Yong-Yeon Keum NAOJ, Mitaka Japan KITPC, Beijing China TeVPA08, IHEP at Beijing

1. Neutrino Mass Boundsfrom beta decays and Cosmological Observations(LCDM vs Interacting Dark-Energy Model) Yong-Yeon Keum NAOJ, Mitaka Japan KITPC, Beijing China TeVPA08, IHEP at Beijing September 26, 2008

2. Primordial Neutrinos in Astrophysics • The connection between cosmological observations and neutrino physics is one of the interesting and hot topic in astro-particle physics. • Precision observations of the cosmic microwave background and large scale structure of galaxies can be used to prove neutrino mass with greater precision than current laboratory experiments.

3. Contents: • Neutrinoless Double beta Decays and Total Neutrino Mass bounds • Neutrino Mass bound from Large Scale Structures (CMB, Power Spectrum,…..) • Discussion Papers: YYK and K. Ichiki, JCAP 0806, 005, 2008; JHEP 0806, 058, 2008; arXiv:0803.3142 References: Massive Neutrinos and Cosmology: J. Lesgourgues and S. Pastor, Phys. Rep. 429:307(2006) Fundamentals of Neutrino Physics and Astrophysics: C. Giunti and C.W. Kim, Oxford University Press

4. Now we enter the era of Precision Neutrino Measurement Science (PMNS era).What do we hope to learn and which information is likely to teach us more about new physics than others. Four most useful items for probing new physics: • Search for neutrinoless double beta decays • Determined the sign of atmospheric mass difference square (neutrino mass hierarchy) • the magnitude of • establish or refute the existence of sterile neutrinos.

5. Neutrino Mixing Matrix

6. Neutrinoless Double Beta Decays Part I

7. Neutrinoless double-beta decay(A,Z)  (A,Z+2) + e- + e- (DL=2)-- the most senstive process to the total lepton number and small majorana neutrino masses

10. 0nbb-decay has not yet been seen experimentally. • The best result has been achieved in the Heidelberg-Moscow (HM) 76Ge experiment: T01/2 > 1.9 x 1025 years  |mbb| < 0.55 eV • Many future ambitious projects: CAMEO,CUORE,COBRA,EXO,GENIUS,MAJORANA, MOON,XMASS

11. Neutrioless Double-beta decay vs Neutrino Mass • Mass Ordering (for simplicity) • The rate of 0nbb decay depends on the mag. of the element of the neutrino mass matrix:

12. Bound of the total neutrino mass • Depends on two parameters; • the scale of atm. Neutrino Osci, (D) • the amplitude of solar Neutrino Osci. ( )

13. Total Nu-Mass vs Mee ( NH vs IH ) Inverse Hierarchy Normal Hierarchy Mee(eV)

14. Sensitivities of the future exps.

15. Mee vs lightest m Normal Hierarchy Inverse Hierarchy Bilenky at al. 2004

16. Tritium beta decays Most sensitive to the electron neutrino mass • Since tritium beta-decay has one of the smallest Q-values among all known beta decays: • Superallowed transition between mirror nuclei with a relatively short half-life time (~12.3 years)  An acceptable number of observed events • Atomic structure is less complicated, which leading to a more accurate calculation of atomic effects.

17. Kurie Function: • Mainz and Troitzk experiments: With neutrino mixing:

18. Summary of Part 1 • Tritium beta decay: Mainz and Troitsk Exp m1 < 2.2 eV • Future Exp. KATRIN: sensitivity m1 ~ 0.25 eV • If the 0nbb decay will not observed in future exp. and |mbb| < a few 10-2 eV ,  Massive neutrinos are either Dirac or Majorana particle, and normal hierarchy

19. The observationof the 0nbb decay with |mbb| > 4.5 10-2 eV will exclude normal hierarchy. • If the 0nbb decay will be observed and it will be an indication of the inverted hierarchy Remarks: It is really difficult to confirm the normal hierarchy in neutrinoless double beta decay.

20. Neutrino Mass bound from Large Scale Structures (CMB, Power Spectrum,…..)Part II

21. Dark Energy 73% (Cosmological Constant) Neutrinos 0.1-3% Ordinary Matter 4% (of this only about 10% luminous) Dark Matter 23% Title

22. The role played by neutrinos: Tdec ~ few me  dominant e-/e+  photons Tg = 2.73 K Tv = 1.96 K = 0.17 meV present neutrino number density: Since Tv is smaller than the neutrino mass scale, CMB neutrinos are today mostly non-relativisitic: Present data: H=100 h km/s Mpc with h=0.7

23. The total energy density in relativistic particles: T~0.3eV; with Nv = 3 (small corrections from the approximation Nv=3.04) • Measurements of CMB anisotropies allow to reconstruct Nv in two different ways: a) from the total energy density in relativisitic particles (rrad) significantly contributes to the measurable expansion rate around recombination b) the energy density in freely moving relativistic ptls (like neutrinos and unlike photons) can be reconstructed, they smooth out inhomogeneities (p= the fraction of freely moving neutrinos) • We remark that these cosmological data cannot measure the relative weight of each neutrino flavor, and cannot discriminate neutrinos from other speculative free-moving relativistic particles.

24. Neutrino free-stream : • If rn is carried by free-moving relativistic particles, we can discriminate between massless vs massive ,and between free vs interacting neutrinos. • Neutrino masses determine two-different things: 1) temperature at which neutrinos cease to be non-relativistic, which controls the length on which neutrinos travel reducing clustering. 2) the function of energy carried by neutrinos, which controls how much neutrinos can smooth inhomogeneities. • In standard cosmology:

25. CMB vs Nv

27. Large Scale Structures

28. Neutrino mass effects • After neutrinos decoupled from the thermal bath, they stream freely and their density pert. are damped on scale smaller than their free streaming scale. • The free streaming effect suppresses the power spectrum on scales smaller than the horizon when the neutrino become non-relativistic. • D Pm(k)/Pm(k) = -8 Ωn /Ωm • Analysis of CMB data are not sensitive to neutrino masses if neutrinos behave as massless particles at the epoch of last scattering. Neutrinos become non-relativistic before last scattering when Ωn h^2 > 0.017 (total nu. Masses > 1.6 eV). Therefore the dependence of the position of the first peak and the height of the first peak has a turning point at Ωn h^2 = 0.017.

29. Mass Power spectrum vs Neutrino Masses

31. Power spectrum Pm(k,z) = P*(k) T2(k,z) Transfer Function: T(z,k) := d(k,z)/[d(k,z=z*)D(z*)] Primordial matter power spectrum (Akn) z*:= a time long before the scale of interested have entered in the horizon Large scale: T ~ 1 Small scale : T ~ 0.1 DPm(k)/Pm(k) ~ -8 Ωn/Ωm = -8 fn M_nu

32. Numerical Analysis

33. 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

37. Within Standard Cosmology Model (LCDM)

39. Equation of State (EoS) W = p/r Dynamical Dark-Energy Models It is really difficult to find the origin of dark-energy with non-interacting dark-energy scenarios.

40. Summary of EoS • Canada-France-Hawaii Wide Synoptic Survey: wo < - 0.8 based on cosmic share data alone • Supernova Lagacy Survey (SNLS): Combined with SDSS measurement of BAO • WMAP3 data: 1) assume flat universe with SNLS data: 2) Drop prior of flat universe, WMAP+LSS+SNLS data:

41. Interacting Neutrino-Dark-Energy Model Interacting dark energy model Example At low energy, The condition of minimization of Vtot determines the physical neutrino mass. nv mv Scalar potential in vacuum

42. Theoretical issue: Adiabatic Instability problem: Afshordi et al. 2005 Gravitational collapse Kaplan, Nelson, Weiner 2004 Khoury et al. 2004 Zhao, Xia, X.M Zhang 2006 Always positive sound velocity No adiabatic instability Brookfield et al,. 2006 YYK and Ichiki, 2007, 2008

43. Background Equations: K. Ichiki and YYK:2007 Perturbation Equations: We consider the linear perturbation in the synchronous Gauge and the linear elements:

48. Energy Density vs scale factoryyk and ichiki, JHEP 0806,085 2008

49. The impact of Scattering term:

50. Varying Neutrino Mass With full consideration of Kinetic term V( f )=Vo exp[- lf] Mn=0.9 eV Mn=0.3 eV