durham-edinburgh extragalactic workshop xiv ifa edinburgh filedurham-edinburgh extragalactic...

Durham-Edinburgh eXtragalactic Workshop XIV

IfA Edinburgh

Cosmology withweak-lensing peak counts

Chieh-An Lin

January 8th, 2018

Durham University, UK

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

Motivation

linc.tw Chieh-An Lin (IfA Edinburgh)

General relativity

Gravitational lensing

(Source: ALMA)

Cosmology with weak-lensing peak counts DEX, Durham — Jan 8th, 2018 4

http://linc.tw/


Unlensed sources Weak lensing


http://linc.tw/


Gaussian information

κ map and 2PCF

But the lensing field is highly non-Gaussian


http://linc.tw/


Weak-lensing peak counts

κ map and peaks 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0Halo mass [log(M/M¯ h

−1)]

10-8

10-7

10-6

10-5

10-4

10-3

10-2

Hal

o nu

mbe

r den

sity

n(logM

) [(M

pc/h)−

3]

Halo mass function

σ8 = 0.76σ8 = 0.82σ8 = 0.88

• Local maxima of the projected mass• Probe the mass function• Constrain cosmology


http://linc.tw/

Problems


Dealing with selection function

Projection effects, irregular sampling, noise, ...

Early studiesCount only the true clusters with high S/N(Kruse & Schneider 1999, 2000; Reblinsky et al. 1999)

Recent studiesInclude the selection effect into the model

• Analytical formalism• N -body simulations• Fast stochastic model (this work)


http://linc.tw/


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


http://linc.tw/

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?

A new model

Sampled mass

PDF

Sample halosfrom a mass function

Assign density profiles,randomize positions

Compute the projectedmass, add noise

Filter maps,create peak catalogues

A stochasticmodel to predict

weak-lensingpeak counts

Lin & Kilbinger (2015a)


AdvantagesFast

Only few seconds for creating a 25-deg2 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 easilyGo beyond the Gaussian likelihood assumption


http://linc.tw/


Validation

We compare the following four cases:

Case 1 — Full N -body runsCase 2 — Replace N -body halos with NFW profiles of the same massCase 3 — Profile replacement and position randomizationCase 4 — Our model

to test two hypotheses:

Comparison 1 & 2 — Ignore unbound matters & halo asphericityComparison 2 & 3 — Absence of the spatial correlationComparison 3 & 4 — Mass function


http://linc.tw/


Lin & Kilbinger (2015a) Validation

2 3 4 5 6 7S/N ν

10-1

100

101

102

Peak

num

ber d

ensi

ty n

pea

k [d

eg−

2∆ν−

1]

Peak abundance histogram

Noise-only

Full N-body runsN-body: halos→NFWN-body: halos→NFW + random positionOur model


http://linc.tw/

Results


0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Ωm

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

σ8

1.00

2.50

4.005.50

7.00

Ωm-σ8 constraints

abd, cg, confidence1-σ, 68.3%2-σ, 95.4%

abd, svg, confidence1-σ, 68.3%2-σ, 95.4%

abd, svg, confidence1-σ, 68.3%2-σ, 95.4%

Cosmology-dependentcovariance

L = cst + ∆xTC−1∆x

cg = constant covariancesvg = varying covariance

cg svgFoM 46 57

Lin & Kilbinger (2015b)


http://linc.tw/

+

+

Combined strategy

Separated strategy


0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Ωm

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

σ8

Ωm-σ8 constraints

Separated strategy1-σ, 68.3%2-σ, 95.4%

Combined strategy1-σ, 68.3%2-σ, 95.4%

Combined strategy1-σ, 68.3%2-σ, 95.4%

Combined vs separated

The combined mapcreates degeneracy

which elongatesthe contours.

Lin et al. (2016)


http://linc.tw/


Data from three surveys

Survey Field size Number of Effective density[deg2] galaxies [deg−2]

CFHTLenS 126 6.1 M 10.74KiDS DR1/2 75 2.4 M 5.33DES SV 138 3.3 M 6.65


http://linc.tw/

0.3

0.8

1.3

σ8

ε= +∞ ε=55.8 ε=50.0 ε=49.2

0.3

0.8

1.3

σ8

ε=48.6 ε=48.2 ε=47.8 ε=47.5

0.1 0.4 0.7Ωm

0.3

0.8

1.3

σ8

ε=47.2

0.1 0.4 0.7Ωm

ε=46.9

PMC ABC posterior evolution

Cosmological constraints

withapproximate Bayesian

computation (ABC)


0.0 0.2 0.4 0.6 0.8 1.0Ωm

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6σ

8

Ωm-σ8 constraints

PMC ABC1-σ, 68.3%2-σ, 95.4%

PMC ABC1-σ, 68.3%2-σ, 95.4%

Cosmological constraints

Width: ∆Σ8 = 0.13Area: FoM = 5.2

Lin (2016)


http://linc.tw/

Perspectives


Improvements

Account forhalo clustering

(Source: HST)

Extend toredshift space distortions

Peacock et al. (2001)


http://linc.tw/


More physics

Massive neutrinos

(Source: MissMJ@Wikimedia/CC BY 3.0)

Modified gravity

0 1 2 3 4 5 6 7 8S/N ν

100

101

102

103

Peak

num

ber d

ensi

ty n

pea

k [d

eg−

2∆ν−

1]

ΛCDM

f(R), fR0 = 10−4

(Preliminary)


http://linc.tw/

Summary

• Peaks provide non-Gaussianinformation

• A stochastic model to predict WLpeak 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:

[1410.6955][1506.01076][1603.06773][1609.03973]

[1612.02264][1612.04041][1704.00258]http://linc.tw

http://github.com/Linc-tw/camelus

https://arxiv.org/abs/1410.6955







http://linc.tw

Backup slides


Liu J et al. (2015)

Peaks vs two-point statistics

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Ωm

0.2

0.4

0.6

0.8

1.0

1.2

σ8

DES SV 2-pt non-tomo

DES SV peaks

Kacprzak et al. (2016)

Cosmology with weak-lensing peak counts DEX, Durham — Jan 8th, 2018 B 1

http://linc.tw/


Approximate Bayesian computation

π

P(π)

πi

prior

ABC posterior

Parameter space

xP(x|πi)

xobs

|x− xobs| ≤ ε

Data space

Distribution of accepted π = prior× green area≈ prior× 2ε× likelihood∝ posterior


http://linc.tw/


Degeneracy with wde0

0.4

0.6

0.8

1.0

1.2

σ8

Parameter constraintswith likelihood

Starlet, θker =2′, 4′, 8′

1-σ, 68.3%2-σ, 95.4%

Starlet, θker =2′, 4′, 8′

1-σ, 68.3%2-σ, 95.4%

0.1 0.3 0.5 0.7Ωm

-1.8

-1.4

-1.0

-0.6

wde

0

0.4 0.6 0.8 1.0 1.2σ8

Lin et al. (2016)


http://linc.tw/


Liu X et al. (2016) fR0 constraints


http://linc.tw/

Liu J et al. (2015)

Other studies

Liu X et al. (2015)


0.16 0.24 0.32 0.40 0.48Ωm

0.60

0.75

0.90

1.05

1.20

σ8

0.0<S/N<4.0

KiDS-450 2PCFs-tomo S8 =0.745±0.039

Planck15 S8 =0.851±0.024

KiDS-450 SP S8 =0.757+0.054−0.053

Other studies

Martinet et al. (2018)


http://linc.tw/

durham-edinburgh extragalactic workshop xiv ifa edinburgh filedurham-edinburgh extragalactic...

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