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Origin of Accelerating Origin of Accelerating Universe:Universe:
Dark-Energy and Particle CosmologyDark-Energy and Particle Cosmology
Yong-Yeon KeumYong-Yeon KeumInstitute for Early Universe,Institute for Early Universe,Ewha Womans Univ, Korea Ewha Womans Univ, Korea
&&CTP-BUE in EgyptCTP-BUE in Egypt
Talk at WHEPP XI workshopTalk at WHEPP XI workshopJan 03, 2010 Jan 03, 2010
Motivations:Motivations: What is the origin of the accelerating UniverseWhat is the origin of the accelerating Universe
and Dark-Energy ?and Dark-Energy ?
The connection between cosmological The connection between cosmological observations and particle physics is one of the observations and particle physics is one of the interesting and hot topic in astro-particle interesting and hot topic in astro-particle physics.physics.
Precision observations of the cosmic Precision observations of the cosmic microwave background and large scale microwave background and large scale structure of galaxies can be used to prove structure of galaxies can be used to prove neutrino mass with greater precision than neutrino mass with greater precision than current laboratory experiments. current laboratory experiments.
ContentsContents
Experimental evidence of accelerating universeExperimental evidence of accelerating universe
Candidates of Dark EnergyCandidates of Dark Energy
Neutrino Model of Dark EnergyNeutrino Model of Dark Energy
(An example of interacting dark matter and dark (An example of interacting dark matter and dark energy model)energy model)
Conclusion and discussions on some issues. Conclusion and discussions on some issues.
Breakthrough of 1998: the WinnerBreakthrough of 1998: the Winner
ASTRONOMY: Cosmic Motion Revealed
Breakthrough of 2003: the WinnerBreakthrough of 2003: the Winner
Illuminating the Dark Universe
ClosedUniverse
FlatUniverse
OpenUniverse
Measurement of the geometryMeasurement of the geometry
AT A GIVEN DISTANCEKnown physical size angle depends on geometry Known luminosity flux depends on geometry
CMB
SN Ia
Standard Candle-SNIaStandard Candle-SNIa
Hubble diagram:Hubble diagram:
Redshift z
m = - 2.5 log F + cst = 5 log (H0 DL) + M - 5 log H0 + 25
H0DL czz 0 measure of H0 Large z : measure of m,
Mag
nit
ud
e m
older
fain
ter
1+z = a(tobs)/a(tem)
At a given z
SupernovaCosmologyProject
Accelerated expansion= smaller rate in the past
= more time to reach a given z= larger distance of propagation of the photons= smaller flux
Back to thermal historyBack to thermal history
Density perturbations (inflation?)
Nucleosynthesis
t = 10-35 s
t ~ 1 mn
t ~ 380000 yrs
Matter: Gravitational collapse
Photons: Free propagation
observable
observable
Galaxies, clusters CMB
Recombination: p+e- H+
What Penzias & Wilson saw in 1965What Penzias & Wilson saw in 1965
CMB black - body temperature = 2.73 K
number density of CMB photons= 407 cm 3
Should the CMB sky be perfectly Should the CMB sky be perfectly smooth (or isotropic)?smooth (or isotropic)?
No. TodayNo. Today’’s s Universe is Universe is homogeneous and homogeneous and isotropic on the isotropic on the largest scales, but largest scales, but there is a fair there is a fair amount of structure amount of structure on small scales, on small scales, such as galaxies, such as galaxies, clusters of galaxies clusters of galaxies etc.etc.
What are these primordial fluctuations (at the level of 100 micro-Kelvin)?
What are the CWhat are the Cℓℓs?s?Qualitatively: ~power in each Qualitatively: ~power in each
multipole modemultipole modeQuantitatively:Quantitatively:
3 regimes of CMB power 3 regimes of CMB power spectrumspectrum
Large scale plateau
Damping tail
Acoustic oscillations
In general….In general….
↓Ωmh2
↑Ωbh2← ← Ωm+ΩΛ
←Age of Universe
↓zre
Max. scale of anisotropiesMax. scale of anisotropies
Max scale relates to total content of Universe tot
Limited by causality (remember?) maximum scale
What we know so farWhat we know so far Our universe is flat, accelerating.Our universe is flat, accelerating. The dominance of a dark energy component The dominance of a dark energy component
with negative pressure in the present era with negative pressure in the present era is responsible for the universe’s accelerated is responsible for the universe’s accelerated
expansion.expansion.
Contents of MatterContents of Matter
TitleTitleDark Energy 73%Dark Energy 73%(Cosmological Constant)(Cosmological Constant)
NeutrinosNeutrinos 0.10.12%2%
Dark MatterDark Matter23%23%
Ordinary Matter 4%Ordinary Matter 4%(of this only about(of this only about 10% luminous)10% luminous)
Perfect fluid – the zeroth-order approximation
p
p
p
000
000
000
000
Einstein Equation
gGG 8
geometric structure matter distribution
P : pressure
)(),(),( tpttR : functions of time
: energy density
(00):33
822
2 G
Rk
RR
(1)
(i i): Gp
Rk
RR
RR 82
2
2
(2)
3
33
4 p
GRR (3)
Supernova Cosmology Projects (1999): 0RR
0 or Quintessence (“Dark Energy”)
Einstein’s General Relativity (GR) & Cosmological Principle (CP):
Negative Pressure
2 2 0 3 0 4 0 2 0 3(1 )0
13(1 )
( ) [ ]
exp{3 [1 ( )]}
wm r k X
w
a
H a H a a a a
dya w y
y
Puzzles in Accelerating UniversePuzzles in Accelerating Universe
Cosmological Constant Problem:Cosmological Constant Problem: Why is the energy of the vacuum so much small ?Why is the energy of the vacuum so much small ?
Dark Energy Puzzle:Dark Energy Puzzle: What is the nature of the smoothly-distributed What is the nature of the smoothly-distributed
energy density which appears to determine the universe. energy density which appears to determine the universe.
Coincidence Scandal:Coincidence Scandal: Why is the dark energy density approximately equal to Why is the dark energy density approximately equal to
the matter density in present epoch.the matter density in present epoch.
Candidates of Dark EnergyCandidates of Dark Energy
(A)(A) Cosmological ConstantCosmological Constant
(B)(B) Dynamical Cosmological constantDynamical Cosmological constant (Time-dependent; Quintessence ) (Time-dependent; Quintessence ) - quintessence: - quintessence: potential termpotential term + canonical kinetic + canonical kinetic
termterm
- K-essence: - K-essence: non-canonical kinetic termnon-canonical kinetic term
- phantom - quintom- phantom - quintom - -Tachyon fieldTachyon field
(C)(C) Modified Gravity Modified Gravity (Modified friedman eq.)(Modified friedman eq.)
(D)(D) Cosmological Back Reaction Cosmological Back Reaction (E)(E) Others ……Others ……
(A)(A) Cosmological ConstantCosmological Constant
Typical scaleTypical scale ::
Hence a new energy density is too lowerHence a new energy density is too lower
from the particle physics point.from the particle physics point.
2 42 20 (10 )H GeV
22 2 40
0 )8 P
N
HM H eV
G
4)particle GeV
8 NG g G T
Cosmological constant problemCosmological constant problem
• Many different contributions to vacuum energies:Many different contributions to vacuum energies:
(a) QCD ~ (a) QCD ~
(b) EW physics ~ (b) EW physics ~ (c) GUT ~(c) GUT ~
(d) SUSY ~ (d) SUSY ~
All these contributions should conspire to cancel down toAll these contributions should conspire to cancel down to . .
Extreme fine tuning !!!Extreme fine tuning !!!
4(1 )GeV
16 4(10 )GeV
3 4(10 )GeV
2 4(10 )GeV
4 4(10 ) eV
( B ) Quintessence( B ) Quintessence Quintessence = dark energy as a scalar field = dynamical Quintessence = dark energy as a scalar field = dynamical
cosmological constantcosmological constant No evidence for evolving smooth energy, but attractive No evidence for evolving smooth energy, but attractive
reasons for dynamical origins ! reasons for dynamical origins !
(a) why small, why not zero, why now ???(a) why small, why not zero, why now ???
(b) suggest the physical cosmological evolution.(b) suggest the physical cosmological evolution. Canonical quintessence:Canonical quintessence:
2
3(1 )
1, ( )
2( )
3 0, 3 ( ) 0
( 1)
K V
dVH H p
d
p a
Quintessence (2)Quintessence (2)
• If potential energy dominates over the kinetic energyIf potential energy dominates over the kinetic energy
Slow-roll limit:Slow-roll limit:
Stiff matter:Stiff matter:
Accelerating exp.:Accelerating exp.:
2 2
0
0 4 40
1 1( ); ( )
2 2
1 ( )
1 1( ) ( ) [ 3(1 ) ]
2 2
(10 )
P
c
V p V
paccelerating
V V ExpM
V eV
2 2
2
8 1[ ( ) ( )]
3 28
[ ( )]3
GH V
a GV
a
0 exp[ 3(1 ) ]daa
2
2 6
( ) 1( )
( ) 1( )
(0 2)m
V const
V a
a m
4 21[ ( ) ( )]2
S d x g V
Quintessence PotentialsQuintessence Potentials
K-essenceK-essenceOriginally kinetic energy driven inflation, called Originally kinetic energy driven inflation, called K-inflation [Armendariz-Picon] ; Originates from string K-inflation [Armendariz-Picon] ; Originates from string
theory.theory. First applied to dark energy by Chiba et al.First applied to dark energy by Chiba et al.
K-essence is characterized by a scalar field with non-K-essence is characterized by a scalar field with non-canonical kinetic energycanonical kinetic energy
Transformed to the Einstein-frame action:Transformed to the Einstein-frame action:
4
2
( , );
1( )
2ˆ( , ) ( ) ( )
S d x g p X
X
p X f p X
4 2
2
2
2
[ / 2 ( ) ( ) ...]
( / ) and ( ) ( ) / ( )
( , ) ( )[ ]
2 ( )[ 3 ]
11 3
1 : 1/ 2;
1/ 3 : 2/ 3
E
ol d ol d
S d x g R K X L X
X L K X f K L
p X f X X
pX p f X X
Xp X
X
X
X
Phantom(ghost field)Phantom(ghost field)
• Negative sign in the kinetic term;Negative sign in the kinetic term;
• We obtain forWe obtain for
4 21[ ( ) ( )]
2S d x g V
2
2
2
2
/ 2 ( );
/ 2 ( );
2 ( )2 ( )
V
p V
p VV
2 / 2 ( )V 1
QuintomQuintom
Feng,Wang and Zhang proposed a hybrid model ofFeng,Wang and Zhang proposed a hybrid model of
quintessence and Phantom (so the name quintom)quintessence and Phantom (so the name quintom)
when while when when while when
2 21 2 1 2
2 21 2 1 2
2 21 2 1 2
2 21 2 1 22 21 2 1 2
1 1( ) ( ) ( , );
2 21 1
( , );2 21 1
( , );2 2
2 ( , )
2 ( , )
DEL V
p V
V
V
V
1 2 21 2 1 2 2
1 2
Big-Rip Singularity in phantom fieldBig-Rip Singularity in phantom field
• Hubble rate diverges as t -> ts, which corresponds to Hubble rate diverges as t -> ts, which corresponds to an infinitely large energy density at a finite time in an infinitely large energy density at a finite time in the future. The curvature also glows to infinity.the future. The curvature also glows to infinity.
• It should be emphasized that we expect quantum It should be emphasized that we expect quantum effects to become important when the curvature of effects to become important when the curvature of
universe become large.universe become large.
2/ 3(1 )s
3(1 )
22
- 1:
( ) ( ) ; t .
;
2; = - 0;
3(1+ )
6 (2 1)6
:
:
(2 ) .( )
s
s
s
a t t t const
a
nH
For phant om fi el d wi t h
Hubbl e r at e
Scal ar Cur vat u
nt t
n
r e
nR H H
t t
Tachyon field (A. Sen)Tachyon field (A. Sen)
2
2
8 ( ) 3(1 )
23 1
a GV TT
a T
An acclerated expansionoccurs for 2 2/ 3.T
Chaplygin gasChaplygin gas
A special case of a tachyon with
a constant potential
2( ) /Tp V
( C ) Idea of the Modified Gravity( C ) Idea of the Modified Gravity Newtonian Cosmology:Newtonian Cosmology: Gravitational Force law determines the Gravitational Force law determines the
evolutionevolution
Combining the above eqs:Combining the above eqs:
Moreover, E = constant and decelleration !!Moreover, E = constant and decelleration !!
2
34
3( )
N
F MR G
m R
M R
R a t r
4( )
3 N
aG t
a
33
2/3
4 1
3
0
E M Ra
a t a
Modified ForceModified Force
For simplicity g=1For simplicity g=1
(1) Early times t << tc so that(1) Early times t << tc so that
matter domination, no accelerationmatter domination, no acceleration(2) Later time, t > tc when (2) Later time, t > tc when
Accelerated expansion !!!Accelerated expansion !!!
22
2
3
( )
4( ) ,
3
( ) 0
Nc
N c
G MFR m Rg R
m R
R G R m g R R
d a
2 2/34, ~
3N c NG m R G R a t
2 2 2, ~ , ~ 0!!!cm tN c c cG m R m R a e a m
Classification of the Modified GravityClassification of the Modified Gravity
Cardassian : Cardassian : Different brane world scenarios:Different brane world scenarios:
a) Dvali, Gabadadze and Porrati (DGP)a) Dvali, Gabadadze and Porrati (DGP)
b) Deffayet, Devali and b) Deffayet, Devali and Gabadadez(DDG)Gabadadez(DDG)
c) Randall and Sundrumc) Randall and Sundrum
d) Shtanov brane Modeld) Shtanov brane Model
e) non-linear gravitye) non-linear gravity
Candidates of DE (Modified Gravity)Candidates of DE (Modified Gravity)
• Modification of Gravity Modification of Gravity 1. Modified Newtonian Dynamics (Milgrom. 83)1. Modified Newtonian Dynamics (Milgrom. 83) 2. Brane Models (Binetaury. 98)2. Brane Models (Binetaury. 98) 3. Cardassian Expansion (Freese. 02)3. Cardassian Expansion (Freese. 02)
Top-ten accelerating cosmological ModelsTop-ten accelerating cosmological Models
Akaike information: AIC = -2 lnL + 2d: d = # of model param.Bayesian factor: BIC = -2 lnL + d lnN: N = # of data point
used in the fit.
(B,n), (z(B,n), (zeqeq,n) or (,n) or (mm,n),n)
Hubble Parameter as Function of z,Hubble Parameter as Function of z, H=HH=H00E(z)E(z)
The Critical/Matter DensityThe Critical/Matter Density
Parameters of MFE cosmology
Observational Constraints onObservational Constraints on MFE Cosmology MFE Cosmology
nBG
H
382 nB
GH 00
20 3
8 0
)1(3)1(3
8 n
eqzG
B
1)1(3 ])1(1[ neqm zmcc,MFE 0
From turnaround redshift zq=0
Observational Constraints on MFE CosmologyObservational Constraints on MFE Cosmology
• zzq=0q=0 depends on both of depends on both of mm
and n. (see eq. below)and n. (see eq. below)
• For each For each mm, there exists one , there exists one
nnpeakpeak((mm), which leads to a ), which leads to a
maximum of zmaximum of zq=0q=0..
• Higher Higher m m is, lower zis, lower zq=0 q=0 is.is.
• For each zFor each zq=0q=0, there exists an , there exists an
upper limit for upper limit for mm, e.g., , e.g.,
zzq=0q=0>0.6, then >0.6, then mm<0.328.<0.328.)1(3/1
)1(3/10 1
1)32()1()32()1(
n
meq
nq nznz
Observational Constraints on Observational Constraints on MFEMFE Cosmology Cosmology
• The thick solid line is zThe thick solid line is zq=0q=0..
• The cross-hatched area is The cross-hatched area is the present optimistic the present optimistic mm=0.330+-0.035.=0.330+-0.035.
• The dashed lines are The dashed lines are mm=0.2 =0.2
and 0.4 respectively.and 0.4 respectively.
• The shaded area gives 0.6 < The shaded area gives 0.6 < zzq=0q=0 <1.7. <1.7.
From turnaround redshift zq=0
Zhu & Fujimoto 2004, ApJ, 602, 12
Observational Constraints on Observational Constraints on MFEMFE Cosmology Cosmology
• A A 22 minimization method minimization method is used to determine is used to determine ((mm,n).,n).
• The best fit happans at The best fit happans at ((mm,n)=(0.38,-0.20).,n)=(0.38,-0.20).
• The 68.3% and 95.4% The 68.3% and 95.4% confidence level in the confidence level in the ((mm,n) plane are shown.,n) plane are shown.
Zhu, Fujimoto & He 2004, ApJ, 603,365
From SNeIa and Fanaroff-Riley type IIb radio galaxies
98
12
2o2 ]),;([
),(i i
imim
ynzyn
A A BBrane rane WWorld orld MModel (odel (BWMBWM): DGP): DGP
A self-accelerating 5-dimensional BWMA self-accelerating 5-dimensional BWM With a noncompact, infinite volume extra With a noncompact, infinite volume extra
dimensiondimension An ordinary 5-dimensional Einstein-Hilbert An ordinary 5-dimensional Einstein-Hilbert
actionaction A 4-dimensional Ricci scalar term induced A 4-dimensional Ricci scalar term induced
on the braneon the brane
Dvali, Gabadadze & Porrati 2000
Comments:Comments:
MFEMFE is an alternative to DE as acceleration is an alternative to DE as acceleration mechanism. Combinations of current mechanism. Combinations of current astronomical data can provide stringent astronomical data can provide stringent constraints on its model parameters.constraints on its model parameters.
MFEMFE cosmology can not be the mechanism cosmology can not be the mechanism for acceleration starting from z > 1.0.for acceleration starting from z > 1.0.
DGPDGP model is disfavored by current SNeIa model is disfavored by current SNeIa and fand fgas gas of galaxy clusters. of galaxy clusters.
Equation of State (EoS)
W = p/
It is really difficult to find the origin of dark-energy It is really difficult to find the origin of dark-energy with non-interacting dark-energy scenarios.with non-interacting dark-energy scenarios.
Summary of EoS Summary of EoS
Canada-France-Hawaii Wide Synoptic Survey:Canada-France-Hawaii Wide Synoptic Survey:
wwoo < - 0.8 based on cosmic share data alone < - 0.8 based on cosmic share data alone Supernova Lagacy Survey (SNLS):Supernova Lagacy Survey (SNLS):
Combined with SDSS measurement of BAOCombined with SDSS measurement of BAO
WMAP3 and WMAP5 data:WMAP3 and WMAP5 data:
1) assume flat universe with SNLS data: 1) assume flat universe with SNLS data:
2) Drop prior of flat universe, WMAP+LSS+SNLS 2) Drop prior of flat universe, WMAP+LSS+SNLS data:data:
1.023 0.090 0.054w
0.070.090.97w
0.128 0.0160.079 0.013 and 0.0241.062 kw
Interacting Dark-Energy modelsInteracting Dark-Energy models
o o interacting between dark-matter and dark-energy: interacting between dark-matter and dark-energy: (Farrar and Peebles, 2004)(Farrar and Peebles, 2004)
o o interacting between photon and dark-energy: interacting between photon and dark-energy: (Feng et al., 2006; Liu et al., 2006)(Feng et al., 2006; Liu et al., 2006)
o o interacting betweeninteracting between neutrinos and dark-energy:neutrinos and dark-energy:(Zhang et al, Fardon et al. 2004, yyk and Ichiki, 2006,2008)(Zhang et al, Fardon et al. 2004, yyk and Ichiki, 2006,2008)
S Lee. IoPAS S Lee. IoPAS
Models of Interacting DE-PhotonModels of Interacting DE-Photon
Coupled Quintessence (S.L, K.Olive, M.Pospelov, 04)Coupled Quintessence (S.L, K.Olive, M.Pospelov, 04)
Potentials :Potentials :
Coupling : Coupling :
S Lee. IoPAS S Lee. IoPAS 5757
Evolution of Background Evolution of Background
S Lee. IoPAS S Lee. IoPAS 5858
Time Varying Alpha (Late time)Time Varying Alpha (Late time)
1010
Motivations for Interacting Motivations for Interacting DE-Massive Neutrinos:DE-Massive Neutrinos:
Why does the mass scale of neutrinos so small Why does the mass scale of neutrinos so small ??
about 10about 10-3-3 eV ~ Eo: accidental or not ? eV ~ Eo: accidental or not ?
If not accidental, are there any relation If not accidental, are there any relation between Neutrinos and Dark Energy ?between Neutrinos and Dark Energy ?
33 210 /m eV m M
2 3 41/ 10 10cL l H H l m M eV
M
Interacting dark energy modelInteracting dark energy model
Example At low energy,
The condition of minimization of Vtot determines the physical neutrino mass.
nv mvScalar potential
in vacuum
Interacting Neutrino-Dark-Energy Model
Mass Varying Neutrino ModelMass Varying Neutrino ModelZhang Zhang etet al,al, Fardon,Kaplan,Nelson,Weiner: PRL93, 2004 Fardon,Kaplan,Nelson,Weiner: PRL93, 2004
Fardon, Nelson and Weiner suggested that Fardon, Nelson and Weiner suggested that
tracks the energy density in neutrinos tracks the energy density in neutrinos
The energy density in the dark sector has two-The energy density in the dark sector has two-components:components:
The neutrinos and the dark-energy are coupled The neutrinos and the dark-energy are coupled because it is assumed that dark energy density is a because it is assumed that dark energy density is a function of the mass of the neutrinos: function of the mass of the neutrinos:
DE
( )m m n
dark DE
( )DE DE n
Since in the present epoch, neutrinos are non-relativistic Since in the present epoch, neutrinos are non-relativistic (NR),(NR),
Assuming dark-energy density is stationary w.r.t. variations in Assuming dark-energy density is stationary w.r.t. variations in the neutrino mass,the neutrino mass,
DefiningDefining
( )dark DEm n m n m
( )0
3 ( )
dark DE mn
m m
H p
,
1
dark
dark
dark dark DE DE
dark DE
p
p p p
m n m n
m n
Lessons:Lessons:
Wanted neutrinos to probe DE, but actually are Wanted neutrinos to probe DE, but actually are DE.DE.
flat scalar potential (log good) flat scalar potential (log good) choice,choice,
mmvv < few eV. < few eV.
Neutrino mass scales as mNeutrino mass scales as mvv ~ 1/n ~ 1/nvv::
- lighter in a early universe, heavier now- lighter in a early universe, heavier now
- lighter in clustered region, heavier in FRW - lighter in clustered region, heavier in FRW regionregion
- lighter in supernovae- lighter in supernovae
Couplings of ordinary matter to such scalars Couplings of ordinary matter to such scalars stronglystrongly
constrained – must be weaker than Planck: 1/Mconstrained – must be weaker than Planck: 1/Mplpl
bb
The FNW scenario is only consistent, If there is no kinetic contributions (K=0) and
the dark-energy is a pure running cosmological constant !!
Theoretical issue: Theoretical issue: Adiabatic Instability problem: Adiabatic Instability problem:
Afshordi et al. 2005Afshordi et al. 2005
Gravitational collapseGravitational collapse
Kaplan, Nelson, Weiner 2004Kaplan, Nelson, Weiner 2004 Khoury et al. 2004Khoury et al. 2004 Zhao, Xia, X.M Zhang 2006Zhao, Xia, X.M Zhang 2006
Always positive sound velocity Always positive sound velocity No adiabatic instabilityNo adiabatic instability
Brookfield et al,. 2006Brookfield et al,. 2006 YYK and Ichiki, 2007, 2008YYK and Ichiki, 2007, 2008
2 2 2/
H (Chameleon DE models)
eff eff
eff
m d V d
m
< H (Slow-rolling Condition)effm
Background Equations:Background Equations:
We consider the linear perturbation in the synchronous Gauge and the linear elements:
Perturbation Equations:
K. Ichiki and YYK:2007
The impact of Scattering term:The impact of Scattering term:
Varying Neutrino MassVarying Neutrino Mass
eV eV
With full consideration of Kinetic term
V( )=Vo exp[- ]
W_effW_eff
eV eV
Neutrino Masses vs zNeutrino Masses vs z
eV
eV
Neutrino mass effects Neutrino mass effects
After neutrinos decoupled from the thermal bath, they stream After neutrinos decoupled from the thermal bath, they stream freely and their density pert. are damped on scale smaller than freely and their density pert. are damped on scale smaller than their free streaming scale. their free streaming scale.
The free streaming effect suppresses the power spectrum on The free streaming effect suppresses the power spectrum on scales smaller than the horizon when the neutrino become non-scales smaller than the horizon when the neutrino become non-relativistic.relativistic.
Pm(k)/Pm(k) = -8 Pm(k)/Pm(k) = -8 ΩΩ / /ΩΩmm
Analysis of CMB data are not sensitive to neutrino masses if Analysis of CMB data are not sensitive to neutrino masses if neutrinos behave as massless particles at the epoch of last neutrinos behave as massless particles at the epoch of last scattering. Neutrinos become non-relativistic before last scattering. Neutrinos become non-relativistic before last scattering when scattering when ΩΩh^2 > 0.017 (total nu. Masses > 1.6 eV). h^2 > 0.017 (total nu. Masses > 1.6 eV). Therefore the dependence of the position of the first peak and the Therefore the dependence of the position of the first peak and the height of the first peak has a turning point at height of the first peak has a turning point at ΩΩ h^2 = 0.017. h^2 = 0.017.
Mass Power spectrum vs Neutrino Masses
Power spectrumPower spectrum
PPmm(k,z) = P(k,z) = P**(k) (k) TT22(k,z) Transfer Function:(k,z) Transfer Function:
T(z,k) := T(z,k) := (k,z)/[(k,z)/[(k,z=z(k,z=z**)D(z)D(z**)])]
Primordial matter power spectrum (AkPrimordial matter power spectrum (Aknn))
zz**:= a time long before the scale of interested have entered := a time long before the scale of interested have entered
in the horizon in the horizon
Large scale: T ~ 1Large scale: T ~ 1
Small scale : T ~ 0.1Small scale : T ~ 0.1
PPmm(k)/P(k)/Pmm(k) ~ -8 (k) ~ -8 ΩΩ//ΩΩmm
= -8 f= -8 f
Numerical Analysis
Within Standard Cosmology Model (LCDM)
Power-spectrum (LSS)Power-spectrum (LSS)
eV eV
Constraints from Constraints from ObservationsObservations
Neutrino mass Bound: M < 0.87 eV @ 95 % C.L.
WMAP3 data on Ho vs WMAP3 data on Ho vs
Neutrino Mass BoundsNeutrino Mass BoundsWithout Ly-alpha Forest data (only 2dFGRS + HST + WMAP3)Without Ly-alpha Forest data (only 2dFGRS + HST + WMAP3) Omega_nu h^2 < 0.0044 ; 0.0095 (inverse power-law potential)Omega_nu h^2 < 0.0044 ; 0.0095 (inverse power-law potential) < 0.0048 ; 0.0090 (sugra type potential)< 0.0048 ; 0.0090 (sugra type potential) < 0.0048 ; 0.0084 ( exponential type potential)< 0.0048 ; 0.0084 ( exponential type potential)
provides the total neutrino mass boundsprovides the total neutrino mass bounds
M_nu < 0.45 eV (68 % C.L.)M_nu < 0.45 eV (68 % C.L.)
< 0.87 eV (95 % C.L.)< 0.87 eV (95 % C.L.)
Including Ly-alpah Forest dataIncluding Ly-alpah Forest data
Omega_nu h^2 < 0.0018; 0.0046 (sugra type potential)Omega_nu h^2 < 0.0018; 0.0046 (sugra type potential)
corresponds tocorresponds to
M_nu < 0.17 eV (68 % C.L.)M_nu < 0.17 eV (68 % C.L.)
< 0.43 eV (95 % C.L.)< 0.43 eV (95 % C.L.)
QuestionsQuestions How can we test mass-varying neutrino model in How can we test mass-varying neutrino model in
Exp. ?Exp. ?
--- by the detection of the neutrino mass variation in --- by the detection of the neutrino mass variation in space via neutrino oscillations.space via neutrino oscillations.
--- by the measurement of the time delay of the --- by the measurement of the time delay of the neutrino emitted from the short gamma ray bursts. neutrino emitted from the short gamma ray bursts.
How much this model can be constrainted from, How much this model can be constrainted from, BBN, CMB, Matter power spectrum observations ?BBN, CMB, Matter power spectrum observations ?
Solar mass-varying neutrino oscillationSolar mass-varying neutrino oscillationV.Barger et al: hep-ph/0502196;PRL2005V.Barger et al: hep-ph/0502196;PRL2005
M.Cirelli et al: hep-ph/0503028M.Cirelli et al: hep-ph/0503028
The evolution eq. in the two-neutrinos framework are:The evolution eq. in the two-neutrinos framework are:
ee-e forward scattering amplitude:-e forward scattering amplitude:
Model dependence in the matter profiles:Model dependence in the matter profiles:
- - k parameterize the dependence of the neutrino mass on n k parameterize the dependence of the neutrino mass on nee
- - ii is the neutrino mass shift at the point of neutrino is the neutrino mass shift at the point of neutrino production.production.
MaVaN results:MaVaN results:
Conclusions-1Conclusions-1
Neutrinos are best probe of SM into DE sectorNeutrinos are best probe of SM into DE sector
Possible origin for dark energyPossible origin for dark energy
Motivates consideration of new matter effects toMotivates consideration of new matter effects to
be seen in oscillations:be seen in oscillations:
- LSND interpretation- LSND interpretation
- Matter/air analyses- Matter/air analyses
- Solar MaVaN oscillation Effects - Solar MaVaN oscillation Effects
- time delay in the gamma ray bursts.- time delay in the gamma ray bursts.
Conclusions-2Conclusions-2 Neutrinoless double beta decays can provides very important Neutrinoless double beta decays can provides very important
properties of neutrinos: Dirac or majorana particles; neutino mass properties of neutrinos: Dirac or majorana particles; neutino mass information;information;
mass-hierarchy pattern. mass-hierarchy pattern. In conclusion, results of precision analysis of CMB and LSS data don’t In conclusion, results of precision analysis of CMB and LSS data don’t
follow only from data, follow only from data, but also can rely on theoretical assumptions.but also can rely on theoretical assumptions.
Prospects:Prospects: Future measurements of gravitational lensing of CMB light and/or of Future measurements of gravitational lensing of CMB light and/or of
photon generated by far galaxies should allow to direct measure the photon generated by far galaxies should allow to direct measure the total density with great accuracy. In this way, total density with great accuracy. In this way, it might be possible to it might be possible to see the cosmological effects of neutrino masses, and measure them see the cosmological effects of neutrino masses, and measure them with an error a few times smaller than the atmospheric mass scalewith an error a few times smaller than the atmospheric mass scale..
This could allow us to discriminate between normal and inverted This could allow us to discriminate between normal and inverted neutrino mass hierarchy.neutrino mass hierarchy.
When the neutrino masses are not constant, but When the neutrino masses are not constant, but vary as a function of time and space, vary as a function of time and space, CPT CPT violationviolation occurs naturally even in thermal occurs naturally even in thermal equilibrium.equilibrium.
CPTV helps to understand the matter-antimatter CPTV helps to understand the matter-antimatter asymmetry of the universeasymmetry of the universe
-> -> spontaneous Baryon Asymmetryspontaneous Baryon Asymmetry
However, since the laboratory experimental limit However, since the laboratory experimental limit on the CPTV in electrons is so stringent that the on the CPTV in electrons is so stringent that the induced CPTV in neutrino sector will be much induced CPTV in neutrino sector will be much below the sensitivity for the current and future below the sensitivity for the current and future experiments.experiments.
Summary of Methods to Obtain Neutrino Masses
Single beta decay
mi2 |Uei|2 Sensitivity
0.2 eV
Double beta decay
m = |mi |Uei|2 i| i = Majorana phases
Sensitivity 0.01 eV
Neutrino oscillations
m2 = m12 - m2
2 Observed ~ 10-5 eV2
Cosmology mi Observed ~ 0.1 eV
Only double beta decay is sensitive to Majorana nature.
Search for the origin of Dark-EnergySearch for the origin of Dark-Energywith Large Scale Structureswith Large Scale Structures
Baryon Acoustic Oscillation (BAO)Baryon Acoustic Oscillation (BAO)
Galaxy Cluster surveys (GL)Galaxy Cluster surveys (GL)
Supernova type Ia surveys (SNIa)Supernova type Ia surveys (SNIa)
Weak Lensing surveys (WL)Weak Lensing surveys (WL)
luminosity distance-redshift relation: luminosity distance-redshift relation: angular distance-redshift relation:angular distance-redshift relation:volume-redshift relation:volume-redshift relation: linear growth-redshift relation:linear growth-redshift relation:
ways to measure dark energy
)(
)(
)(
)(
zg
zV
zd
zd
A
L
Dark Energy ProbesDark Energy Probesby LSS samplesby LSS samples
ProbeProbe MeasurementsMeasurements RemarksRemarks
supernovae (SN)supernovae (SN)
GRB(?)GRB(?)
ddLL((zz)) standard candlestandard candle
evolution effectsevolution effects
clusters (CL)clusters (CL)
QSO’s Ly-alpha QSO’s Ly-alpha absorption absorption
ddAA((zz), ), V V ((zz)),, & & gg((zz))
g(z)g(z)
standard samples.standard samples.
identifications ( mass—observable relationidentifications ( mass—observable relation
nonlinear evolution (mass function,..)nonlinear evolution (mass function,..)
biasbias
nonlinear evolution, nonlinear evolution,
UV photon background UV photon background
baryon acousticbaryon acoustic
oscillation (BAO)oscillation (BAO)
ddAA((zz) & ) & V V (z)(z) standard rulerstandard ruler
relation between dark matter and galaxiesrelation between dark matter and galaxies
weak Lensingweak Lensing
(WL)(WL)
ddAA((zz) & ) & gg((zz)) How to calibrateHow to calibrate
Systematic errorsSystematic errors
Power of combining techniquesPower of combining techniques
ConcordanceConcordance
CMB
LSS
2000 2002
Expected precision with JDEM (>2013)
Cosmological weak lensingCosmological weak lensing
present
z=zs
z=zl
z=0
past
Large-scale structure
Arises from total matter clusteringArises from total matter clustering Note affected by galaxy bias Note affected by galaxy bias
uncertainty uncertainty Well modeled based on simulations Well modeled based on simulations
(current accuracy <10%, White & Vale (current accuracy <10%, White & Vale 04) 04)
Tiny 1-2% level effectTiny 1-2% level effect Intrinsic ellipticity per galaxy, ~30%Intrinsic ellipticity per galaxy, ~30% Needs numerous number (10^8) of Needs numerous number (10^8) of
galaxies for the precise measurementgalaxies for the precise measurement
Weak Lensing Tomography- MethodWeak Lensing Tomography- Method
Warning ! In conclusion, results of precision analysis of CMB and LSS
data don’t follow only from data but also rely on theoretical assumptions.
Prospects: Future measurements of gravitational lensing of CMB light
and/or of light generated by far galaxies should allow to direct measure the total density with great accuracy. In this way, it might be possible to see the cosmological effects of neutrino masses, and measure them with an error a few times smaller than the atmospheric mass scale.
This could allow us to discriminate between normal and inverted neutrino mass hierachy.
Thanks Thanks For For your your attention!attention!
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