Cosmology with weak-lensing peak counts

Transcription

1 Durham-Edinburgh extragalactic Workshop XIV IfA Edinburgh Cosmology with weak-lensing peak counts Chieh-An Lin January 8 th, 2018 Durham University, UK

2 Outline Motivation Why do we study WL peaks? Problems How to model WL peaks? Methodology A stochastic approach Results Cosmological constraints and others Perspectives Improvements and new physics

3 Motivation

4 General relativity Gravitational lensing (Source: ALMA) Cosmology with weak-lensing peak counts DEX, Durham Jan 8th,

5 Unlensed sources Weak lensing Cosmology with weak-lensing peak counts DEX, Durham Jan 8th,

6 Gaussian information κ map and 2PCF But the lensing field is highly non-gaussian Cosmology with weak-lensing peak counts DEX, Durham Jan 8th,

7 Weak-lensing peak counts Halo number density n(logm) [(Mpc/h) 3 ] Halo mass function σ 8 = 0.76 σ 8 = 0.82 σ 8 = 0.88 κ map and peaks Halo mass [log(m/m h 1 )] Local maxima of the projected mass Probe the mass function Constrain cosmology Cosmology with weak-lensing peak counts DEX, Durham Jan 8th,

8 Problems

9 Dealing with selection function Projection effects, irregular sampling, noise,... Early studies Count only the true clusters with high S/N (Kruse & Schneider 1999, 2000; Reblinsky et al. 1999) Recent studies Include the selection effect into the model Analytical formalism N -body simulations Fast stochastic model (this work) Cosmology with weak-lensing peak counts DEX, Durham Jan 8th,

10 Difficulties Analytical models Fan et al. (2010) and series; Shirasaki (2017) Difficult to handle masks and photo-z bias Difficult to include baryons or intrinsic alignment Need external covariances N -body simulations Dietrich & Hartlap (2010) and series; Kratochvil et al. (2010) and series Very expensive time costs Cosmology with weak-lensing peak counts DEX, Durham Jan 8th,

11 Challenges How to model properly weak-lensing peak counts? How to resolve the trade off between flexibility and speed? What cosmological information can we extract from peaks?

12 A new model

13 Sample halos from a mass function PDF A stochastic model to predict weak-lensing peak counts Sampled mass Assign density profiles, randomize positions Compute the projected mass, add noise Filter maps, create peak catalogues Lin & Kilbinger (2015a)

14 Fast Advantages Flexible Full PDF information Cosmology with weak-lensing peak counts DEX, Durham Jan 8th,

15 Fast Advantages Only few seconds for creating a 25-deg 2 field, without MPI or GPU Flexible Full PDF information Cosmology with weak-lensing peak counts DEX, Durham Jan 8th,

16 Fast Advantages Only few seconds for creating a 25-deg 2 field, without MPI or GPU Flexible Straightforward to include observational effects and additional features (mask, photo-z bias, IA, baryons,...) Full PDF information Cosmology with weak-lensing peak counts DEX, Durham Jan 8th,

17 Fast Advantages Only few seconds for creating a 25-deg 2 field, without MPI or GPU Flexible Straightforward to include observational effects and additional features (mask, photo-z bias, IA, baryons,...) Full PDF information Estimate covariances easily Go beyond the Gaussian likelihood assumption Cosmology with weak-lensing peak counts DEX, Durham Jan 8th,

18 Validation We compare the following four cases: Case 1 Full N -body runs Case 2 Replace N -body halos with NFW profiles of the same mass Case 3 Profile replacement and position randomization Case 4 Our model to test two hypotheses: Comparison 1 & 2 Ignore unbound matters & halo asphericity Comparison 2 & 3 Absence of the spatial correlation Comparison 3 & 4 Mass function Cosmology with weak-lensing peak counts DEX, Durham Jan 8th,

19 Lin & Kilbinger (2015a) Peak abundance histogram Validation Peak number density n peak [deg 2 ν 1 ] Noise-only Full N-body runs N-body: halos NFW N-body: halos NFW + random position Our model S/N ν Cosmology with weak-lensing peak counts DEX, Durham Jan 8th,

20 Results

21 Ω m -σ 8 constraints abd, cg, confidence 1-σ, 68.3% 2-σ, 95.4% Cosmology-dependent covariance σ abd, svg, confidence 1-σ, 68.3% 2-σ, 95.4% L = cst + x T C 1 x cg = constant covariance svg = varying covariance cg svg FoM Ω m Lin & Kilbinger (2015b) Cosmology with weak-lensing peak counts DEX, Durham Jan 8th,

22 Combined strategy + + Separated strategy

23 1.2 Ω m -σ 8 constraints σ Separated strategy 1-σ, 68.3% 2-σ, 95.4% Combined strategy 1-σ, 68.3% 2-σ, 95.4% Combined vs separated The combined map creates degeneracy which elongates the contours Ω m Lin et al. (2016) Cosmology with weak-lensing peak counts DEX, Durham Jan 8th,

24 Data from three surveys Survey Field size Number of Effective density [deg 2 ] galaxies [deg 2 ] CFHTLenS M KiDS DR1/ M 5.33 DES SV M 6.65 Cosmology with weak-lensing peak counts DEX, Durham Jan 8th,

25 1.3 PMC ABC posterior evolution ɛ = + ɛ =55.8 ɛ =50.0 ɛ =49.2 σ ɛ =48.6 ɛ =48.2 ɛ =47.8 ɛ =47.5 σ ɛ =47.2 ɛ =46.9 Cosmological constraints σ Ω m Ω m with approximate Bayesian computation (ABC)

26 Ω m -σ 8 constraints PMC ABC 1-σ, 68.3% 2-σ, 95.4% Cosmological constraints 1.2 σ Width: Σ 8 = 0.13 Area: FoM = Ω m Lin (2016) Cosmology with weak-lensing peak counts DEX, Durham Jan 8th,

27 Perspectives

28 Improvements Account for halo clustering Extend to redshift space distortions (Source: HST) Peacock et al. (2001) Cosmology with weak-lensing peak counts DEX, Durham Jan 8th,

29 More physics Massive neutrinos (Source: BY 3.0) Peak number density npeak [deg 2 ν 1 ] Modified gravity ΛCDM f(r), f R0 = S/N ν (Preliminary) Cosmology with weak-lensing peak counts DEX, Durham Jan 8th,

30 Summary Peaks provide non-gaussian information A stochastic model to predict WL peak counts Fast, flexible, full PDF information A public code: Camelus@GitHub Collaborators: Martin Kilbinger (CEA Saclay) François Lanusse (CMU) Austin Peel (CEA Saclay) Sandrine Pires (CEA Saclay) References: [ ] [ ] [ ] [ ] [ ] [ ] [ ]

31 Backup slides

32 Peaks vs two-point statistics σ DES SV 2-pt non-tomo DES SV peaks Ω m Liu J et al. (2015) Kacprzak et al. (2016) Cosmology with weak-lensing peak counts DEX, Durham Jan 8th, 2018 B 1

33 Approximate Bayesian computation Parameter space Data space prior P(π) ABC posterior P(x πi) x x obs ɛ π i π x obs x Distribution of accepted π = prior green area prior 2ɛ likelihood posterior Cosmology with weak-lensing peak counts DEX, Durham Jan 8th, 2018 B 2

34 Degeneracy with w de 0 σ Parameter constraints with likelihood Starlet, θ ker =2, 4, 8 1-σ, 68.3% 2-σ, 95.4% w de Ω m σ 8 Lin et al. (2016) Cosmology with weak-lensing peak counts DEX, Durham Jan 8th, 2018 B 3

35 Liu X et al. (2016) f R0 constraints Cosmology with weak-lensing peak counts DEX, Durham Jan 8th, 2018 B 4

36 Other studies Liu J et al. (2015) Liu X et al. (2015)

37 KiDS-450 2PCFs-tomo S 8 =0.745 ±0.039 Planck15 S 8 =0.851 ±0.024 KiDS-450 SP S 8 = Other studies σ <S/N < Ω m Martinet et al. (2018) Cosmology with weak-lensing peak counts DEX, Durham Jan 8th, 2018 B 6