Cross-Correlation of CFHTLenS Galaxy Catalogue and Planck CMB Lensing

Transcription

1 Cross-Correlation of CFHTLenS Galaxy Catalogue and Planck CMB Lensing A 5-month internship under the direction of Simon Prunet Adrien Kuntz Ecole Normale Supérieure, Paris July 08, 2015

2 Outline 1 Introduction 2 Theoretical Cosmology Cosmological Perturbation Theory Gravitational Lensing and Galaxy Density Cross-Correlation The Halo Model 3 Data Maps Galaxies Convergence 4 Results Bayesian Analysis Consistency Checks 5 Conclusions A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

3 The Initial Motivation Introduction A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

4 Aims of my Internship Introduction Achieve a good comprehension of the cosmological perturbation theory and of the halo model (1 month1/2) Implement a python program to compute covariances from the halo model (1 month 1/2) Retrieve data from both the CFHTLenS and the Planck collaboration, format them in a sky map, and perform simulations (1 month) Use a bayesian analysis to fit galaxy bias from the correlation of the two maps (1 week) Write an insternship report and a presentation(2 weeks) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

5 Aims of my Internship Introduction Achieve a good comprehension of the cosmological perturbation theory and of the halo model (1 month1/2) Implement a python program to compute covariances from the halo model (1 month 1/2) Retrieve data from both the CFHTLenS and the Planck collaboration, format them in a sky map, and perform simulations (1 month) Use a bayesian analysis to fit galaxy bias from the correlation of the two maps (1 week) Write an insternship report and a presentation(2 weeks) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

6 Aims of my Internship Introduction Achieve a good comprehension of the cosmological perturbation theory and of the halo model (1 month1/2) Implement a python program to compute covariances from the halo model (1 month 1/2) Retrieve data from both the CFHTLenS and the Planck collaboration, format them in a sky map, and perform simulations (1 month) Use a bayesian analysis to fit galaxy bias from the correlation of the two maps (1 week) Write an insternship report and a presentation(2 weeks) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

7 Aims of my Internship Introduction Achieve a good comprehension of the cosmological perturbation theory and of the halo model (1 month1/2) Implement a python program to compute covariances from the halo model (1 month 1/2) Retrieve data from both the CFHTLenS and the Planck collaboration, format them in a sky map, and perform simulations (1 month) Use a bayesian analysis to fit galaxy bias from the correlation of the two maps (1 week) Write an insternship report and a presentation(2 weeks) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

8 Aims of my Internship Introduction Achieve a good comprehension of the cosmological perturbation theory and of the halo model (1 month1/2) Implement a python program to compute covariances from the halo model (1 month 1/2) Retrieve data from both the CFHTLenS and the Planck collaboration, format them in a sky map, and perform simulations (1 month) Use a bayesian analysis to fit galaxy bias from the correlation of the two maps (1 week) Write an insternship report and a presentation(2 weeks) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

9 Outline 1 Introduction Theoretical Cosmology Cosmological Perturbation Theory 2 Theoretical Cosmology Cosmological Perturbation Theory Gravitational Lensing and Galaxy Density Cross-Correlation The Halo Model 3 Data Maps Galaxies Convergence 4 Results Bayesian Analysis Consistency Checks 5 Conclusions A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

10 Theoretical Cosmology Friedmann-Lemaître Model Cosmological Perturbation Theory ds 2 = c 2 dt 2 a 2 (t) dx 2 Physical coordinates : r = a (t) x Friedmann equations : ȧ 2 +kc 2 a 2 ä a = 4πG 3 = 8πGρ+Λc2 3 ( ) ρ + 3p + Λc2 c 2 3 Solution : p = wρc 2 ρ a 3(1+w) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

11 Theoretical Cosmology Friedmann-Lemaître Model Cosmological Perturbation Theory ds 2 = c 2 dt 2 a 2 (t) dx 2 Physical coordinates : r = a (t) x Friedmann equations : ȧ 2 +kc 2 a 2 ä a = 4πG 3 = 8πGρ+Λc2 3 ( ) ρ + 3p + Λc2 c 2 3 Solution : p = wρc 2 ρ a 3(1+w) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

12 Theoretical Cosmology Friedmann-Lemaître Model Cosmological Perturbation Theory ds 2 = c 2 dt 2 a 2 (t) dx 2 Physical coordinates : r = a (t) x Friedmann equations : ȧ 2 +kc 2 a 2 ä a = 4πG 3 = 8πGρ+Λc2 3 ( ) ρ + 3p + Λc2 c 2 3 Solution : p = wρc 2 ρ a 3(1+w) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

13 Theoretical Cosmology Friedmann-Lemaître Model Cosmological Perturbation Theory ds 2 = c 2 dt 2 a 2 (t) dx 2 Physical coordinates : r = a (t) x Friedmann equations : ȧ 2 +kc 2 a 2 ä a = 4πG 3 = 8πGρ+Λc2 3 ( ) ρ + 3p + Λc2 c 2 3 Solution : p = wρc 2 ρ a 3(1+w) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

14 Perturbation Theory Theoretical Cosmology Cosmological Perturbation Theory ρ (x, t) ρ (t) (1 + δ (x, t)) Linear solution : δ (x, t) = D + 1 (t) A (x) Non-linear solution : δ (k, t) = + n=1 an (t) δ n (k) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

15 Perturbation Theory Theoretical Cosmology Cosmological Perturbation Theory ρ (x, t) ρ (t) (1 + δ (x, t)) Linear solution : δ (x, t) = D + 1 (t) A (x) Non-linear solution : δ (k, t) = + n=1 an (t) δ n (k) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

16 Perturbation Theory Theoretical Cosmology Cosmological Perturbation Theory ρ (x, t) ρ (t) (1 + δ (x, t)) Linear solution : δ (x, t) = D + 1 (t) A (x) Non-linear solution : δ (k, t) = + n=1 an (t) δ n (k) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

17 Theoretical Cosmology Linear and Non-Linear Scales Cosmological Perturbation Theory Credit : Baghram et al (2011) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

18 Theoretical Cosmology Cosmological Perturbation Theory Correlation Function and Power Spectrum Primordial quantum fluctuations and inflation Gaussian initial conditions Gravitational instability ξ (r) = δ (x) δ (x + r) δ (k) δ (k ) = (2π) 3 δ D (k + k ) P (k) and higher order : B, T... A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

19 Theoretical Cosmology Cosmological Perturbation Theory Correlation Function and Power Spectrum Primordial quantum fluctuations and inflation Gaussian initial conditions Gravitational instability ξ (r) = δ (x) δ (x + r) δ (k) δ (k ) = (2π) 3 δ D (k + k ) P (k) and higher order : B, T... A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

20 Theoretical Cosmology Cosmological Perturbation Theory Correlation Function and Power Spectrum Primordial quantum fluctuations and inflation Gaussian initial conditions Gravitational instability ξ (r) = δ (x) δ (x + r) δ (k) δ (k ) = (2π) 3 δ D (k + k ) P (k) and higher order : B, T... A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

21 Theoretical Cosmology Cosmological Perturbation Theory Correlation Function and Power Spectrum Primordial quantum fluctuations and inflation Gaussian initial conditions Gravitational instability ξ (r) = δ (x) δ (x + r) δ (k) δ (k ) = (2π) 3 δ D (k + k ) P (k) and higher order : B, T... A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

22 Theoretical Cosmology Cosmological Perturbation Theory Correlation Function and Power Spectrum Primordial quantum fluctuations and inflation Gaussian initial conditions Gravitational instability ξ (r) = δ (x) δ (x + r) δ (k) δ (k ) = (2π) 3 δ D (k + k ) P (k) and higher order : B, T... A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

23 Outline 1 Introduction Theoretical Cosmology Gravitational Lensing and Galaxy Density 2 Theoretical Cosmology Cosmological Perturbation Theory Gravitational Lensing and Galaxy Density Cross-Correlation The Halo Model 3 Data Maps Galaxies Convergence 4 Results Bayesian Analysis Consistency Checks 5 Conclusions A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

24 Lens Equation Theoretical Cosmology Gravitational Lensing and Galaxy Density S α α given in General Relativity D LS L D OS θ D OL θ s O Lens equation : θ = f (θ s ) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

25 Illustration Theoretical Cosmology Gravitational Lensing and Galaxy Density Figure: Distortion of an extended source by a point-like lens A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

26 Illustration Theoretical Cosmology Gravitational Lensing and Galaxy Density A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

27 Illustration Theoretical Cosmology Gravitational Lensing and Galaxy Density A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

28 Theoretical Cosmology Gravitational Lensing and Galaxy Density Effect on the CMB Deformation of the photon paths κ (θ) = A. Kuntz (ENS Ulm) χcmb 0 Correlation of CFHTLenS and Planck W κ (χ) δ (χθ, χ) dχ 07/08/ / 57

29 Theoretical Cosmology Gravitational Lensing and Galaxy Density Effect on the CMB Deformation of the photon paths κ (θ) = A. Kuntz (ENS Ulm) χcmb 0 Correlation of CFHTLenS and Planck W κ (χ) δ (χθ, χ) dχ 07/08/ / 57

30 Galaxy Overdensity Theoretical Cosmology Gravitational Lensing and Galaxy Density δ gal (χθ, χ) = b (χ) δ (χθ, χ) g (θ) = χ CMB 0 W g (χ) δ (χθ, χ) dχ W g (χ) b (χ) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

31 Galaxy Overdensity Theoretical Cosmology Gravitational Lensing and Galaxy Density δ gal (χθ, χ) = b (χ) δ (χθ, χ) g (θ) = χ CMB 0 W g (χ) δ (χθ, χ) dχ W g (χ) b (χ) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

32 Galaxy Overdensity Theoretical Cosmology Gravitational Lensing and Galaxy Density δ gal (χθ, χ) = b (χ) δ (χθ, χ) g (θ) = χ CMB 0 W g (χ) δ (χθ, χ) dχ W g (χ) b (χ) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

33 Lensing kernels Theoretical Cosmology Gravitational Lensing and Galaxy Density A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

34 Outline 1 Introduction Theoretical Cosmology Cross-Correlation 2 Theoretical Cosmology Cosmological Perturbation Theory Gravitational Lensing and Galaxy Density Cross-Correlation The Halo Model 3 Data Maps Galaxies Convergence 4 Results Bayesian Analysis Consistency Checks 5 Conclusions A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

35 Theoretical Cosmology Cross-Correlation Spherical Harmonics and Correlation κ (θ) lm κ lmyl m (θ) and g (θ) lm g lmyl m (θ) κlm g l m = δll δ mm C κg l C κg l = ) dχ W κ (χ)w g (χ) P (k = l χ 2 χ, z (χ) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

36 Covariance Theoretical Cosmology Cross-Correlation Covariance : Σ κg ij = C κg κg l i C l j C κg l i C κg l j Σ κg ij = Gaussian Term + Non-Gaussian Term Non-Gaussian term involves T = δ (k 1 ) δ (k 2 ) δ (k 3 ) δ (k 4 ) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

37 Covariance Theoretical Cosmology Cross-Correlation Covariance : Σ κg ij = C κg κg l i C l j C κg l i C κg l j Σ κg ij = Gaussian Term + Non-Gaussian Term Non-Gaussian term involves T = δ (k 1 ) δ (k 2 ) δ (k 3 ) δ (k 4 ) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

38 Covariance Theoretical Cosmology Cross-Correlation Covariance : Σ κg ij = C κg κg l i C l j C κg l i C κg l j Σ κg ij = Gaussian Term + Non-Gaussian Term Non-Gaussian term involves T = δ (k 1 ) δ (k 2 ) δ (k 3 ) δ (k 4 ) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

39 Correlation Matrix Theoretical Cosmology Cross-Correlation A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

40 Outline 1 Introduction Theoretical Cosmology The Halo Model 2 Theoretical Cosmology Cosmological Perturbation Theory Gravitational Lensing and Galaxy Density Cross-Correlation The Halo Model 3 Data Maps Galaxies Convergence 4 Results Bayesian Analysis Consistency Checks 5 Conclusions A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

41 Spherical Collapse Theoretical Cosmology The Halo Model Expansion δ sc = 1.69 Turnaround ρ halo = sc ρ background, sc 340 Gravitational collapse Virialization A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

42 Spherical Collapse Theoretical Cosmology The Halo Model Expansion δ sc = 1.69 Turnaround ρ halo = sc ρ background, sc 340 Gravitational collapse Virialization A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

43 Spherical Collapse Theoretical Cosmology The Halo Model Expansion δ sc = 1.69 Turnaround ρ halo = sc ρ background, sc 340 Gravitational collapse Virialization A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

44 Ingredients Theoretical Cosmology The Halo Model n (m, z) Press & Schechter (1974) ρ (r; m) NFW profile (1997) δ h (x,z; m) = k>0 b k (m, z) δ (x) k /k! Mo & White (1995) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

45 Correlation Function Theoretical Cosmology The Halo Model 1-halo ρ tot (x) = i ρ (x x i, m i ) ξ (r) = ρ(x)ρ(x+r) ρ halo ρ (x) ρ (x + r) = 1-halo term + 2-halo term A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

46 Correlation Function Theoretical Cosmology The Halo Model 1-halo ρ tot (x) = i ρ (x x i, m i ) ξ (r) = ρ(x)ρ(x+r) ρ halo ρ (x) ρ (x + r) = 1-halo term + 2-halo term A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

47 Correlation Function Theoretical Cosmology The Halo Model 1-halo ρ tot (x) = i ρ (x x i, m i ) ξ (r) = ρ(x)ρ(x+r) ρ halo ρ (x) ρ (x + r) = 1-halo term + 2-halo term A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

48 Power Spectrum Theoretical Cosmology The Halo Model Credit : Cooray & Sheth (2002) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

49 Trispectrum Theoretical Cosmology The Halo Model T hhhh (k 1, k 1, k 2, k 2 ) = T 1h + T 2h + T 3h + T 4h A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

50 Outline 1 Introduction 2 Theoretical Cosmology Data Maps Galaxies Cosmological Perturbation Theory Gravitational Lensing and Galaxy Density Cross-Correlation The Halo Model 3 Data Maps Galaxies Convergence 4 Results Bayesian Analysis Consistency Checks 5 Conclusions A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

51 Data Maps The CFHTLenS Catalogue Galaxies Analysis of the CFHT Legacy Survey specialized in the production of a galaxy catalogue for lensing measurement CFHTLS : 171 MegaCam pointings , more than 2300 hours 4 patches, 154 deg 2 Galaxy catalogue and accurate photometric redshifts : σ 0.04 (1 + z) 0.2 < z < 1.3 and 18 < i AB < 24 A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

52 Redshift Distribution Data Maps Galaxies dn dz = α z 0 ( z z 0 ) λ exp ( ( z z 0 ) β ) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

53 Healpix Data Maps Galaxies JPL / NASA Pixels of equal area Iso-latitude Interface in Python 1 pixel = 1.7 arcmin A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

54 Data Maps Galaxies Mask Healpix pixel Mask Weight : w i = S unmasked S tot Galaxy overdensity : δ i = N i /w i N N n = 15.1 gal / arcmin 2 A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

55 Data Maps Galaxies Mask Healpix pixel Mask Weight : w i = S unmasked S tot Galaxy overdensity : δ i = N i /w i N N n = 15.1 gal / arcmin 2 A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

56 Data Maps Galaxies Mask Healpix pixel Mask Weight : w i = S unmasked S tot Galaxy overdensity : δ i = N i /w i N N n = 15.1 gal / arcmin 2 A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

57 Data Maps Galaxies Mask Healpix pixel Mask Weight : w i = S unmasked S tot Galaxy overdensity : δ i = N i /w i N N n = 15.1 gal / arcmin 2 A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

58 Mask Data Maps Galaxies A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

59 Galaxy Map Data Maps Galaxies A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

60 Galaxy Map Data Maps Galaxies A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

61 Noise Data Maps Galaxies Poisson process : shot noise C gg l C gg l + N gg l, N gg l = 1/ n ( n in galaxies / steradian!) Small effect A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

62 Outline 1 Introduction 2 Theoretical Cosmology Data Maps Convergence Cosmological Perturbation Theory Gravitational Lensing and Galaxy Density Cross-Correlation The Halo Model 3 Data Maps Galaxies Convergence 4 Results Bayesian Analysis Consistency Checks 5 Conclusions A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

63 Convergence Map Data Maps Convergence A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

64 Noise Data Maps Convergence Obtained from the Planck simulations Dominant over C κκ l! A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

65 Data Maps Convergence A Consequence of the High Level of Noise Σ κg ij = 1 [ (2π) 2 ( (C δ K κκ ij l 4πf sky Ω i i + Nl κκ ) ( ) ( ) ) 2 i C gg l j + N gg l i + C κg l i + ] κg T ij A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

66 Outline 1 Introduction 2 Theoretical Cosmology Results Bayesian Analysis Cosmological Perturbation Theory Gravitational Lensing and Galaxy Density Cross-Correlation The Halo Model 3 Data Maps Galaxies Convergence 4 Results Bayesian Analysis Consistency Checks 5 Conclusions A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

67 Results Bayesian Analysis Bayes Theorem C κg l C gg l = A b C κg l = b 2 C gg l P (A, b C) = P(A,b)P(C A,b) P(C) { P (C A, b) = N exp 1 ( ) ( ) } C C (A, b) Σ 1 C C (A, b) 2 A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

68 Results Bayesian Analysis Bayes Theorem C κg l C gg l = A b C κg l = b 2 C gg l P (A, b C) = P(A,b)P(C A,b) P(C) { P (C A, b) = N exp 1 ( ) ( ) } C C (A, b) Σ 1 C C (A, b) 2 A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

69 Results Bayesian Analysis Bayes Theorem C κg l C gg l = A b C κg l = b 2 C gg l P (A, b C) = P(A,b)P(C A,b) P(C) { P (C A, b) = N exp 1 ( ) ( ) } C C (A, b) Σ 1 C C (A, b) 2 A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

70 MCMC 2013 Results Bayesian Analysis A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

71 MCMC 2015 Results Bayesian Analysis A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

72 Best-Fit Values Results Bayesian Analysis Patch A b χ 2 /ν A b χ 2 /ν All / /36 A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

73 C κg l Results Bayesian Analysis A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

74 C gg l Results Bayesian Analysis A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

75 Outline 1 Introduction 2 Theoretical Cosmology Results Consistency Checks Cosmological Perturbation Theory Gravitational Lensing and Galaxy Density Cross-Correlation The Halo Model 3 Data Maps Galaxies Convergence 4 Results Bayesian Analysis Consistency Checks 5 Conclusions A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

76 κg, simu Cl Results Consistency Checks A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

77 gg, simu Cl Results Consistency Checks A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

78 Recovered A and b Results Consistency Checks A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

79 Outline Conclusions 1 Introduction 2 Theoretical Cosmology Cosmological Perturbation Theory Gravitational Lensing and Galaxy Density Cross-Correlation The Halo Model 3 Data Maps Galaxies Convergence 4 Results Bayesian Analysis Consistency Checks 5 Conclusions A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

80 Summary Conclusions Learned Cosmological Perturbation Theory and Halo Model Implemented a Python program to compute the trispectrum in the halo model Created a galaxy and convergence map Used a Bayesian analysis to fit a galaxy bias Performed consistency checks A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

81 Summary Conclusions Learned Cosmological Perturbation Theory and Halo Model Implemented a Python program to compute the trispectrum in the halo model Created a galaxy and convergence map Used a Bayesian analysis to fit a galaxy bias Performed consistency checks A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

82 Summary Conclusions Learned Cosmological Perturbation Theory and Halo Model Implemented a Python program to compute the trispectrum in the halo model Created a galaxy and convergence map Used a Bayesian analysis to fit a galaxy bias Performed consistency checks A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

83 Summary Conclusions Learned Cosmological Perturbation Theory and Halo Model Implemented a Python program to compute the trispectrum in the halo model Created a galaxy and convergence map Used a Bayesian analysis to fit a galaxy bias Performed consistency checks A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

84 Summary Conclusions Learned Cosmological Perturbation Theory and Halo Model Implemented a Python program to compute the trispectrum in the halo model Created a galaxy and convergence map Used a Bayesian analysis to fit a galaxy bias Performed consistency checks A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

85 Conclusions Conclusions b = : good tracers of matter A 2013 = and A2015 = : compatible but different Partly confirm Omori & Holder (2015) A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

86 Forthcoming Work Conclusions SDSS data : much better coverage of the sky If still a difference : investigate! A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

87 Questions? Comments? Conclusions A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57

88 Conclusions Thank You CFHT! A. Kuntz (ENS Ulm) Correlation of CFHTLenS and Planck 07/08/ / 57