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NEUTRINO MASS MEASUREMENTS FROM COSMOLOGY

NEUTRINO MASS MEASUREMENTS FROM COSMOLOGY. n e n m n t. STEEN HANNESTAD FERMILAB, 9 JULY 2009. Nuclear Reactors. . Sun. . Supernovae (Stellar Collapse). Particle Accelerators. . SN 1987A . Earth Atmosphere (Cosmic Rays). . Astrophysical

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NEUTRINO MASS MEASUREMENTS FROM COSMOLOGY

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  1. NEUTRINO MASS MEASUREMENTS FROM COSMOLOGY ne nm nt STEEN HANNESTAD FERMILAB, 9 JULY 2009

  2. Nuclear Reactors  Sun  Supernovae (Stellar Collapse) Particle Accelerators  SN 1987A Earth Atmosphere (Cosmic Rays)  Astrophysical Accelerators Soon ? Earth Crust (Natural Radioactivity) Big Bang (Today 330 n/cm3) Indirect Evidence Where do Neutrinos Appear in Nature? (2005)

  3. FLAVOUR STATES PROPAGATION STATES MIXING MATRIX (UNITARY) LATE-TIME COSMOLOGY IS (ALMOST) INSENSITIVE TO THE MIXING STRUCTURE q12 is the “solar’’ mixing angle q23 is the “atmospheric’’ mixing angle q13 d Dirac CP violating phase Possibly 2 additional Majorana phases

  4. If neutrino masses are hierarchical then oscillation experiments do not give information on the absolute value of neutrino masses ATMO. n K2K MINOS SOLAR n KAMLAND Normal hierarchy Inverted hierarchy However, if neutrino masses are degenerate no information can be gained from such experiments. Experiments which rely on either the kinematics of neutrino mass or the spin-flip in neutrinoless double beta decay are the most efficient for measuring m0

  5. HIERARCHICAL DEGENERATE INVERTED NORMAL LIGHTEST Lesgourgues and Pastor 2006

  6. Tritium decay endpoint measurements have provided limits on the electron neutrino mass Mainz experiment, final analysis (Kraus et al.) This translates into a limit on the sum of the three mass eigenstates

  7. KATRIN experiment Karlsruhe Tritium Neutrino Experiment at Forschungszentrum Karlsruhe Data taking starting early 2011 TLK 25 m

  8. A BIT OF COSMOLOGY

  9. Thermal evolution of standard, radiation dominated cosmology Total energy density

  10. In a radiation dominated universe the time-temperature relation is then of the form

  11. The number and energy density for a given species, X, is given by the Boltzmann equation Ce[f]: Elastic collisions, conserves particle number but energy exchange possible (e.g. ) [scattering equilibrium] Ci[f]: Inelastic collisions, changes particle number (e.g. ) [chemical equilibrium] Usually, Ce[f] >> Ci[f] so that one can assume that elastic scattering equilibrium always holds. If this is true, then the form of f is always Fermi-Dirac or Bose-Einstein, but with a possible chemical potential.

  12. Particle decoupling The inelastic reaction rate per particle for species X is In general, a species decouples from chemical equlibrium when

  13. The prime example is the decoupling of light neutrinos (m < TD) After neutrino decoupling electron-positron annihilation takes place (at T~me/3) Entropy is conserved because of equilibrium in the e+- e--g plasma and therefore The neutrino temperature is unchanged by this because they are decoupled and therefore

  14. Upper limit on the mass of light neutrinos: For light neutrinos, m << Tdec, the present day density is Assuming that the three active species have the same mass A conservative limit (Wnh2 < 0.1) on the neutrino mass is then For any of the three active neutrino species

  15. THE ABSOLUTE VALUES OF NEUTRINO MASSES FROM COSMOLOGY NEUTRINOS AFFECT STRUCTURE FORMATION BECAUSE THEY ARE A SOURCE OF DARK MATTER FROM HOWEVER, eV NEUTRINOS ARE DIFFERENT FROM CDM BECAUSE THEY FREE STREAM SCALES SMALLER THAN dFS DAMPED AWAY, LEADS TO SUPPRESSION OF POWER ON SMALL SCALES

  16. STRUCTURE FORMATION IN THE UNIVERSE

  17. GROWTH OF PERTURBATIONS, THE OLD JEANS ANALYSIS (APPLIES ALSO TO STAR FORMATION) CONTINUITY: EULER: POISSON: THESE EQUATIONS CAN BE LINEARIZED

  18. FROM THIS ASSUMPTION THE FOLLOWING EQUATIONS ARE DERIVED FOR THE FIRST ORDER TERMS FOR r THIS CAN BE COMBINED INTO A SINGLE SECOND ORDER DIFFERENTIAL EQUATION

  19. THIS IS RECOGNISEABLE AS A SIMPLE HARMONIC OSCILLATOR EQUATION (WAVE EQUATION), I.E. THE SOLUTIONS ARE DIVIDING WAVENUMBER (INVERSE LENGTH SCALE) IS CALLED THE JEANS’ WAVENUMBER

  20. THE NATURE OF MODES ON A GIVEN SCALE IS SIMPLY DETERMINED FROM THE RELATIVE STRENGTH OF GRAVITATIONAL AND PRESSURE FORCES NOW, WHAT HAPPENS IF THE UNIVERSE IS EXPANDING? EXACTLY THE SAME ANALYSIS CAN BE PERFORMED, WITH THE ONE EXCEPTION THAT THE UNPERTURBED SOLUTIONS ARE THEN

  21. THE CORRESPONDING EQUATIONS FOR THE FIRST ORDER QUANTITIES ARE THEN IT TURNS OUT THAT IN FOURIER SPACE THESE EQUATIONS ARE MUCH SIMPLER, SO ALL QUANTITIES SHOULD BE EXPANDED IN FOURIER MODES

  22. THE EQUATION FOR THE DENSITY PERTURBATION THEN BECOMES THIS IS EXACTLY THE SAME EQUATION AS IN THE NON-EXPANDING CASE, EXCEPT FOR THE SECOND TERM THE EXPANSION OF THE UNIVERSE ACTS LIKE A FRICTION FORCE EVEN IF THERE ARE GROWING MODES, THEY CANNOT BE EXPONENTIAL

  23. IN A FLAT MODEL WITH ONLY CDM THE EQUATION BECOMES WITH SOLUTIONS

  24. WHAT DOES THE PERTURBATION EQUATION LOOK LIKE FOR NEUTRINOS? THE PREVIOUS EQUATION WAS DERIVED ASSUMING A PERFECT FLUID, I.E. NO VISCOSITY BUT NEUTRINOS DO HAVE VISCOSITY BECAUSE OF FREE-STREAMING THE PERTURBATION EQUATION NOW HAS TO INCLUDE A VISCOUS TERM ACTUALLY, ONE HAS TO SOLVE THE UNDERLYING BOLTZMANN EQUATION TO GET THE CORRECT RESULT (E.G. MA & BERTSCHINGER 95)

  25. N-BODY SIMULATIONS OF LCDM WITH AND WITHOUT NEUTRINO MASS (768 Mpc3) – GADGET 2 256 Mpc T Haugboelle, University of Aarhus

  26. THE R.M.S. AMOUNT OF DENSITY FLUCTUATIONS IN THE UNIVERSE CAN BE WRITTEN AS THIS FLUCTUATION CAN BE DECOMPOSED NATURALLY IN FOURIER MODES WHERE IS CALLED THE POWER SPECTRUM (NORMALLY CALLED P(k)) IT IS THE FOURIER TRANSFORM OF THE TWO-POINT CORRELATION FUNCTION

  27. AVAILABLE COSMOLOGICAL DATA

  28. THE COSMIC MICROWAVE BACKGROUND

  29. WMAP-5 TEMPERATURE POWER SPECTRUM M NOLTA ET AL., arXiv:0803.0593

  30. LARGE SCALE STRUCTURE SURVEYS - 2dF AND SDSS

  31. SDSS SPECTRUM TEGMARK ET AL. 2006 astro-ph/0608632

  32. FINITE NEUTRINO MASSES SUPPRESS THE MATTER POWER SPECTRUM ON SCALES SMALLER THAN THE FREE-STREAMING LENGTH Sm = 0 eV P(k)/P(k,mn=0) Sm = 0.3 eV Sm = 1 eV

  33. Ly-a forest analysis • Raw data: quasar spectra remove data not tracing (quasi-linear) Lya absorption • Flux power spectrum PF(k) hydrodynamical simulations + assumptions on thermodynamics of IGM • Linear power spectrum P(k)

  34. Power Spectrum of Cosmic Density Fluctuations SDSS BAO FROM MAX TEGMARK

  35. NOW, WHAT ABOUT NEUTRINO PHYSICS?

  36. WHAT IS THE PRESENT BOUND ON THE NEUTRINO MASS? WMAP-5 ONLY ~ 1.3 eV WMAP + OTHER 0.67 eV Komatsu et al., arXiv:0803.0547

  37. HOW CAN THE BOUND BE AVOIDED? THERE IS A VERY STRONG DEGENERACY BETWEEN NEUTRINO MASS AND THE DARK ENERGY EQUATION OF STATE WHEN CMB, LSS AND SNI-A DATA IS USED. THIS SIGNIFICANTLY RELAXES THE COSMOLOGICAL BOUND ON NEUTRINO MASS IF A LARGE NEUTRINO MASS IS MEASURED EXPERIMENTALLY THIS SEEMS TO POINT TO w < -1 STH, ASTRO-PH/0505551 (PRL) DE LA MACORRA ET AL. ASTRO-PH/0608351

  38. HOW CAN THE BOUND BE STRENGTHENED? MAKING THE BOUND SIGNIFICANTLY STRONGER REQUIRES THE USE OF OTHER DATA: ADDITIONAL DATA TO BREAK THE Wm, w, h DEGENERACY THE BARYON ACOUSTIC PEAK H(z) MEASUREMENTS OR FIXING THE SMALL SCALE AMPLITUDE LYMAN – ALPHA DATA

  39. 10 FREE PARAMETERS 10 FREE PARAMETERS WMAP, BOOMERANG, CBI SDSS, 2dF SNLS SNI-A WMAP, BOOMERANG, CBI SDSS, 2dF SNLS SNI-A, SDSS BARYONS JUST ONE EXAMPLE: GOOBAR, HANNESTAD, MÖRTSELL, TU (astro-ph/0602155, JCAP) USING THE BAO DATA THE BOUND IS STRENGTHENED, EVEN FOR VERY GENERAL MODELS BAO BAO+ LY-a LY-a No BAO 12 FREE PARAMETERS WMAP-3, BOOMERANG, CBI SDSS, 2dF, HST SNLS SNI-A, SDSS BARYONS IN MORE RESTRICTED MODELS THE BOUND IS STRONGER (BUT BEWARE OF THE PARAMETER DEGENERACIES)

  40. THE NEUTRINO MASS FROM COSMOLOGY PLOT More data +Ly-alpha ~ 0.2 eV 0.2-0.3 eV 0.2-0.3 eV + SNI-a +WL ~ 0.5 eV 0.5-0.6 eV 0.5-0.6 eV + SDSS 0.7 eV ~ 1 eV 1-2 eV CMB only 1.3 eV ~ 2 eV 2.? eV ??? eV Minimal LCDM +Nn +w+…… Larger model space

  41. WHAT IS IN STORE FOR THE FUTURE? BETTER CMB TEMPERATURE AND POLARIZATION MEASUREMENTS (PLANCK, to be launched 29/4) LARGE SCALE STRUCTURE SURVEYS AT HIGH REDSHIFT MEASUREMENTS OF WEAK GRAVITATIONAL LENSING ON LARGE SCALES

  42. WEAK LENSING – A POWERFUL PROBE FOR THE FUTURE Distortion of background images by foreground matter Unlensed Lensed

  43. FROM A WEAK LENSING SURVEY THE ANGULAR POWER SPECTRUM CAN BE CONSTRUCTED, JUST LIKE IN THE CASE OF CMB MATTER POWER SPECTRUM (NON-LINEAR) WEIGHT FUNCTION DESCRIBING LENSING PROBABILITY (SEE FOR INSTANCE JAIN & SELJAK ’96, ABAZAJIAN & DODELSON ’03, SIMPSON & BRIDLE ’04)

  44. STH, TU, WONG 2006

  45. THE SENSITIVITY TO NEUTRINO MASS WILL IMPROVE TO < 0.1 eV AT 95% C.L. USING WEAK LENSING COULD POSSIBLY BE IMPROVED EVEN FURTHER USING FUTURE LARGE SCALE STRUCTURE SURVEYS STH, TU & WONG 2006 (ASTRO-PH/0603019, JCAP)

  46. WHY IS WEAK LENSING TOMOGRAPHY SO GOOD? IF MEASURED AT ONLY ONE REDSHIFT THE NEUTRINO SIGNAL IS DEGENERATE WITH OTHER PARAMETERS CHANGING DARK ENERGY EQUATION OF STATE INITIAL CONDITIONS WITH BROKEN SCALE INVARIANCE HOWEVER, BY MEASURING AT DIFFERENT REDSHIFTS THIS DEGENERACY CAN BE BROKEN

  47. ADVANTAGES OF PROBING STRUCTURE AT HIGH REDSHIFT STRUCTURES ARE MORE LINEAR VOLUME IS LARGER (THE HORIZON VOLUME IS ~ 1000 TIMES LARGER THAN THE SDSS-LRG VOLUME) HOW TO DO IT? LYMAN-ALPHA? BAO? (WFMOS) GALAXIES? (LSST) 21-CM? (SKA)

  48. z~1100 z~5 z~0.35

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