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

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

TitleTitle

Georg Raffelt, Max-Planck-Institut für Physik, Georg Raffelt, Max-Planck-Institut für Physik, MünchenMünchen

36th CAST Collaboration Meeting, 29-30 May 2008, Paris36th CAST Collaboration Meeting, 29-30 May 2008, Paris

Update and interpretation of theUpdate and interpretation of theaxion hot dark matter limitaxion hot dark matter limit


MotivationMotivation

Observations of the mass-density distribution in the universeObservations of the mass-density distribution in the universeprovides very restrictive limits on a possible hot dark matterprovides very restrictive limits on a possible hot dark mattercomponent component

Restrictive limits exist on neutrino masses (in the sub-eV range) Restrictive limits exist on neutrino masses (in the sub-eV range)

Analogous arguments for hypothetical particles (e.g. axions)Analogous arguments for hypothetical particles (e.g. axions)In principle relevant for CAST search (sub-eV to eV range)In principle relevant for CAST search (sub-eV to eV range)

What are the particle-physics assumptions entering such limits?What are the particle-physics assumptions entering such limits?

How reliable are the cosmological limits?How reliable are the cosmological limits?


Limits from CAST-I and CAST-IILimits from CAST-I and CAST-II

CAST-I results: PRL 94:121301 (2005) and JCAP 0704 (2007) 010 CAST-I results: PRL 94:121301 (2005) and JCAP 0704 (2007) 010 CAST-II results (He-4 filling): preliminaryCAST-II results (He-4 filling): preliminary


SDSS SurveySDSS Survey


Structure Formation in the UniverseStructure Formation in the Universe

SmoothSmooth StructuredStructured

Structure forms byStructure forms by gravitational instabilitygravitational instability of primordialof primordial density fluctuationsdensity fluctuations

A fraction of hot dark matter A fraction of hot dark matter suppresses small-scale structuresuppresses small-scale structure


What is wrong with neutrino dark matter?What is wrong with neutrino dark matter?

Galactic Phase Space (“Tremaine-Gunn-Limit”)Galactic Phase Space (“Tremaine-Gunn-Limit”)

mm >> 20 20 40 eV 40 eV

2

3escape

n

2

3max

max3

)vm(m

3

pm

max

2

3escape

n

2

3max

max3

)vm(m

3

pm

max

Maximum mass density of a degenerateMaximum mass density of a degenerateFermi gasFermi gas

mm >> 100 100 200 eV 200 eV

SpiralSpiral galaxiesgalaxies

DwarfDwarf galaxiesgalaxies

• Nus are “Hot Dark Matter”Nus are “Hot Dark Matter”• Ruled out Ruled out by structure formationby structure formation

Neutrino Free Streaming (Collisionless Phase Mixing)Neutrino Free Streaming (Collisionless Phase Mixing)

• AtAt TT << 11 MeVMeV neutrinoneutrino scatteringscattering inin earlyearly universeuniverse ineffectiveineffective• Stream freely until non-relativisticStream freely until non-relativistic• Wash out density contrasts on small scales Wash out density contrasts on small scales

NeutrinosNeutrinosNeutrinosNeutrinos

Over-densityOver-density


Structure Formation with Hot Dark MatterStructure Formation with Hot Dark Matter

Troels Haugbølle, http://whome.phys.au.dk/~haugboelTroels Haugbølle, http://whome.phys.au.dk/~haugboel

Neutrinos with Neutrinos with mm = 6.9 eV = 6.9 eVStandard Standard CDM ModelCDM Model

Structure fromation simulated with Gadget codeStructure fromation simulated with Gadget codeCube size 256 Mpc at zero redshiftCube size 256 Mpc at zero redshift


Power Spectrum of Density FluctuationsPower Spectrum of Density Fluctuations

Field of density fluctuationsField of density fluctuations

)x(

)x(

)x()x(

Fourier transformFourier transform

)x(exd xik3k )x(exd xik3k

Power spectrum essentially squarePower spectrum essentially squareof Fourier transformationof Fourier transformation

)k(Pkkˆ2 3kk )k(Pkkˆ2 3kk

Power spectrum is Fourier transform ofPower spectrum is Fourier transform oftwo-point correlation function (two-point correlation function (x=xx=x22xx11) )

)k(Pe

2

kd)x()x()x( xik

3

3

12

)k(Pe

2

kd)x()x()x( xik

3

3

12

)k(

2

3xik

2

2

)k(Pke

kdk

4d

)k(

2

3xik

2

2

)k(Pke

kdk

4d

with the with the -function-function

Gaussian random field (phases ofGaussian random field (phases ofFourier modes Fourier modes kk uncorrelated) is fully uncorrelated) is fully

characterized by the power spectrumcharacterized by the power spectrum2

k)k(P 2k)k(P

or equivalently byor equivalently by

2k

2

)k(Pk)k( k

2321

2

3

2k

2

)k(Pk)k( k

2321

2

3


Power Spectrum of Cosmic Density Power Spectrum of Cosmic Density FluctuationsFluctuations


Neutrino Free Streaming – Transfer FunctionNeutrino Free Streaming – Transfer Function

Hannestad, Neutrinos in Cosmology, hep-ph/0404239Hannestad, Neutrinos in Cosmology, hep-ph/0404239

Transfer functionTransfer function

P(k) = T(k) PP(k) = T(k) P00(k)(k)

Effect of neutrino freeEffect of neutrino freestreaming on small scalesstreaming on small scales

T(k) = 1 T(k) = 1 8 8//M M

valid forvalid for

88//M M ≪ ≪ 11

Power suppression for Power suppression for FSFS ≳ ≳ 100 Mpc/h100 Mpc/h

mm = 0 = 0

mm = 0.3 eV = 0.3 eV

mm = 1 eV = 1 eV


Lyman-alpha ForestLyman-alpha Forest

• Hydrogen clouds absorb from QSOHydrogen clouds absorb from QSO continuum emission spectrumcontinuum emission spectrum

• Absorption dips at Ly-Absorption dips at Ly- wavelengh wavelengh corresponding to redshiftcorresponding to redshift

www.astro.ucla.edu/~wright/Lyman-alpha-forest.htmlwww.astro.ucla.edu/~wright/Lyman-alpha-forest.html

Examples for Lyman-Examples for Lyman- forest in forest inlow- and high-redshift quasarslow- and high-redshift quasars

http://www.astr.ua.edu/keel/agn/forest.gifhttp://www.astr.ua.edu/keel/agn/forest.gif


Some Recent Cosmological Limits on Neutrino Some Recent Cosmological Limits on Neutrino MassesMassesmm/eV/eV(limit 95%CL)(limit 95%CL)

Data / PriorsData / Priors

Spergel et al. (WMAP) 2003Spergel et al. (WMAP) 2003 [astro-ph/0302209] [astro-ph/0302209] 0.690.69 WMAP-1, 2dF, HST, WMAP-1, 2dF, HST, 88

Hannestad 2003Hannestad 2003 [astro-ph/0303076][astro-ph/0303076]1.011.01 WMAP-1, CMB, 2dF, HSTWMAP-1, CMB, 2dF, HST

Crotty et al. 2004Crotty et al. 2004 [hep-ph/0402049][hep-ph/0402049]

1.01.00.60.6

WMAP-1, CMB, 2dF, SDSSWMAP-1, CMB, 2dF, SDSS& HST, SN& HST, SN

Hannestad 2004Hannestad 2004 [hep-ph/0409108][hep-ph/0409108] 0.650.65 WMAP-1, SDSS, SN Ia gold sample,WMAP-1, SDSS, SN Ia gold sample,

Ly-Ly- data from Keck sample data from Keck sample

Seljak et al. 2004Seljak et al. 2004 [[astro-ph/0407372]astro-ph/0407372]0.420.42 WMAP-1, SDSS, Bias,WMAP-1, SDSS, Bias,

Ly-Ly- data from SDSS sample data from SDSS sample

Spergel et al. 2006Spergel et al. 2006 [hep-ph/0409108][hep-ph/0409108] 0.680.68 WMAP-3, SDSS, 2dF, SN Ia, WMAP-3, SDSS, 2dF, SN Ia, 88

Seljak et al. 2006Seljak et al. 2006 [astro-ph/0604335][astro-ph/0604335]0.140.14 WMAP-3, CMB-small, SDSS, 2dF,WMAP-3, CMB-small, SDSS, 2dF,

SN Ia, BAO (SDSS), SN Ia, BAO (SDSS), Ly-Ly- (SDSS) (SDSS)

Hannestad et al. 2006Hannestad et al. 2006 [hep-ph/0409108][hep-ph/0409108] 0.300.30 WMAP-1, CMB-small, SDSS, 2dF,WMAP-1, CMB-small, SDSS, 2dF,

SN Ia, BAO (SDSS), SN Ia, BAO (SDSS), Ly-Ly- (SDSS) (SDSS)


Weak Lensing Weak Lensing A Powerful Probe for the Future A Powerful Probe for the Future

UnlensedUnlensed LensedLensed

Distortion of background images by foreground matterDistortion of background images by foreground matter


Sensitivity Forecasts for Future LSS Sensitivity Forecasts for Future LSS ObservationsObservations

Kaplinghat, Knox & Song,Kaplinghat, Knox & Song,astro-ph/0303344astro-ph/0303344

σσ(m(mνν) ~ 0.15 eV ) ~ 0.15 eV (Planck)(Planck)

σσ(m(mνν) ~ 0.044 eV (CMBpol)) ~ 0.044 eV (CMBpol)CMB lensing CMB lensing

Lesgourgues, PastorLesgourgues, Pastor& Perotto,& Perotto,hep-ph/0403296 hep-ph/0403296

Planck & SDSS Planck & SDSS mm > 0.21 eV detectable > 0.21 eV detectable

at 2at 2

mm > 0.13 eV detectable > 0.13 eV detectable

at 2at 2Ideal CMB & 40 x SDSS Ideal CMB & 40 x SDSS

Abazajian & DodelsonAbazajian & Dodelsonastro-ph/0212216astro-ph/0212216

Future weak lensingFuture weak lensingsurvey 4000 degsurvey 4000 deg22

σσ(m(mνν) ~ 0.1 eV) ~ 0.1 eV

Wang, Haiman, Hu, Wang, Haiman, Hu, Khoury & May,Khoury & May,astro-ph/0505390astro-ph/0505390

Weak-lensing selectedWeak-lensing selectedsample of > 10sample of > 105 5 clustersclusters

σσ(m(mνν) ~ 0.03 eV) ~ 0.03 eV

Hannestad, Tu & WongHannestad, Tu & Wongastro-ph/0603019astro-ph/0603019

Weak-lensing tomographyWeak-lensing tomography(LSST plus Planck)(LSST plus Planck) σσ(m(mνν) ~ 0.05 eV) ~ 0.05 eV


Low-Mass Particle Densities in the UniverseLow-Mass Particle Densities in the Universe

PhotonsPhotons

NeutrinosNeutrinos

Axions (QCD)Axions (QCD)

ALPsALPs(two photon vertex)(two photon vertex)

410 cm410 cm33Cosmic microwave backgroundCosmic microwave backgroundradiation radiation T = 2.725 KT = 2.725 K

Freeze out at Freeze out at T ~ 2 MeVT ~ 2 MeVbefore ebefore eee annihilation annihilation

nn 113 nn 113

112 cm112 cm33 ( in one flavor)( in one flavor)

For fFor faa ~ 10 ~ 1077 GeV (m GeV (maa ~ 1 eV) ~ 1 eV)

Freeze out at Freeze out at T ~ 80 MeVT ~ 80 MeV((a interaction)a interaction)

~ 50 cm~ 50 cm33

Primakoff freeze outPrimakoff freeze out

(g(gaa ~ 10 ~ 101010 GeV GeV11))

T T ≫≫ T TQCDQCD ~ 200 MeV ~ 200 MeV< 10 cm< 10 cm33

• No useful hot dark matter limit on ALPs in the CAST search rangeNo 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 Axion mass limit comparable to limit on mm

(Axion number density comparable to one neutrino flavor)(Axion number density comparable to one neutrino flavor)


Axion Hot Dark Matter from Thermalization Axion Hot Dark Matter from Thermalization after after QCDQCD

Freeze-out temperatureFreeze-out temperature

Cosmic thermal degrees ofCosmic thermal degrees offreedom at axion freeze-outfreedom at axion freeze-out

Cosmic thermal degrees ofCosmic thermal degrees offreedom freedom

a)2

(ff

CL

0

00

a

aa

a)2

(ff

CL

0

00

a

aa

aa

Chang & Choi, PLB 316 (1993) 51Chang & Choi, PLB 316 (1993) 51Hannestad, Mirizzi & Raffelt, JCAP 07 (2005) 02Hannestad, Mirizzi & Raffelt, JCAP 07 (2005) 02

094.0)z1(3

z1Ca

094.0)z1(3

z1Ca

104 105 106 107

104 105 106 107

fa (GeV)

fa (GeV)


Axion Hot Dark Matter Limits from Precision Axion Hot Dark Matter Limits from Precision DataData

mmaa < 1.0 eV (95% CL) < 1.0 eV (95% CL)

mmaa < 0.4 eV (95% CL) < 0.4 eV (95% CL)

WMAP-5, LSS, BAO, SNIaWMAP-5, LSS, BAO, SNIa

WMAP-3, small-scale CMB,WMAP-3, small-scale CMB,HST, BBN, LSS, HST, BBN, LSS, Ly-Ly-

Hannestad, Mirizzi, RaffeltHannestad, Mirizzi, Raffelt& Wong [arXiv:0803.1585]& Wong [arXiv:0803.1585]

Melchiorri, Mena & SlosarMelchiorri, Mena & Slosar[arXiv:0705.2695] [arXiv:0705.2695]

Marginalizing over unknown neutrino hot dark matter componentMarginalizing over unknown neutrino hot dark matter component

Credible regions for neutrino plus axion hotCredible regions for neutrino plus axion hotdark matter (WMAP-5, LSS, BAO, SNIa)dark matter (WMAP-5, LSS, BAO, SNIa)Hannestad, Mirizzi, Raffelt & WongHannestad, Mirizzi, Raffelt & Wong[arXiv:0803.1585][arXiv:0803.1585]

Dashed (red) curves: Same with WMAP-3Dashed (red) curves: Same with WMAP-3From HMRW [arXiv:0706.4198] From HMRW [arXiv:0706.4198]


Evolution of Axion Hot Dark Matter LimitsEvolution of Axion Hot Dark Matter Limits

mmaa < 1.0 eV (95% CL) < 1.0 eV (95% CL)

mmaa < 0.4 eV (95% CL) < 0.4 eV (95% CL)

WMAP-5WMAP-5, LSS, BAO, SNIa, LSS, BAO, SNIano Ly-no Ly-

mmmarginalizedmarginalized

WMAP-3WMAP-3, small-scale CMB,, small-scale CMB,HST, BBN, LSS, HST, BBN, LSS, Ly-Ly-



Melchiorri, Mena & SlosarMelchiorri, Mena & Slosar[arXiv:0705.2695] [arXiv:0705.2695]

mmaa < 1.05 eV (95% CL) < 1.05 eV (95% CL)

WMAP-1WMAP-1, LSS, HST, SNIa,, LSS, HST, SNIa,

Ly-Ly-mm

22 statisticsstatistics

Hannestad, Mirizzi & RaffeltHannestad, Mirizzi & Raffelt[hep-ph/0504059][hep-ph/0504059]

mmaa < 1.2 eV (95% CL) < 1.2 eV (95% CL)

WMAP-3WMAP-3, LSS, BAO, SNIa, LSS, BAO, SNIano Ly-no Ly-



• Including Ly-a together with WMAP-5 will likely worsen the limit of 0.4 eVIncluding 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 expectedHas not been done, but for neutrinos this is expected• WMAP-5 and Ly-WMAP-5 and Ly- more consistent with each other more consistent with each other• More consensus now that Ly-More consensus now that Ly- is dangerous is dangerous


ConclusionConclusion

For general ALPs (only two-photon coupling)For general ALPs (only two-photon coupling)no “competition” with CAST no “competition” with CAST

Most “aggressive” limits (using Ly-a) at ~ 0.4 eV (95Most “aggressive” limits (using Ly-a) at ~ 0.4 eV (95%% CL) CL)Probably large systematic uncertaintiesProbably large systematic uncertaintiesDO NOT STOP CAST NOW !!!DO NOT STOP CAST NOW !!!

Constraints can improve by better data (weak lensing)Constraints can improve by better data (weak lensing)Eventual detection of hot dark matter component ?Eventual detection of hot dark matter component ?(neutrinos guaranteed at ~ 0.05 eV)(neutrinos guaranteed at ~ 0.05 eV)

If neutrino masses are detected in the laboratory (0If neutrino masses are detected in the laboratory (022, KATRIN), KATRIN) Less room for axions in the hot dark matter inventoryLess room for axions in the hot dark matter inventory


TitleTitleCAST search and cosmological limitsCAST search and cosmological limits

are nicely complementary!are nicely complementary!


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

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