Relieving tensions related to the lensing of CMB temperature power spectra (astro-ph )

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1 Relieving tensions related to the lensing of CMB temperature power spectra (astro-ph15176) F. Couchot, S. Henrot-Versillé, O. Perdereau, S. Plaszczynski, B. Rouillé d Orfeuil, M. Spinelli and M. Tristram Laboratoire de l Accélérateur Linéaire January 2, 216 S. Plaszczynski : relieving Planck tensions 1 / 49

2 Estimating parameters in cosmology Parameters θ = (Ω, ν) 1 cosmo Ω = (ωb, ω c, θ s,...) 2 nuisances ν =(calibs, beams,foregrounds...) Likelihood L (θ) = L (C l (Ω), ν) Boltzmann solver : C l (Ω) camb (fortran) or class (C) Statistics 1 point estimate: max likelihood solution (or minχ 2 (= 2 ln L )= best-fit 2 individual parameters= intervals 1 sample L (MCMC)+ histogram (marginalize)=bayesian 2 focus on L shape (profile likelihood)=frequentist S. Plaszczynski : relieving Planck tensions 2 / 49

3 Profile-likelihood χ n s each point can be computed independently (//) but heavy for all variables multi-dim min must be extremely precise (Minuit + increase Boltzmann precision) 1 minimum always coincides with global best-fit 2 interval has coverage properties 3 invariant on change of variables:f(θ) ˆf = f(ˆθ) 4 OK for non-linear cases 5 no priors, no volume effects Planck Collaboration Int. XVI (214) S. Plaszczynski : relieving Planck tensions 3 / 49

4 Volume effects p(x 1 ) L (x 1, x 2 )dx 2 L (x 1 ) max x2 L (x 1, x 2 ) S. Plaszczynski : relieving Planck tensions 4 / 49

5 Statistics does not matter.....when problem is well constrained: Planck high+low l likelihoods ΛCDM par MCMC profile L Ω b h ± ± 23 Ω c h ± ± 22 H ± ±.98 τ 78 ± ± 2 ln(1 1 A s ) 3.89 ± ± 37 n s.9655 ± ± 63 Planck Collaboration XIII (215) NB: different Boltzman solvers S. Plaszczynski : relieving Planck tensions 5 / 49

6 Planck likelihoods L (C l, ν) 1 high-l(l 3 Gaussian) cross-spectra HFI, masks + param foregrounds : Plik }{{}, Hillipop, CamSpec, Mspec: Planck papers TT, //// pol, TT+pol ////////// 2 low-l: auto-spectrum LFI, low resolution pixel based : lowteb: TT+pol (constrains τ) S. Plaszczynski : relieving Planck tensions 6 / 49

7 The high-l HiLLiPOP likelihood 6 maps: 2x HFI 1 GHz,143 GHz, 217 GHz 15 cross-spectra: 1Ax1B,1Ax143A etc.. C XY l = 1 2l + 1 l m= l a X lma Y lm masking strategy to limit contamination from foregrounds parametric models for residuals foregrounds S. Plaszczynski : relieving Planck tensions 7 / 49

8 The high-l HiLLiPOP likelihood C XY l for l > 5 Gaussian approx (central limit theorem) 2lnL (Cl CMB, ν) = (Cl data Cl model modes cross ) Σ 1 (Cl data Cl model ) modes T T, EE, T E Σ: l-by-l, cross-by-cross, mode-by-mode covariance matrix ( C model,xy l = c xc y Cl CMB (Ω) + ) fg A fgc fg l from Planck templates Planck Collaboration XXII (215),Planck Collaboration XXX (214) A fg is a scaling factor +calibrations (c i ) C fg l S. Plaszczynski : relieving Planck tensions 8 / 49

1 diag Σsim/ diag Σana diag Σ [µk4] 14 12 1-4 1 Semi-analytical calculation (+data: no need for noise model) S. Plaszczynski S.

9 Parameters estimation Planck results very-high-` References Full covariance matrix Monte Carlo validation of approximations (15k sims) % precision residual effects from point source masks do not bias the results 143x x diag Σsim/ diag Σana diag Σ [µk4] Semi-analytical calculation (+data: no need for noise model) S. Plaszczynski S. Plaszczynski : relieving Planck tensions.9 analytic TT EE TE multipole 1 1 multipole Laboratoire de l Acce le rateur Line aire 9 / 49

10 Hillipop [µkcmb 2] D TT l 4 2 [µkcmb 2] D TT l l S. Plaszczynski : relieving Planck tensions 1 / 49

11 Residual foreground modeling galactic dust (TT, EE, TE) unresolved Point Sources background from galaxies (CIB) clusters (SZ) S. Plaszczynski : relieving Planck tensions 11 / 49

12 Residual foreground modeling galactic dust (TT, EE, TE) unresolved Point Sources background from galaxies (CIB) clusters (SZ) S. Plaszczynski : relieving Planck tensions 12 / 49

13 Hillipop nuisances name definition prior (if any) instrumental c map calibration (1-hm1) ± 2 c 1 map calibration (1-hm2) ± 2 c 2 map calibration (143-hm1) fixed to 1. c 3 map calibration (143-hm2) ± 2 c 4 map calibration (217-hm1) 25 ± 2 c 5 map calibration (217-hm2) 25 ± 2 A absolute calibration ± 25 foreground modelling A 1 1 PS PS amplitude in TT (1x1 GHz) A PS PS amplitude in TT (1x143 GHz) A PS PS amplitude in TT (1x217 GHz) A PS PS amplitude in TT (143x143 GHz) A PS PS amplitude in TT (143x217 GHz) A PS PS amplitude in TT (217x217 GHz) A SZ scaling for the tsz template (TT) A CIB scaling for the CIB template (TT) ±.2 A ksz scaling for the ksz template (TT) A SZxCIB scaling parameter for the cross correlation between ksz and CIB A TT dust scaling parameter for the dust in TT ±.2 A EE dust scaling parameter for the dust in EE ±.2 A TE dust scaling parameter for the dust in TE ±.2 S. Plaszczynski : relieving Planck tensions 13 / 49

14 Differences with Plik all cross-spectra used more calibration coefficients (map level) cleaned point-sources mask galactic dust parametrized as in Planck Collaboration Int. XXX (214) Planck foreground templates (SZ, CIB...) all l values (no binning)... S. Plaszczynski : relieving Planck tensions 14 / 49

15 Any difference on ΛCDM parameters? ΛCDM par Plik + lowteb Hillipop + lowteb Ω b h ± ± 23 Ω c h ± ± 22 H ± ±.97 τ 78 ± ± 2 ln(1 1 A s ) 3.89 ± ± 38 n s.9655 ± ± 71 σ ± ± 15 (MCMC) lowteb in common τ, ln(1 1 A s ) correlated through C l A s e 2τ S. Plaszczynski : relieving Planck tensions 15 / 49

CMB lensing We do not measure C l but C l CMB light deflected by matter structures : tiny (σ 3 )- parametrized by lensing potential with spectrum Lewis and Challinor (26): C Φ l dk = 16π k P

16 CMB lensing We do not measure C l but C l CMB light deflected by matter structures : tiny (σ 3 )- parametrized by lensing potential with spectrum Lewis and Challinor (26): C Φ l dk = 16π k P R(k) [ χ ( )] χ 2 χ dχ T (k, η χ) χχ P R (k) = A s (k/k ) ns C Φ l A s mostly in linear regime : C Φ l σ 2 8 Planck Collaboration XV (215) S. Plaszczynski : relieving Planck tensions 16 / 49

17 A L Boltzmann code: 1 Ω (Cl, C Φ l ) C l L 2 (Ω, AL ) (C l, A L C Φ l ) C l L Interest: 1 TEST1: AL should be compatible with 1 ( otherwise: data problem or modify GR) 2 marginalize (or left free in fits): neglect lensing effect (to 1st order) in estimations C Φ l A s A L S. Plaszczynski : relieving Planck tensions 17 / 49

18 Plik results : A L (TEST1) 4 3 Plik+lowTEB Plik χ A L A L = (Plik+lowTEB, class/profile) A L = 1.24 ±.1 A L = 1.22 ±.1 (Plik+lowTEB, class/mcmc) (Plik+lowTEB, camb/mcmc) Planck Collaboration XIII (215) S. Plaszczynski : relieving Planck tensions 18 / 49

19 Can we measure τ only with high-l? high-l only: C l = A s e 2τ (τ, ln(1 1 A s )) degenerate but C l (Cl Φ A s ) breaks it! = one can get a measurement of τ with only a high-llikelihood. TEST2: compare high-l only likelihood results to low-l. S. Plaszczynski : relieving Planck tensions 19 / 49

20 Plik results : τ (TEST2) 4 3 lowteb Plik Plik (A L ) χ τ τ = (lowteb) v.s τ = (Plik) 2.2σ mismatch S. Plaszczynski : relieving Planck tensions 2 / 49

21 A methodology issue?.8 L(τ) p(τ) τ τ = (lowteb) v.s τ = (Plik) 1.9σ S. Plaszczynski : relieving Planck tensions 21 / 49

22 The [τ, A s, A L ] correlation TEST1 (A L ) performed on high-l+low-l. For fixed data: low-l: pulls τ high-l: amplitude C l A s e 2τ A s high-l: to preserve lensing information (C Φ l A s A L ) : A L../plikTT_tau7_Alens_MC../plikTT_tau17_Alens_MC omega_b omega_cdm *theta_s tau_reio log(1^1a_s) n_s Alens H Omega_M S. Plaszczynski : relieving Planck tensions 22 / 49

23 Hillipop results : τ (TEST2) 4 3 lowteb Hillipop Hillipop (A L ) χ τ τ = (lowteb) τ = (Hillipop) 1.3σ S. Plaszczynski : relieving Planck tensions 23 / 49

24 Plik results : τ (TEST2) 4 3 lowteb Plik Plik (A L ) χ τ τ = (lowteb) τ = (Plik) 2.2σ S. Plaszczynski : relieving Planck tensions 24 / 49

25 Hillipop results : A L (TEST1) 4 3 Hillipop+lowTEB Hillipop χ A L A L = (Hillipop+lowTEB) S. Plaszczynski : relieving Planck tensions 25 / 49

26 Plik results : A L (TEST1) 4 3 Plik+lowTEB Plik χ A L A L = (Plik+lowTEB) S. Plaszczynski : relieving Planck tensions 26 / 49

27 More CMB data: very-high-l (VHL) ACT+SPT/ essentially constrain foregrounds Dataset l range freq (GHz) #spectra #nuisances ref ACT south/equat [15,1] 148, Das et al. (214) SPT high [2,13] 95, 15, Reichardt et al. (212) SPT low [65,3] Story et al. (212) each provides window functions + cov matrix for SPT high: prefer Reichardt et al. (212) over George et al. (214) since the latter include calibrations based on Planck 213 results: both give similar results. S. Plaszczynski : relieving Planck tensions 27 / 49

28 Consistency with 1 HFI (143x143 GHz) ACT south (148x148 GHz) ACT equat (148x148 GHz) SPT high (15x15 GHz) SPT low (15x15 GHz) [µkcmb 2] D TT l 1 1 [µkcmb 2] D TT l l S. Plaszczynski : relieving Planck tensions 28 / 49

29 data model CMB CIB PS ksz tsz tszxcib Dust data model CMB CIB PS ksz tsz tszxcib Dust data model CMB CIB PS ksz tsz tszxcib Dust data model CMB CIB PS ksz tsz tszxcib Dust data model CMB CIB PS ksz tsz tszxcib Dust data model CMB CIB PS ksz tsz tszxcib Dust ACT D l TT [µkcmb 2] D l TT [µkcmb 2] D l TT [µkcmb 2] D l TT [µkcmb 2] l D l TT [µkcmb 2] l D l TT [µkcmb 2] l (a) ACT equat (b) ACT equat (c) ACT equat D l TT [µkcmb 2] D l TT [µkcmb 2] D l TT [µkcmb 2] D l TT [µkcmb 2] D l TT [µkcmb 2] D l TT [µkcmb 2] l l l (d) ACT south (e) ACT south (f) ACT south χ 2 /ndof = 651/71 S. Plaszczynski : relieving Planck tensions 29 / 49

30 data model CMB CIB PS ksz tsz tszxcib Dust data model CMB CIB PS ksz tsz tszxcib Dust data model CMB CIB PS ksz tsz tszxcib Dust data model CMB CIB PS ksz tsz tszxcib Dust data model CMB CIB PS ksz tsz tszxcib Dust data model CMB CIB PS ksz tsz tszxcib Dust SPT high D l TT [µkcmb 2] D l TT [µkcmb 2] D l TT [µkcmb 2] D l TT [µkcmb 2] D l TT [µkcmb 2] D l TT [µkcmb 2] l l l (g) SPT high (h) SPT high (i) SPT high D l TT [µkcmb 2] D l TT [µkcmb 2] D l TT [µkcmb 2] D l TT [µkcmb 2] l D l TT [µkcmb 2] l D l TT [µkcmb 2] l (j) SPT high (k) SPT high (l) SPT high χ 2 /ndof = 77/9 S. Plaszczynski : relieving Planck tensions 3 / 49

31 SPT low [µkcmb 2] data model CMB CIB PS ksz tsz tszxcib Dust D l TT 1.1 [µkcmb 2] D l TT l (m) SPT low GHz χ 2 /ndof = 58/47 S. Plaszczynski : relieving Planck tensions 31 / 49

32 More consistency tests build a L V HL (Gaussian with cov matrix+window functions from expts) Is VHL cosmology consistent with Planck? sample independently L Hillipop (full) and L V HL (dashed) Ωbh 2 Ωch θs ln(1 1 As) τ ns S. Plaszczynski : relieving Planck tensions 32 / 49

33 Combined likelihood put A SZ, A CIB, A ksz, A SZ CIB in common in L Hillipop and L V HL Hillipop w/o VHL (full/dashed): ACIB ASZ AkSZ ASZxCIB A TT dust APS A PS APS APS A PS APS A CIB, A ksz, A SZ CIB, A T dust T are scalings 1 S. Plaszczynski : relieving Planck tensions 33 / 49

34 τ Hillipop 4 3 lowteb Hillipop Hillipop (A L ) χ τ τ = (lowteb) τ = (Hillipop) S. Plaszczynski : relieving Planck tensions 34 / 49

35 τ Hillipop+VHL 4 3 lowteb Hillipop+VHL Hillipop+VHL (A L ) χ τ τ = (lowteb) 52 ± 35 (Hillipop+VHL) S. Plaszczynski : relieving Planck tensions 35 / 49

36 A L Hillipop 4 3 Hillipop+lowTEB Hillipop χ A L A L = (Hillipop+lowTEB) S. Plaszczynski : relieving Planck tensions 36 / 49

37 A L Hillipop+VHL 4 Hillipop+lowTEB Hillipop+lowTEB+VHL 3 χ A L A L = 3 ± 8 (Hillipop+lowTEB+VHL) S. Plaszczynski : relieving Planck tensions 37 / 49

38 Various VHLs Hillipop+lowTEB+... A L ±.11 SPT low 1.16 ±.1 SPT high 1.12 ±.1 ACT 1.19 ±.1 SPT low+spt high 2 ± 8 SPT low+act 9 ± 9 SPT high+act 1.12 ± 9 SPT low+spt high+act 3 ± 8 SPT low+spt high214 +ACT 4 ± 8 many combinations OK S. Plaszczynski : relieving Planck tensions 38 / 49

39 More checks on SPT high to improve on SPT high increase dust level A L = 1.12 ±.1 (Hillipop+lowTEB+SPT high) = 1.13 ±.1 (Hillipop+lowTEB+SPT high, A SPT dust 3) A L = 3 ± 8 (Hillipop+lowTEB+VHL) = 4 ± 8 (Hillipop+lowTEB+VHL, A SPT dust 3) S. Plaszczynski : relieving Planck tensions 39 / 49

40 ΛCDM revisited all now OK fix A L = Ωbh 2 Ωch θs τ ln(1 1 As) H ns σ8 Hillipop+lowTEB+VHL : full Plik+lowTEB+cor(SZ): dashed S. Plaszczynski : relieving Planck tensions 4 / 49

41 ΛCDM parameters revisited (Hillipop) Parameter Hillipop + lowteb Hillipop + lowteb Hillipop + lowteb +V HL +V HL + BAO + SN Ω b h ± ± ± 18 Ω c h ± ± ± 12 1θ s 4175 ± ± ± 36 τ 72 ± 2 59 ± ± 17 n s.9645 ± ± ± 4 ln(1 1 A s ) 3.68 ± ± ± 32 Ω m.311 ± ± ± 7 H ± ± ±.53 σ ± ± ± 13 stable reionization depth is low σ 8.81 not so in tension with local measurements (WL, SZ cluster counts..) S. Plaszczynski : relieving Planck tensions 41 / 49

42 Conclusions to first order Planck data are OK (for ΛCDM) but some 2σ tensions: low vs hi-ell τ, A L (hi+low) another Planck high-l likelihood (Hillipop) is less in tension [τ, A s, A L, σ 8 ] lower using more CMB data seems to cure all those tensions (no need to modify GR!) cosmology is now dominated by systematics: CMB is a clean probe! should be the main focuss in the next decade (in particular for m ν, N eff...) S. Plaszczynski : relieving Planck tensions 42 / 49

43 References Planck Collaboration Int. XVI. Planck intermediate results. XVI. Profile likelihoods for cosmological parameters. A&A, 566:A54, 214. Planck Collaboration XIII. Planck 215 results. XIII. Cosmological parameters. ArXiv e-prints, 215. Planck Collaboration XXII. Planck 215 results. XXII. A map of the thermal Sunyaev-Zeldovich effect. ArXiv e-prints, 215. Planck Collaboration XXX. Planck 213 results. XXX. Cosmic infrared background measurements and implications for star formation. A&A, 571:A3, 214. Planck Collaboration Int. XXX. Planck intermediate results. XXX. The angular power spectrum of polarized dust emission at intermediate and high Galactic latitudes. A&A, in press, 214. A. Lewis and A. Challinor. Weak gravitational lensing of the CMB. Phys. Rep., 429:1 65, 26. doi:1.116/j.physrep Planck Collaboration XV. Planck 215 results. XV. Gravitational lensing. ArXiv e-prints, 215. S. Das, T. Louis, M. R. Nolta et al. The Atacama Cosmology Telescope: temperature and gravitational lensing power spectrum measurements from three seasons of data. J. Cosmology Astropart. Phys., 4:14, 214. doi:1.188/ /214/4/14. C. L. Reichardt, L. Shaw, O. Zahn et al. A Measurement of Secondary Cosmic Microwave Background Anisotropies with Two Years of South Pole Telescope Observations. ApJ, 755:7, 212. doi:1.188/4-637x/755/1/7. K. T. Story, C. L. Reichardt, Z. Hou et al. A Measurement of the Cosmic Microwave Background Damping Tail from the 25-square-degree SPT-SZ survey. ArXiv e-prints, 212. E. M. George, C. L. Reichardt, K. A. Aird et al. A measurement of secondary cosmic microwave background anisotropies from the 25-square-degree SPT-SZ survey. ArXiv e-prints, 214. S. Plaszczynski : relieving Planck tensions 43 / 49

44 class v.s camb Planck uses camb we use class. compare both on same cosmo: 2 Dl [µk 2 ] class(default)-camb class(hq)-camb class(vhq)-camb l below % not that satisfactory but sufficient for our studies (see next) S. Plaszczynski : relieving Planck tensions 44 / 49

t/k SZ correlation Planck states VHL cor(asz). Not for Hillipop: A L = 1.26 +.12.

45 t/k SZ correlation Planck states VHL cor(asz). Not for Hillipop: A L = (Hillipop+lowTEB+SZ-cor) Improvement comes from the whole cov. matrix S. Plaszczynski : relieving Planck tensions 45 / 49

46 A L vs. m ν effect on TT spectra S. Plaszczynski : relieving Planck tensions 46 / 49

47 Plik+VHL? Plik: τ =.17 ± 3 A L = 1.26 ±.1 (Plik) (Plik+lowTEB) Adding VHL (but keep Plik templates since hard-coded) τ = 8 ± 2 A L = 1.14 ± 8 (Plik+VHL) (Plik+lowTEB+VHL) S. Plaszczynski : relieving Planck tensions 47 / 49

48 Addison et al. (215) use Plik+lowTEB and cut at 1: above 1 only Plik. use same τ = 7 ± 2 prior, but we saw Plik only consistent with S. Plaszczynski : relieving Planck tensions 48 / 49

49 Cosmological Analysis with Minuit Exploration of the Likelihood pure C/C++ OO project Boltzmann = class (J.Lesgourgues etal), pure C. Likelihoods: all recent measurements implemented (CMB, JLA, BAO2D) stat: minimization (bestfit): Minuit adaptive MCMC profile likelihoods debugged and heavily used (at ccin2p3) for papers. S. Plaszczynski : relieving Planck tensions 49 / 49

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