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Massive'neutrinos'and'the' Tension Massive'neutrinos'and'the' CMB vstension'between'CMB'&'LSS'' LSS: Is there a tension? AdamRichard'Ba8ye'' Moss UniversityJodrell'Bank'Centre'for'Astrophysics' of Nottingham In'collaboraAon'with'Adam'Moss,'Tom'Charnock,'Anna'Bonaldi,' In collaborationSam'Cusworth,'Sco8'Kay'&'the''Planck'CollaboraAon' with Richard Battye and Tom Charnock Sunday, 23 March 14 Planck'CollaboraAon,'2013' Constraints'from'SZ+priorsConstraintsSZ ' Clusters SZ+HST SZ+BAO 1Jb=0.8' ► Planck SZ (see talk by Anna Bonaldi) found ~1/2 the number of clusters predicted by Planck CMB cosmology ► Main uncertainty is thedegeneracy mass bias b - parameterizes extent in which σ (⌦ /0.29)0.32 X ray observations don’t8 m measure true mass ► Will consider fixed 1-b = 0.8, and 1-b = [0.7, 1.0] Planck'CollaboraAon,'2013' Comparison'with'CMB' ► Implication for fixed bias 1 b =0.59 0.05 0.9 − ± ns, Ωb, Y*, α, S marginalised0.3 over [+BBN prior & (1-b)=0.8] TT'from'Planck'+'WP' Ωm 0.88 M. Douspis, 03/04/2013, Cosmology fromσ8 Planck SZ cluster counts =0.782 0.010 9 !0.27" ± 0.86 0.84 Low'compared'' 0.82 to'expectaAons'' ► Discrepant with Planck 8 0.8 from'XJrays' CMB only at ~3σ 0.78 0.76 ► Or the mass bias is 1-b 0.74 ~0.6 0.72 0.7 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.4 0.5 0.6 0.7 0.8 m 1−b Sunday, 23 March 14 5 −4 We compute the usual CMB observables: the CMB 10 10 c2 = 1 temperature and polarization angular power spectra, as s φφ c2 = 10−4 φφ well as the lensing potential power spectrum, C` .We ! s −6 C 4 + 5 ! also compute the galaxy lensing convergence power spec- ξ 10 7 trum, Pij(`), which in the absence of anisotropic stress 10 can be written in terms of the matter power spectrum, −8 0 P (k, z). However, since our models include anisotropic 10 0 2 stress, we use the more general form of the convergence 10 10 0 500 1000 θ [arcmin] ! power spectrum 5 (a) TDI (g)models L 4 2 −4 We compute the usual CMB observables: the CMB` 8⇡ 10dχ 10 2 −4 Pij(`) gi (χ) gj (χ) P (`/fK (χ), χ) ,(22) c = 1 10 10 temperature and polarization angular power spectra,⇡ as 4 `3 χ s = 1 φφ Z 2 c2 = 10−4 1 Galaxy Lensing φφ well as the lensing potential power spectrum, C` .We ! s = 1.5 C 1 φφ −6 ! 4 where we have made+ use of the Limber approximation,5 ! C also compute the galaxy lensing0.59 convergence power spec- ξ 10 7 −6 4 ing and the constraint of σ (⌦ /0.27) =0.79 0.03 + 5 8 m ! ξ 10 7 f (χ) is the angular diameter distance, and10 P is the from thetrum, CFHTLenSPij(`), are which both symptoms in the absence of this tension.of± anisotropicK stress 10 A simple► Usecan illustration be data written from of in this terms CFHTLenS, point of is the to just matter compare154 power squarepower spectrum, degrees spectrum of the Weyl potential, defined in terms of −8 0 P (k, z). However, since our models include anisotropicthe Newtonian potentials10 φ and by =( + φ ) /2. For the expected lensing spectra for the best fitting mod- 0 2 −8 0 ► 10 10 0 500 101000 els to Planck2Dstress, dataCMB+WP+BAO we use (Kilbinger the more reported general et. inal.), [ form9]. Inshear of Fig. the1 convergencecorrelationa flat Universe functionfK (χ)=χ on, and angular we shall assume flatness 0 2 θ [arcmin] ! 10 10 0 500 1000 we havepower plotted spectrum the measurements of the CMB lensing from now on. The lensing efficiency is given by θ [arcmin] ! scales 0.8φφ to 350 arcmin (a) TDI (g)models power spectrum, C` , and the galaxy lensing correlation L + (b) GSF models with ↵ =0, β2 =1 β1 function, ⇠ (✓) (the Hankel4 2 transform of the convergence 1 χ0 χ − ` 8⇡ dχ −4 gi(χ)= dχ0ni (χ0) − , (23) power spectrumPij(`) P), along with modelgi (χ predictions) gj (χ) P colour(`/fK (χ), χ) ,(22) 10 10 ⇡ 4 `3 χ χ χ0 = 1 coded by their likelihood. ItZ is clear that, in both cases, Z 1 = 1.5 Figure1 2: Lensing observations in the TDI (g)andGSF those parameter combinations that are a good fit to the φφ where we have made use of the Limber approximation,where n (χ) is the radial distribution of source! galaxies in L i Source galaxy−6 distribution, peaked at z~0.75C models with w = 0.8. On the left we plot the predictions 4 CMB+BAO data predict a higher level of lensing corre- + 5 ! ξ 10 − + fK (χ) is the angular2 diameter distance, andbinP i.is In the the case of no anisotropic stress, the7 convergence lations► than observed (∆χ 20), indicating that there of the weak lensing correlation ⇠ spectra, as well as the 3D data (Heymans et. al.), shear 10 could bepower something spectrum missing of⇠ the within Weyl the potential, model. We defined will power in terms spectrum of can be written in the usual form data taken from CFHTLenS. On the right we plot the lens- 4 make thiscorrelationthe explicit Newtonian by performing potentialsfunction aφ full andon joint angularby likelihood =( + φ) /102.− For ing of the CMB Cφφ spectra, with observations from Planck −8 98350 ` 910 analysisa of flat the Universe publicly availablefK (χ)= lensingχ, and data we and shall com- assume flatness 2 0 4 2 (red/circles) and SPT (black/diamonds). Here we see that scales 1.5 to 35 arcmin,0.3 6 Pij(`)= ⌦10mH0 10 98320 500 1000 bining this with a prior on σ8(⌦m/0.27) coming from 5 ! decreasing the sound speed decreases the large-scale cluster- from now on. The lensing efficiency is given by 10− 4 θ [arcmin] 9829 the SZredshift cluster counts, bins which will lead to a significant 1 gi(χ)gj(χ) ing of the dark energy. [fixed] (b) GSF models with ↵ =0− , β2 =1 β1 P (`/χ, χ)d9826χ . (24) preference for such models. We1 note that thisχ0 isχ not 2 2 log − g (χ)= dχ0n (χ0) , + (23)6 ⇥ 0 a (χ) equivalent► In toboth performing casesi a fullobserved joint analysisi including− ξ 10− 9823 Z L the SZ likelihood – which is notχ publicly availableχ0 – but Z 9820 we havecorrelation tested that this function leads to similar is resultshigher to those thanThe convergenceFigure can also 2: Lensing be written observations in terms in of the the TDI cor- (g)andGSFIt is most interesting to note that some of the spectra 7 9817 L presentedPlanckwhere in [10n].i (cosmologyχ) is the radial distribution of sourcerelation galaxies10− functions in models⇠± via with w = 0.8. On the left we plot themostly predictions lie inside the error bars from CMB lensing, but − + Therebin arei. two In the separate case of analyses no anisotropic that we stress, have per- the convergence of the weak lensing correlation ⇠9814 spectra, as well as the 1 lie outside the error bars of galaxy weak lensing obser- formed:power a model spectrum with the can standard be written six parameters, in the usualp, form 8 data taken from CFHTLenS. On9811 the right we plot the lens- 10− ⇠± (✓)= d` Pij(`)J0/4(`✓), (25) vations: the CFHTLenS galaxy weak lensing data alone 100 i,j 101 φφ102 and 1 extra parameter m⌫ with N⌫ =3(N⌫ is the ing of2 the⇡ CMB C` spectra, with observations from Planck θ [arcmin]Z could rule out a range of parameter space. number of massive neutrinos)9 and2 N4e↵ =3.046; a model (red/circles) and SPT (black/diamonds). Here we see that Pij(`)=P ⌦mH0 e↵ with a total of 8 parameters – p + m ,Ne↵ – and where J0,4 aredecreasing Bessel functions the sound of the speed zeroth decreases and the fourth large-scaleIn cluster- Fig. 3 we plot the fractional di↵erences in observa- 4 { ⌫, sterile } FIG. 1: The CMB lensing power spectrum (top) data points m⌫ =0.06 eV, N⌫ = 1. The first1 representsgi(χ)gj(χ a) degener- order respectively.ing of the dark energy. [fixed] tional spectra for GSF models with a range of values of Sunday, 23 March 14 P (`/χ, χ)dχfrom. Planck(24) (green squares) and SPT (blue squares) andφφ ate active neutrino scenario, that is appropriate2 for large In Fig. 2 we plot the predictions of the CMB C spec- ↵, β1 and β2, relative to a fiducial quintessence scenario. P ⇥ 0 a (χ) the shear correlation function ⇠+ from CFHTLenS (bottom),` values of m⌫ , whereas the secondZ is a sterile neutrino trum and galaxy correlation function ⇠+, for the TDI For all of the models shown, the di↵erences in the CTT scenario with active neutrinos in a standard hierarchy compared to predictions for parameters from samples of the ` (g) and GSF models (for simplicity we take ↵, β to be spectra are negligible for angular scales ` > 50. However, that hasThe theP convergence lowest value of can alsom allowed be written by the in solar terms ofPlanck the cor-CMB+WP+BAOIt is most MCMC interesting chains with to non-linear note that cor-1 some of the spectra ⌫ Lrections [18, 19]. In both cases, the data is systematically¨ the di↵erences for the Cdd spectra remain roughly con- and atmosphericrelation functions constraints⇠ on± via the mass di↵erences. constants and mostlyβ2 =1 lieβ inside1,whichremovesthe the error bars fromh-term). CMB lensing, but ` P lower than theory, although− the significance is somewhat lower stant for all scales and, markedly, di↵erences in the ⇠+ In both cases we will follow the procedure out- For galaxy lensing,lie outside we use the the error single bars bin ⇠ of± galaxy⇠1±,1 distri- weak lensing obser- 1 than the eye would suggest in the case of CFHTLenS⌘ due to spectra increase with angular size.
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