1. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, FranceTitle Georg Raffelt, Max-Planck-Institut für Physik, München 36th CAST Collaboration Meeting, 29-30 May 2008, Paris Update and interpretation of the axion hot dark matter limit

2. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, FranceMotivation Observations of the mass-density distribution in the universe provides very restrictive limits on a possible hot dark matter component Restrictive limits exist on neutrino masses (in the sub-eV range) Analogous arguments for hypothetical particles (e.g. axions) In principle relevant for CAST search (sub-eV to eV range) What are the particle-physics assumptions entering such limits? How reliable are the cosmological limits?

3. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France Limits from CAST-I and CAST-II CAST-I results: PRL 94:121301 (2005) and JCAP 0704 (2007) 010 CAST-II results (He-4 filling): preliminary

4. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France SDSS Survey

5. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France Structure Formation in the Universe SmoothStructured Structure forms by Structure forms by gravitational instability gravitational instability of primordial of primordial density fluctuations density fluctuations A fraction of hot dark matter A fraction of hot dark matter suppresses small-scale structure suppresses small-scale structure

6. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France What is wrong with neutrino dark matter? Galactic Phase Space (Tremaine-Gunn-Limit) m > 20 40 eV Maximum mass density of a degenerate Fermi gas m > 100 200 eV Spiral Spiral galaxies galaxies Dwarf Dwarf galaxies galaxies Nus are Hot Dark Matter Nus are Hot Dark Matter Ruled out Ruled out by structure formation by structure formation Neutrino Free Streaming (Collisionless Phase Mixing) At T < 1 MeV neutrino scattering in early universe ineffective At T < 1 MeV neutrino scattering in early universe ineffective Stream freely until non-relativistic Stream freely until non-relativistic Wash out density contrasts on small scales Wash out density contrasts on small scales NeutrinosNeutrinos Over-density

7. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France Structure Formation with Hot Dark Matter Troels Haugbølle, http://whome.phys.au.dk/~haugboel Neutrinos with m = 6.9 eV Standard CDM Model Structure fromation simulated with Gadget code Cube size 256 Mpc at zero redshift

8. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France Power Spectrum of Density Fluctuations Field of density fluctuations Fourier transform Power spectrum essentially square of Fourier transformation Power spectrum is Fourier transform of two-point correlation function (x=x 2 x 1 ) with the -function Gaussian random field (phases of Fourier modes k uncorrelated) is fully characterized by the power spectrum or equivalently by

9. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France Power Spectrum of Cosmic Density Fluctuations

10. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France Neutrino Free Streaming – Transfer Function Hannestad, Neutrinos in Cosmology, hep-ph/0404239 Transfer function P(k) = T(k) P 0 (k) P(k) = T(k) P 0 (k) Effect of neutrino free streaming on small scales T(k) = 1 8 / M T(k) = 1 8 / M valid for 8 / M 1 8 / M 1 Power suppression for FS 100 Mpc/h m = 0 m = 0.3 eV m = 1 eV

11. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France Lyman-alpha Forest Hydrogen clouds absorb from QSO Hydrogen clouds absorb from QSO continuum emission spectrum continuum emission spectrum Absorption dips at Ly- wavelengh Absorption dips at Ly- wavelengh corresponding to redshift corresponding to redshiftwww.astro.ucla.edu/~wright/Lyman-alpha-forest.html Examples for Lyman- forest in low- and high-redshift quasars http://www.astr.ua.edu/keel/agn/forest.gif

12. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France Some Recent Cosmological Limits on Neutrino Masses m /eV m /eV (limit 95%CL) Data / Priors Spergel et al. (WMAP) 2003 [astro-ph/0302209] [astro-ph/0302209]0.69 WMAP-1, 2dF, HST, 8 Hannestad 2003 [astro-ph/0303076] [astro-ph/0303076]1.01 WMAP-1, CMB, 2dF, HST Crotty et al. 2004 [hep-ph/0402049] [hep-ph/0402049]1.00.6 WMAP-1, CMB, 2dF, SDSS & HST, SN Hannestad 2004 [hep-ph/0409108] [hep-ph/0409108]0.65 WMAP-1, SDSS, SN Ia gold sample, Ly- data from Keck sample Seljak et al. 2004 [astro-ph/0407372] [astro-ph/0407372]0.42 WMAP-1, SDSS, Bias, Ly- data from SDSS sample Spergel et al. 2006 [hep-ph/0409108] [hep-ph/0409108]0.68 WMAP-3, SDSS, 2dF, SN Ia, 8 Seljak et al. 2006 [astro-ph/0604335] [astro-ph/0604335]0.14 WMAP-3, CMB-small, SDSS, 2dF, SN Ia, BAO (SDSS), Ly- (SDSS) Hannestad et al. 2006 [hep-ph/0409108] [hep-ph/0409108]0.30 WMAP-1, CMB-small, SDSS, 2dF, SN Ia, BAO (SDSS), Ly- (SDSS)

13. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France Weak Lensing A Powerful Probe for the Future UnlensedLensed Distortion of background images by foreground matter

14. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France Sensitivity Forecasts for Future LSS Observations Kaplinghat, Knox & Song, astro-ph/0303344 σ (m ν ) ~ 0.15 eV (Planck) σ (m ν ) ~ 0.044 eV (CMBpol) CMB lensing Lesgourgues, Pastor & Perotto, hep-ph/0403296 Planck & SDSS m > 0.21 eV detectable m > 0.21 eV detectable at 2 at 2 m > 0.13 eV detectable m > 0.13 eV detectable at 2 at 2 Ideal CMB & 40 x SDSS Abazajian & Dodelson astro-ph/0212216 Future weak lensing survey 4000 deg 2 σ (m ν ) ~ 0.1 eV Wang, Haiman, Hu, Khoury & May, astro-ph/0505390 Weak-lensing selected sample of > 10 5 clusters σ (m ν ) ~ 0.03 eV Hannestad, Tu & Wong astro-ph/0603019 Weak-lensing tomography (LSST plus Planck) σ (m ν ) ~ 0.05 eV

15. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France Low-Mass Particle Densities in the Universe Photons Neutrinos Axions (QCD) ALPs (two photon vertex) 410 cm 3 Cosmic microwave background radiation T = 2.725 K Freeze out at T ~ 2 MeV before e e annihilation 112 cm 3 ( in one flavor) For f a ~ 10 7 GeV (m a ~ 1 eV) Freeze out at T ~ 80 MeV ( a interaction) ~ 50 cm 3 Primakoff freeze out (g a ~ 10 10 GeV 1 ) T T QCD ~ 200 MeV < 10 cm 3 No useful hot dark matter limit on ALPs in the CAST search range No useful hot dark matter limit on ALPs in the CAST search range (too few of them today if they couple only by two-photon vertex) (too few of them today if they couple only by two-photon vertex) Axion mass limit comparable to limit on m Axion mass limit comparable to limit on m (Axion number density comparable to one neutrino flavor) (Axion number density comparable to one neutrino flavor)

16. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France Axion Hot Dark Matter from Thermalization after QCD Freeze-out temperature Cosmic thermal degrees of freedom at axion freeze-out Cosmic thermal degrees of freedoma Chang & Choi, PLB 316 (1993) 51 Hannestad, Mirizzi & Raffelt, JCAP 07 (2005) 02 10 4 10 5 10 6 10 7 10 4 10 5 10 6 10 7 f a (GeV)

17. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France Axion Hot Dark Matter Limits from Precision Data m a < 1.0 eV (95% CL) m a < 0.4 eV (95% CL) WMAP-5, LSS, BAO, SNIa WMAP-3, small-scale CMB, HST, BBN, LSS, Ly- HST, BBN, LSS, Ly- Hannestad, Mirizzi, Raffelt & Wong [arXiv:0803.1585] Melchiorri, Mena & Slosar [arXiv:0705.2695] Marginalizing over unknown neutrino hot dark matter component Credible regions for neutrino plus axion hot dark matter (WMAP-5, LSS, BAO, SNIa) Hannestad, Mirizzi, Raffelt & Wong [arXiv:0803.1585] Dashed (red) curves: Same with WMAP-3 From HMRW [arXiv:0706.4198]

18. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France Evolution of Axion Hot Dark Matter Limits m a < 1.0 eV (95% CL) m a < 0.4 eV (95% CL) WMAP-5, LSS, BAO, SNIa no Ly- no Ly- m marginalized m marginalized WMAP-3, small-scale CMB, HST, BBN, LSS, Ly- HST, BBN, LSS, Ly- m marginalized m marginalized Hannestad, Mirizzi, Raffelt & Wong [arXiv:0803.1585] Melchiorri, Mena & Slosar [arXiv:0705.2695] m a < 1.05 eV (95% CL) WMAP-1, LSS, HST, SNIa, Ly- m 2 statistics 2 statistics Hannestad, Mirizzi & Raffelt [hep-ph/0504059] m a < 1.2 eV (95% CL) WMAP-3, LSS, BAO, SNIa no Ly- no Ly- m marginalized m marginalized Hannestad, Mirizzi, Raffelt & Wong [arXiv:0706.4198] Including Ly-a together with WMAP-5 will likely worsen the limit of 0.4 eV Including Ly-a together with WMAP-5 will likely worsen the limit of 0.4 eV from WMAP-3 + Ly- from WMAP-3 + Ly- Has not been done, but for neutrinos this is expected Has not been done, but for neutrinos this is expected WMAP-5 and Ly- more consistent with each other WMAP-5 and Ly- more consistent with each other More consensus now that Ly- is dangerous More consensus now that Ly- is dangerous

19. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, FranceConclusion For general ALPs (only two-photon coupling) no competition with CAST Most aggressive limits (using Ly-a) at ~ 0.4 eV (95% CL) Probably large systematic uncertainties DO NOT STOP CAST NOW !!! Constraints can improve by better data (weak lensing) Eventual detection of hot dark matter component ? (neutrinos guaranteed at ~ 0.05 eV) If neutrino masses are detected in the laboratory (0 2, KATRIN) Less room for axions in the hot dark matter inventory Less room for axions in the hot dark matter inventory

20. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, FranceTitle CAST search and cosmological limits are nicely complementary! Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France