cosmological aspects of neutrino physics (ii) sergio pastor (ific) 61st sussp st andrews, august...
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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
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
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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
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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
2ν
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
2ν
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
accélération
accélération
décélération lente
décélération rqpide
accélération
accélération
décélération lente
décélération rqpide
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
Cosmological observables: LSS
accélération
accélération
décélération lente
décélération rqpide
accélération
accélération
décélération lente
décélération rqpide
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
Cosmological observables : LSS
accélération
accélération
décélération lente
décélération rqpide
accélération
accélération
décélération lente
décélération rqpide
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
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
accélération
accélération
décélération lente
décélération rqpide
accélération
accélération
décélération lente
décélération rqpide
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
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