Neutrino Mass InformationNeutrino Mass Information from from Cosmological Cosmological ProbesProbes

(LCDM vs Interacting Dark-Energy Model)(LCDM vs Interacting Dark-Energy Model)

Yong-Yeon KeumYong-Yeon KeumSeoul National University Seoul National University

ASK2011 Workshop ASK2011 Workshop Seoul, Korea Seoul, Korea

April 11-12, 2011April 11-12, 2011

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)

If the 0If the 0 decay will be observed and decay will be observed and

it will be an indication of the inverted hierarchyit will be an indication of the inverted hierarchy

Normal Hierarchy : M_nu > 0.03 eVNormal Hierarchy : M_nu > 0.03 eV Inverted Hierarchy: M_nu > 0.07 eVInverted Hierarchy: M_nu > 0.07 eV

Remarks: It is really difficult to confirm Remarks: It is really difficult to confirm the normal hierarchy in neutrinoless the normal hierarchy in neutrinoless double beta decay in future double beta decay in future experiments.experiments.

How can we reach there ?How can we reach there ?

2 20.42 atm atmm m m

Contents:Contents:

Neutrino Masses from Large Scale Neutrino Masses from Large Scale Structures (CMB, Power Spectrum,…..)Structures (CMB, Power Spectrum,…..)

Lambda CDM vs INuDE-ModelLambda CDM vs INuDE-Model DiscussionsDiscussions

Papers: YYK and K. Ichiki, JCAP 0806, 005, 2008;Papers: YYK and K. Ichiki, JCAP 0806, 005, 2008; JHEP 0806, 058, 2008;JHEP 0806, 058, 2008; arXiv:0803.3142, and in preparing arXiv:0803.3142, and in preparing for WMAP-7 year datafor WMAP-7 year data

References: References: Massive Neutrinos and Cosmology: J. Lesgourgues and S. Massive Neutrinos and Cosmology: J. Lesgourgues and S.

Pastor, Phys. Rep. 429:307(2006)Pastor, Phys. Rep. 429:307(2006)

Primordial Neutrinos Primordial Neutrinos in Astrophysicsin Astrophysics

The connection between cosmological The connection between cosmological observations and neutrino physics is one of observations and neutrino physics is one of the interesting and hot topic in astro-particle the 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.

What we know right Now:What we know right Now:

neutrinos have mass (NuOsc-exp.)neutrinos have mass (NuOsc-exp.)

the rough magnitude of the leptonic the rough magnitude of the leptonic mixing angles (two large and one mixing angles (two large and one relatively small angles)relatively small angles)

the masses of all three neutrino species the masses of all three neutrino species are very small compared with charged are very small compared with charged fermions fermions

What we donWhat we don’’t know:t know:

Are neutrinos their own anti-particles ?Are neutrinos their own anti-particles ?

( Dirac vs Majorana particles )( Dirac vs Majorana particles )

What is the absolute mass of neutrinos and What is the absolute mass of neutrinos and their mass ordering, i.e.their mass ordering, i.e.

(normal, inverted or quasi-degenerate ?)(normal, inverted or quasi-degenerate ?)

Is there CP violation in the leptonic sectorIs there CP violation in the leptonic sector ? ?

Neutrino Mass bound from Neutrino Mass bound from Large Scale Structures Large Scale Structures

(CMB, Power Spectrum,(CMB, Power Spectrum,……..)..)

Neutrino free-stream :Neutrino free-stream : If If is carried by free-moving relativistic particles, is carried by free-moving relativistic particles, we can discriminate between massless vs massive ,andwe can discriminate between massless vs massive ,and between free vs interacting neutrinos.between free vs interacting neutrinos.

Neutrino masses determine two-different things:Neutrino masses determine two-different things:

1) temperature at which neutrinos cease to be non-1) temperature at which neutrinos cease to be non-relativistic, which controls the length on which neutrinos relativistic, which controls the length on which neutrinos travel reducing clustering.travel reducing clustering.

2) the function of energy carried by neutrinos, which 2) the function of energy carried by neutrinos, which controlscontrols

how much neutrinos can smooth inhomogeneities.how much neutrinos can smooth inhomogeneities.

In standard cosmology:In standard cosmology:

CMB vs NCMB vs Nvv

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

M_nu

Nonlinear EffectsNonlinear Effects

Numerical Analysis

Cosmological parameters Omega_c : fraction of the dark-matter density Omega_b: fraction of the baryon matter

density Theta: the (approx) sound horizon to the

angular diameter distance tau: optical depth n_s : scale spectral index Ln[10^10 As] : primordial superhorizon power in the curvature perturbation on 0.05 Mpc^-1 scale

Experimental Obs.Experimental Obs.(WMAP)(WMAP)

2

2

28 2

si n( ) cos( )4 ( )[3 ]

( )M kr kr kr

dk k P kM kr

n_s: Spectral indextau: optical depth

sigma_8: rms fluctuation parameterA_s: the amp. of the primordial scalar

power spectrum

Within Standard Cosmology Model (LCDM)

What is the upper bound of neutrino masses beyond Lambda CDM Model ?

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.

Dynamical Dark-Energy Models

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

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

Energy Density vs scale factorEnergy Density vs scale factoryyk and ichiki, JHEP 0806,085 2008yyk and ichiki, JHEP 0806,085 2008

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

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

Joint 3-dimensional intercorrelations between Cosmological Joint 3-dimensional intercorrelations between Cosmological Parameters and Model ParametersParameters and Model Parameters

Summary: Neutrino Mass BoundsSummary: Neutrino Mass Boundsin Interacting Neutrino DE Modelin Interacting Neutrino DE Model

Without 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.)

We have weaker bounds in the interacting DE modelsWe have weaker bounds in the interacting DE models

Future Prospects from Astrophysical Observations

SummarySummary LCDM model provides LCDM model provides M_nu < 0.6-0.7 eV (LSS + CMB +BAO) M_nu < 0.6-0.7 eV (LSS + CMB +BAO) < 0.2-0.3 eV (including Lya data)< 0.2-0.3 eV (including Lya data)

Interacting Neutrino Dark-Energy Model Interacting Neutrino Dark-Energy Model provides more weaker bounds:provides more weaker bounds:

M_nu < 0.8-0.9 eV (LSS + CMB ) M_nu < 0.8-0.9 eV (LSS + CMB ) < 0.4-0.5 eV (including Lya data)< 0.4-0.5 eV (including Lya data) Lya-forest data includes the uncertainty Lya-forest data includes the uncertainty

fromfrom - continuum errors- continuum errors - unidentified metal lines- unidentified metal lines - noise- noise

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.

Thanks Thanks For For your your attention!attention!

Backup SlidesBackup Slides

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

Questions :Questions :

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.

Barger et al., M. Cirelli et al., 2005Barger et al., M. Cirelli et al., 2005

--- 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.

X.M. Zhang et al. yyK in preparingX.M. Zhang et al. yyK in preparing

How much this model can be constrained from, BBN, How much this model can be constrained from, BBN, CMB, Matter power spectrum observations ?CMB, Matter power spectrum observations ?

Ichiki and YYK, 2008, 2010Ichiki and YYK, 2008, 2010

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: