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!

Backup SlidesBackup Slides