Absolute Neutrino Mass from Cosmology

Manoj KaplinghatUC Davis

Kinematic Constraints on Neutrino Mass

n Tritium decay

(Mainz Collaboration, Bloom et al, Nucl. Phys. B91, 273, 2001)

n p and t decay

Future of Laboratory Constraints

n Kinematic: KATRINn Aim: mne < 0.35 eV at 95% CL.

n Double beta decay:n Proposed reach 0.05 eVn Typical sources ~ 1 tonn Issues: Background and theoretical uncertaintiesn Many proposals: CUORE, EXO, GENIUS, MAJORANA, MOON, …n Double beta decay experiments only probe majorana mass terms

Neutrino Oscillation Summary

n Super-Kamiokande, K2Kn Atmospheric nm oscillationsn dm2 ~ (0.07 eV)2

n Mixing ~ Maximal

n SNO, Kamlandn Solar ne oscillationsn dm2 ~ (0.007 eV)2

n Mixing ~ Large

n LSND ?, MiniBoonen Electron anti-neutrino appearancen dm2 ~ 0.1 – 1 eV2

n Mixing ~ Smalln If LSND is right, a fourth sterile neutrino is required. This is probably

not populated in cosmologically relevant amounts.

Mass Schemes and 50 milli-eV

LSND

Atm

Sol Sol

Atm

LSND

3+1 2+2

At least one active neutrino with mass greater than ~ 0.05 eV

We can probe this regime in the lab and the cosmos.

At least one active neutrino with mass greater than ~ 0.3 eV

Massive Neutrinos and Cosmology: Outline

Early Phase

BBN

Primary CMB

Galaxies

Lensing

Lensed CMB

Galaxy Shear

Neutrinos and Big Bang Nucleosynthesis

Increase Nn

Speed-up Expansion rate

Larger n/p

4He and D/H increase

1.7 < Nn < 3.5 (95%) ) sterile n (if it exists) must not thermalize.

Both 2+2 and 3+1 schemes disfavored.K. N. Abazajian, Astropart. Phys. 19 (2003) 303

Massive Neutrino and Primary CMB

Expansion rate at early times smaller. Angle subtended by sound horizon at LSS larger. Peaks move to the left.

Damping length increases less than sound horizon and hence the effective damping is smaller. Peaks have more power.

Presence of a not quite non-relativistic neutrino at LSS causes gravitational potential decay boosting the first peak height.

Massive Neutrino and Matter Power Spectrum

kJ(EQ)

kJ(now)

H0

Jeans Instability for Neutrinos

Neutrino perturbations on length scales larger thanthe Jeans length become unstable and collapse intodark matter potential wells.

Neutrino Mass from Galaxies

n The matter power spectrum measured using galaxy surveys can beused together with CMB experiments to determine the neutrinomass. Sloan Digital Sky Survey and WMAP together can measurethe neutrino mass at 2s if

where N is the number of neutrinos with degenerate mass mn.Hu, Eisenstein and Tegmark, PRL 80 (1998) 5255

WMAP Limit on Neutrino Mass

n WMAP team put a stringent bound on the sum of the neutrinomasses. The combination of WMAP, CBI, ACBAR (CMB experiments)and 2dFGRS (galaxy survey) yields at 95% CL

n For a single massive neutrino this implies

n For three degenerate massive neutrinos this implies

A Preference for Non-Zero Neutrino Mass

n Allen, Schmidt and Bridle, MNRAS, 2003 combined CMB, 2dF, Gasfraction in X-ray clusters and X-ray cluster luminosity functionmeasurements. The data prefer a non-zero neutrino mass at the2s level.

n The likely value for the sum of neutrino masses from the analysisof Allen, Schmidt and Bridle is 0.6 eV or 0.2 eV for threedegenerate neutrinos.

Future

Early Phase

BBN

Primary CMB

Galaxies

Lensing

Lensed CMB

Galaxy Shear

Lensing of the CMB

n Lensing softens the exponential drop-off of primary CMB signaldue to Silk damping. Mixes E and B mode polarization.

n Lensing potential

n Lensing potential can probe fundamental physics.

Hu and Okamoto, ApJ 574, 566 (2002)

Zaldarriaga and Seljak 1998

Coherence of Lensing Deflection

Coherence ~ 10 degreesPeak sensitivity ~ z=2

Method

n Fisher Matrix approach. Unlensed temperature and polarizationspectra. Lensing information added through the power spectrum ofthe deflection angle (lensing potential).

n Important to choose parameter set carefully.

Jungman, Kamionkowski, Kosowksy and Spergel, PRD 54, 1332 (1996)Eisenstein, Hu and Tegmark, ApJ 518, 2 (1999)Efstathiou and Bond, MNRAS 304, 75 (1999)Hu, Fukugita, Zaldarriaga and Tegmark, ApJ 549, 669 (2001)Kosowsky, Milosavljevic and Jimenez, PRD 66, 63007 (2002)

Experiments

n Planckn 100, 143 and 217 GHz channels.n For a single massive neutrino

n CMBpoln 1 mK per pixel.

n Angular resolution 3 arcminutes.n One channel at 217 GHz.n Full Sky.n For a single massive neutrino

Fundamental Physics with Future CMB Data Alone

Of Direct Relevance to Inflation:n Gravity waves from Inflation.n Precision measure of the amplitude of the scalar perturbations to

1%.n Tilt and its variation with scale. Vital for differentiating between

models of inflation.

Others:n Detect the acceleration of the universe at 3s independent of

supernova Ia observations.n Map reionization history.

Kaplinghat, Knox and Song, 2003

Galaxy Lensing Tomography

n Weak lensing distorts the shape of galaxies. This distortion ismeasurable when averaged over a large number of galaxies.

n The distortion (shear) depends on the projected mass densityalong the photon’s geodesic.

n Look at the shear of galaxies in specific redshift bins. This providesthe redshift evolution of the projected mass density.

Hu ApJ, 522, 21 (1999)Hu and Keeton, PRD 66, 063506 (2002)Hu, PRD 66, 083515 (2002)

Prospects

n The projected mass density depends (among other things) on darkenergy and neutrino mass.

n In order to extract the neutrino mass, the power spectrum at earlytimes (LSS) has to be well constrained.

n With a deep survey over 10% of the sky, it is possible to constrainthe mass of a single massive neutrino with a precision of

n Lensing tomography also provides an independent test of theacceleration of the universe

Abazajian and Dodelson, PRL, 2003

Summary

It is possible to measure the absolute neutrino mass with an accuracy of 0.05 eV with different techniques.

Cosmological probes: Lensing of the CMB and galaxies.

Laboratory: Double beta decay experiments.