΩK≡−
Ka2( t0)H
2(t 0)
Ωm∼0.3, ΩΛ∼0.7, Ωr∼10−5
∣ΩK∣
-
● Solutions in some limits:
– Radiation domination:
– Matter domination:
– Vacuum energy domination:
Friedmann equation: solutions...
a∝ t1 /2
a∝ t 2/3
a∝exp(H 0√ΩΛ t)
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1.2 Particles in cosmology: the hot universe...
-
● The early universe was a very dense and hot place.
→ Frequent particle interactions.
● If the interaction rate is so large
such that
→ the interaction is in a state of equilibrium.
The hot universe...
Interaction rate, Γ >> Expansion rate, H
=n 〈 v〉
-
● When an interaction is in a state of equilibrium, all participating particles have phase space distributions described by one of the equilibrium forms.
– All scattering processes lead to kinetic/thermal equilibrium:
– Annihilation processes XX ↔ YY ↔ γγ lead to chemical equilibrium:
f eq( p)=1
exp [(E ( p)−μ)/T ]±1
X=− X
+ Fermi-Dirac- Bose-Einstein
μ = Chemical potential
f(p) = Phase space distribution
Equilibrium thermodynamics...
Same temperature for all participating particle species
-
● Number density:
● Energy density:
● Pressure:
ρ= g(2π)3
∫ d 3 pE f ( p⃗)
n= g(2π)3
∫ d 3 p f ( p⃗) g = Internal d.o.f. = 2 for neutrinos
P= g(2π)3
∫ d 3 p∣p⃗∣2
3Ef ( p⃗)
Compare with g = 4 for electrons/positrons = 2 for photons
-
Relativistic Non-Bose Fermi relativistic
Number density, n:
Energy density, ρ:
Pressure, P:
32
g T 3 g mT2 3/2
e−m /T3432
gT 3
2
30g T 4 7
82
30gT 4 mn
132
30g T 4 1
3782
30gT 4 negligible
Assuming T >> μ
-
● As the temperature drops, some interactions become unable to keep up with the expansion.
→ These interactions falls out of equilibrium, i.e., they freeze out.
● A rough “out-of-equilibrium” condition:
● Particle species is decoupled when all of its interactions satisfy this condition, because then it has no more thermal contact with other particle species in the universe.
Interaction rate, Γ
-
● At temperatures O(1) < T < O(100) MeV, weak interactions keep neutrinos coupled to other particles in the thermal bath:
– Weak interaction rate:
– Hubble expansion rate:
● When the weak rate drops below the Hubble expansion rate, the neutrinos lose thermal contact with other particles → neutrinos decouple.
Neutrino decoupling
Γ=σ νe ne∼G F2 T 5
H=√ 8πG3 ∑i ρ̄i∼ T2
mpl
ν+ e↔ν+ e , ν ν̄↔e+ e-
T νdec∼1 MeV Neutrino decoupling temperature
-
Time
Photon temperature, Tγ
Events
Neutrino temperature
Phase spacedensity
Thermal history of neutrinos...
-
T =T
Time
Photon temperature, Tγ
~GF2 T 5
H~ T2
mplanck
Weak interaction:
Expansion rate:H
Neutrinos in thermal contact with cosmic plasma
Events
Neutrino temperature
Phase spacedensity Relativistic Fermi-Dirac
Thermal history of neutrinos...
1 MeV
f E≃1
exp [ p /T ]1
-
T =T
Time
Photon temperature, Tγ 1 MeV
Neu
trino
deco
uplin
g
~GF2 T 5
H~ T2
mplanck
Weak interaction:
Expansion rate:H
H ⇒~H
Neutrinos in thermal contact with cosmic plasma
Events
Neutrino temperature
Phase spacedensity
No thermal contact
Relativistic Fermi-Dirac
Thermal history of neutrinos...
f E≃1
exp [ p /T ]1
-
T =T T = 411 1 /3
T
Time
Photon temperature, Tγ 1 MeV 0.2 MeV
Neu
trino
deco
uplin
g
~GF2 T 5
H~ T2
mplanck
Weak interaction:
Expansion rate:
e+e-
ann
ihila
tion
HH ⇒~H
Neutrinos in thermal contact with cosmic plasma
Events
Neutrino temperature
Phase spacedensity
No thermal contact
Relativistic Fermi-Dirac
Thermal history of neutrinos...
f E≃1
exp [ p /T ]1
e-e+→γ γbecomes “one-way”
-
● Before annihilation: Entropy mainly from: photons, electrons/positrons, and neutrinos.
● After annihilation: Entropy from photons and (colder) neutrinos:
● Using
s a1=4390
2T 3 a1
s a2=22
45 [2T 3 a2 78 6T 3 a2]a1
3 s a1=a 23 s a2 ; a1T a1=a2T a2
T = 411 1 /3
T Neutrino temperatureafter annihilation
s≡∑i
iPiT i
∝a−3Entropy
Neutrino temperature...
-
● Neutrino decoupling and electron/positron annihilation occur at similar times (T ~ 1 MeV vs T ~ 0.2 MeV).
– Some neutrinos are still decoupled to the plasma when the annihilation happens.
→ Neutrinos at the high energy tail are affected by the entropy released in the annihilation.
– Expect neutrinos to be a little hotter than .
Non-instantaneous decoupling...
T = 411 1 /3
T
-
● To track the decoupling and reheating processes properly, we use the Boltzmann equation.
● Suppose we have a process:
● Then:
d f 1 p , t d t
= 12 E1∫∏
i=2
4 d 3 pi23 2 E i
244P1P2−P3−P4∣M∣2
× f 3 f 41± f 11± f 2− f 1 f 2 1± f 31± f 4
1234
9D phase space Energy-momentumconservation Matrix element
Phase space density of 1
Statistical factors+ for boson- for fermion
-
From S. Pastor
10× f
Relativistic FD
Real νµ,τ
Real νe
Neutrino phase space distribution after e+e- annihiliation
-
● It is convenient to express the increase of neutrino energy density in terms of an increase in the effective number of neutrino families:
∑ii≡N eff× , 0
“Standard” energy density per flavourassuming the “standardneutrino temperature
Total energy density in neutrinos
N eff=3.04
● Non-instantaneous decoupling and finite temperature QED effects together lead to:
-
● Temperature:
● Number density per flavour:
T ,0= 411 1 /3
T CMB ,0=1.95 K~10−4 eV
n ,0 =611
32
T CMB , 03 =
311nCMB ,0 = 112 cm
−3
CMB number density
TCMB,0 = 2.725 ± 0.001 K
A summary: the relic neutrino background today...
-
● Energy density per flavour:
● Closure bound:
Nonrelativistic= Neutrinodark matter
i≡i ,0crit , 0
; crit ,0=3H 0
2
8G
Gerstein & Zel'dovich 1966; Cowsik & McClelland 1972
ρν ,0={ 78 ( 411 )4/3
ρCMB ,0 ⇒ Ων ,0h2 = 6×10−6
mν nν ,0 ⇒ Ων ,0h2 =
mν94 eV
} m≪T ,0~10−4 eVm≫T ,0~10
−4 eV
If relativistic today
If nonrelativistic today
1 ⇒ m90 eVMore on this tomorrow
-
● Nonrelativistic neutrinos cluster gravitationally in dark matter halos.
– Expect mν-dependent variations in number density and phase space distribution.
Ringwald & Y3W 2004
mν =
mν =
mν =
mν =
Distance from the Galactic centre
Ove
rden
sity
nν/n
ν in
the
Milk
y W
ay
Solar system (~ 8 kpc)Local variations...
-
● Nonrelativistic neutrinos cluster gravitationally in dark matter halos.
– Expect mν-dependent variations in number density and phase space distribution.
Ringwald & Y3W 2004
Local variations... Rel. Fermi-DiracClustered
Pha
se s
pace
den
sity
at r
= 8
kpc
Neutrino momentum/temperature
-
1.3 Evidence for relic neutrinos...
-
● Big Bang nucleosynthesis
● Precision cosmology– Cosmic microwave background
– Large-scale structure distribution
(Indirect) evidence for relic neutrinos...
-
● Relevant temperatures:
● Production of
– Deuterium
– Helium-3
– Helium-4
– Lithium-7
– small amounts of others● Two phases
Big Bang nucleosynthesis...
T~O 100O 10 keV(after neutrino decoupling)
-
Phase 1: Setting the n/p ratio...
e p en
en e− p
n=885.6±0.8 s
● At T > 1 MeV the neutron-to-proton ratio is set by the interactions:
● After freeze-out neutron decay can still change the n/p ratio:
np eq≃exp −mn−mpT
Freeze-out
Relevant temperatures:T ~ 0.1 → 0.01 MeV
-
Phase 2: Formation of nuclei... Relevant temperatures:T ~ 0.1 → 0.01 MeV
● Beginning with Deuterium.
● Starting time set by the baryon-to-photon ratio η.
– Large entropy (small η) leads to the destruction of nuclei by photo-disintegration.
● The rest is governed by (known) nuclear physics.
→ Standard BBN has only one free parameter, η.
-
Standard BBN predictions as functions of the baryon-to-photon ratio η
-
Deuterium Destroyed in stars. 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 analyses.
Helium-4 Produced in stars by H burning. Data from low metallicity, extragalactic HII regions.
Lithium-7 Destroyed in stars, produced in cosmic ray interactions.
Data from the oldest, most metal poor stars in the Galaxy.
Measuring primordial abundances...
● Light element abundances we observe in astrophysical systems today are generally not at their primordial values.
● For measurements, low metallicity systems with as little evolution as possible are the best bets!
-
● Neutrinos affect Phase 1 of BBN through the interactions:
● Two ways:
– Change the freeze-out termpature of the interactions.
– Directly affect the weak interaction rates.
e p en
en e− p
Neutrinos and BBN... ...One
-
● Expansion of the universe described by the Friedmann equation:
● At and before the time of nucelosynthesis, radiation dominates energy density:
ρtotal≃ργ+∑iρν , i=ργ+N eff ρν
H 2=(1a d ad t )2
=8πG3
ρ total
Effective number of thermalised neutrinospecies
Energy density inone thermalisedneutrino species
First effect: freeze-out time
Total energy density:radiation, mattervacuum energy...
Photons
N eff=3.04Standard:
-
e p en
en e− p
● Increasing Neff raises the freeze-out temperature and hence the neutron-to-proton ratio:
np freeze≃exp −mn−m pT freeze Freeze-out
-
Helium-4 is most sensitive to Neff...
e p e n
en e− p
n p e − e
● Nearly all neutrons end up in Helium-4.
∣Y He≡4nHenN ≈ 2n / p1n / p∣t BBNHelium-4 mass fraction ~ 0.25for n/p ~ 1/7
Freeze-out
n pe − e
Depends onexpansion rate,and hence Neff
-
N eff=4
N eff=3
N eff=2
Baryon-to-photon ratio
Hel
ium
-4 a
bund
ance
Helium-4 is most sensitive to Neff...
-
Strumia & Vissani 2006
Neff
Helium-4 mass fraction, YHe
Time
BBN prefers Neff > 0.
Neff = 3
He-4 measurements in low metallicityextragalactic HII regions
-
● Recent analyses suggest a mild preference for Neff > 3 (or Ns > 0) from the Deuterium+Helium-4 abundance.
Evidence for Neff > 3 from BBN??
τn=878.5sτn=885.7s+ CMB prior onbaryon density
Hamann, Hannestad, Raffelt & Y3W 2011
-
● Neutrinos affect Phase 1 of BBN through the interactions:
● Two ways:
– Change the freeze-out termpature of the interactions.
– Directly affect the weak interaction rates.
e p en
en e− p
Neutrinos and BBN... ...Two
-
● Electron neutrinos affect directly the interactions:
before the interactions freeze out.
● In the standard model, neutrinos and antineutrinos have the same abundance.
– If there is an asymmetry in the neutrino and antineutrino number densities, it will affect the neutron-to-proton ratio primarily through these interactions.
Second effect: weak interaction rate
e p en
en e− p
-
● Neutrino-anitneutrino asymmetries are usually parameterised in terms of a finite chemical potential in the equilibrium phase space distribution:
● Effects on the neutron-to-proton ratio:
– i.e., a large asymmetry in the electron neutrinos drives down n/p.– Current constraint:
np≈exp [−mn−mpT − e] , ≡T
f e E =1
exp [ p−/T ]1, f eE =
1exp[ p /T ]1
Neutrinos Antineutrinos
µ = Chemical potential
e0.1 e.g., Raffelt & Serpico 2004
Assuming chemcialequilibrium holds
ξ = Degeneracy parameter
-
● BBN is also sensitive to neutrino-antineutrino asymmetries in the muon and tau neutrino sector, because:
– A large lepton asymmetry also contributes to the energy density:
– More importantly, flavour oscillations equilibrate all asymmetries prior to weak freeze-out.
A large lepton asymmetry in νμ,τ?
N eff=3+∑i[ 307 ( ξνiπ )
2
+157( ξνiπ )
4]
-
Dolgov et al. 2002Y3W 2002Abazajian et al. 2002
e. ,0.1
Bound on applies to all neutrino flavours!
e
time
Che
mic
al p
oten
tial ντ
νµ
νe
1. νμ ↔ ντ equilibration at T ~ 10 MeV.
2. νe ↔ νμ,ντ equilibration at T ~ 2 – 3 MeV.
BBN
matm2 ,atm msun
2 ,sun
-
● Big Bang nucleosynthesis
● Precision cosmology– Cosmic microwave background
– Large scale structure distribution
(Indirect) evidence for relic neutrinos...
-
Precision cosmological probes
Cosmic microwave background
CMB temperature anisotropy spectrum
-
Galaxy clustering
Lyman-α forest
Gravitationallensing
Cluster abundance
Precision cosmological probes
Large-scale structure distribution
Matter power spectrum
-
● For CMB and LSS, the main role of relic neutrinos is to fix the epoch of matter-radiation equality.
log(ρ)
log(a)
ρ̄Λ=const
ρ̄m∝a−3
Radiation domination Matter domination Λ domination
Matter-radiationequality
Matter-Λequality
aeq
ρ̄r∝a−4
-
CMB TT
● CMB: Delaying matter-radiation equality enhances the first peak of the temperature anisotropies relative to the plateau via the early Integrated Sachs-Wolfe (ISW) effect.
-
● Sachs-Wolfe effect:
ObserverRedshift
Ψ=0
Gravitational potential Blueshift
Observed temperature fluctuation
ΔTT observed
=ΔTT intrinsic
+Ψ
Ψ
-
● Integrated Sachs-Wolfe (ISW) effect:
● Except during matter domination, gravitational potentials decay with time.
→ Photons suffer less redshift than in the case of constant Ψ → Larger observed temperature fluctuations.
ObserverRedshift
Observer
time
Ψ=0
Gravitational potential
-
● LSS: Delaying matter-radiation equality shifts the turning point of the matter power spectrum to a smaller k (larger comoving Hubble radius at equality).
N eff=1 ,3 ,5 ,7 ,9
Large-scale structure
k eq=4.7×10−4√Ωm(1+ zeq)hMpc−1
-
● Recent CMB+LSS data appear to prefer Neff > 3!
Dunkley et al. [Atacama Cosmology Telescope] 2010 Keisler et al. [South Pole Telescope] 2011
WMAP+ACTWMAP+ACT+H0+BAO
WMAP
Stan
dard
val
ue
Stan
dard
val
ue
Evidence for Neff > 3 from CMB+LSS??
-
● Neff>3 trend has been there since WMAP-5.
● Exact numbers depend on the cosmological model, and the combination of data.
● Many model+data combinations find Neff>3 at 95% – 99% C.L.
● Central value Neff ~ 4.
W-5=WMAP-5; W-7=WMAP-7
= >95% C.L.
Abazajian et al., “Light sterile neutrinos: a white paper”, 2012
-
Planck and Neff...
Bashinsky & Seljak 2004Helium fractionas a free parameter
68% sensitivities
● If Neff is as large as 4, it will be settled almost immediately by Planck (launched May 14, 2009; public data release early 2013).
-
1.4 Prospects for direct detection...
-
● G. B. Gelmini, Prospects for relic neutrino searches, Phys. Scripta T121 (2005) 131 [hep-ph/0412305].
● A. Ringwald, Prospects for direct detection of the cosmic neutrino background, arXiv:0901.1529.
Useful references...
-
Direct detection is difficult because...
● Neutrinos interact weakly.
● Momentum transfer per scattering is too small to cross most interaction thresholds.
– A zero threshold interaction?
N~G F
2 m2
≃10−56 meV
2
cm2
p~m vearth≃10−3m
Speed of Earth wrt to the CMB,~ 370 km s-1
cf wimp detection, ~ 10-46 cm2
Neutrino-nucleoncross-section
-
Weinberg 1962
N N 'e − e1.
2.
3.
Assuming massless neutrinos
β-decay and related...
Qβ
Electronenergy
β-de
cay
end-
poin
t spe
ctru
m
-
QβQβ-EF
Weinberg 1962
N N 'e − eN N 'e − e , e
RNB~degenerate
Phase space blocking
EF = Fermi energy of degenerate relic (anti-)neutrinos
1.
2.
3.
Assuming massless neutrinos
β-decay and related...β-
deca
y en
d-po
int s
pect
rum
Electronenergy
-
Qβ+EF
Weinberg 1962
N N 'e − eN N 'e − e , e
RNB~degenerate
eRNBN N 'e − , e
RNB~degenerate
Phase space blocking
EF = Fermi energy of degenerate relic (anti-)neutrinos
1.
2.
3.
Assuming massless neutrinos
Capture of degeneraterelic neutrinos
β-decay and related...
QβQβ-EF
Electronenergy
β-de
cay
end-
poin
t spe
ctru
m
-
● In 1962, detection required:
● Present limit from BBN:
→ Impossible even for KATRIN (end-point resolution ~ 1 eV).
N N 'e − e
Phase space blocking
1.
2.
3.
S. Weinberg, Phys. Rev. 128 (1962) 1457
0.1
~EFT , 0
200 eV10−4 eV
~106
Relic neutrino temperature
Degeneracyparameter
⇒E F10−5 eV
-
QβQβ-mν Qβ+mν
Cocco, Mangano & Messina 2007Lazauskas, Vogel & Volpe 2007Blennow 2008
2mν
N N 'e − e e
RNBN N 'e −1.
2.
mν = Neutrino mass
Monochromatic signal from relic neutrino captureRate~6.5 nn / year / 100 g 3 H
… and a recent revival...β-
deca
y en
d-po
int s
pect
rum
Electronenergy
-
Lazauskas, Vogel & Volpe 2007
● The challenge: energy resolution!!!!
– Otherwise signal will be swamped by the β-decay tail.
Signal
Tritium β-decay tail folded with ∆E = 0.5 eV resolution
Fiducial mν = 1 eV
EmFor S/N > 1:
-
Blennow 2008
Signal vs background : fiducial mν = 0.05 eV
E=0.03 eV E=0.06 eV
⇒ S /N1⇒ S /N1
-
This is what it takes to get an end-point energy resolution of ~1 eV...
KATRIN main spectrometer
-
Summary...
● Relic neutrinos = a fundamental prediction of hot big bang theory.
● Good (indirect) evidence for their existence from BBN and CMB/LSS observations.
– Maybe there are even more than three neutrino species....
– Planck will tell!
● Direct detection (with existing technology) is still a long way away.
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