Cosmological Weak Gravitational Lensing Hendrik Hildebrandt - - - PowerPoint PPT Presentation

Cosmological Weak Gravitational Lensing

Hendrik Hildebrandt - Ruhr-Universität Bochum

Credit: LSST

Cosmological Constant / Vacuum Energy / Dark Energy

ΛCDM

Credit: Planck

Credit: Michael Sachs

Gravitational light deflection

MASS

Gravitational lens

Optical lens

Gravitational lens analogue

Spherical abberation!

Mellier (1999)

h✏i = D ✏(s)E + hgi = hgi

✏ = ✏(s) + g

Weak lensing

Dark matter in the bullet cluster separated from the hot X-ray gas

Credit: NASA, ESA, and D. Clowe

Dark matter maps

Cosmic shear

Wittman et al. (2000)

Sensitive to:

• Matter

distribution

• Geometry

Observables:

• Ellipticities
• Photo-z

Statistical measurement

• f many

galaxies

2pt shear correlation functions

10-7 10-6 10-5 10-4 1 10 100 Shear correlation ϑ [arcmin] ξ+(ϑ) ξ−(ϑ)

Kilbinger et al. (2013)

Very directly related to the matter power spectrum Pδ.

ξ±(θ) = ⟨γtγt⟩ (θ) ± ⟨γ×γ×⟩ (θ)

Observation -> theory

ξ+(θ) = ∞ dℓ ℓ 2π J0(ℓθ) Pκ(ℓ) ; ξ−(θ) = ∞ dℓ ℓ 2π J4(ℓθ) Pκ(ℓ)

Pκ(ℓ) = 9H4

0Ω2 m

4c4 χh dχ g2(χ) a2(χ) Pδ

• ℓ

fK(χ), χ

• g(χ) =

χh

χ

dχ′ pχ(χ′)fK(χ′ − χ) fK(χ′)

Cosmological constraints

Kilbinger et al. (2013)

• Measure amount
• f clustered

matter

• S8 = σ8 (Ωm/0.3)0.5

S8 results over the years

Kilbinger (2015)

2006 2008 2010 2012 2014 year 0.5 0.6 0.7 0.8 0.9 1.0 1.1 σ8(Ωm/0.3)α

COSMOS 100 deg2 CFHTLS/CFHTLenS SDSS-Stripe82 DLS SDSS-DR7 CMB

Dark energy e.o.s.

w = p/ρ ; w(a) = w0 + wa(1-a) ; a = 1/(1+z)

Joudaki et al. (2017b)

Massive neutrinos

Joudaki et al. (2017b)

Warm dark matter

10

−5

10

−4

l(l+1)Cl/2!

mWDM = 250 eV mWDM = 500 eV mWDM = 1 keV CDM 0.1 10

2

10

3

10

4

multipole, l

Markovič et al. (2011)

mWDM>2.5keV with Euclid

Systematic errors

• Shapes measurement systematics:
• PSF residuals
• B modes
• Multiplicative and additive biases
• Photo-z systematics:
• Calibration sample and technique
• Inhomogeneous multi-band data
• Theoretical “systematics”:
• Intrinsic alignments
• Baryon feedback
• Neutrinos
• WDM
• Psychological systematics:
• Blinding

KiDS: Kilo Degree Survey DES: Dark Energy Survey HSC: Hyper-Suprime Cam Survey

0.1 0.2 0.3 0.4

Ωm

0.6 0.8 1.0 1.2

σ8

KiDS-450 CFHTLenS (MID J16) WMAP9+ACT+SPT Planck15

1

2

0.1 0.2 0.3 0.4

Ωm

0.6 0.8 1.0 1.2

σ8

KiDS-450 CFHTLenS (MID J16) WMAP9+ACT+SPT Planck15

3

0.1 0.2 0.3 0.4

Ωm

0.6 0.8 1.0 1.2

σ8

KiDS-450 CFHTLenS (MID J16) WMAP9+ACT+SPT Planck15

?

KiDS-450

Hildebrandt et al. (2017)

0.16 0.24 0.32 0.40

Ωm

0.6 0.8 1.0 1.2

σ8

KiDS-450 CFHTLenS (MID J16) WMAP9+ACT+SPT Planck15 0.16 0.24 0.32 0.40

Ωm

0.64 0.72 0.80 0.88

σ8(Ωm/0.3)0.5

DES-Y1

Troxel et al. (2018)

HSC-DR1

Hikage et al. (2019)

Other probes

McCarthy et al. (2017)

Extended cosmologies

• Massive neutrinos
• Non-zero curvature
• Modified gravity
• Running spectral index
• DE with constant EoS
• Evolving dark energy EoS

Joudaki et al. (2017b)

Evolving dark energy

0.1 0.2 0.3 0.4

Ωm

0.75 1.00 1.25 1.50

σ8

KiDS-450 (w0waCDM) Planck 2015 (w0waCDM) KiDS (ΛCDM) Planck (ΛCDM) −2.4 −1.8 −1.2 −0.6 0.0

w0

−5.0 −2.5 0.0 2.5 5.0

wa

KiDS-450 Planck 2015 JLA 2014 KiDS+Planck KiDS+Planck+H0

• Resolves tension between KiDS and Planck.
• Only extension that is moderately favoured by the data.
• Resolves tension between Riess et al. (2016) and Planck.

Joudaki et al. (2017b)

Sum of neutrino masses

Joudaki et al. (2017b)

Σmν < 4eV (95% CL) from 
 KiDS-450 alone

VIKING@VISTA

• Same footprint as KiDS.
• Already finished (1350deg2).
• ZYJHKs images.
• 5σ depths of 21.2 (Ks) to 23.1 (Z).

Benefits of NIR

• 20% smaller errors due to high-z galaxies alone.
• More robust redshifts -> better calibration.

Wright et al. (2018)

Cosmological constraints

= σ8 (Ωm/0.3)0.5

Hildebrandt et al. (2018)

Cosmological constraints

= σ8 (Ωm/0.3)0.5

Hildebrandt et al. (2018)

Credit: NASA, Mauro Giavalisco, Lexi Moustakas, Peter Capak, Len Cowie and the GOODS Team.

Credit: NASA, Mauro Giavalisco, Lexi Moustakas, Peter Capak, Len Cowie and the GOODS Team.

Infrared background

9 deg

Credit: 2MASS

Euclid - Overview

• Only observe those things from space

that you can’t do well from the ground!

• ESA/NASA 1.2m Space Telescope
• optical + NIR imaging (cosmic shear)
• NIR spectroscopy (BAO)
• Launch in ∼2022 to L2 like e.g. Planck
• survey 15 000 sq. deg. in 7 years
• 1 billion lensing sources with 0<z<2

Euclid - Science Goals

• Measure w0 to <2% and wa to <10%
• Measure γ (growth factor ~0.5) to <0.02
• Constrain Σmν to <0.03eV
• PS slope ~3x better than Planck
• Lots of legacy science (NIR, deep 


fields, “all-sky” cross-correlations)

• Open huge parameter space

• 8.4m optical wide-field imaging telescope
• Huge camera, rapid survey speed, 18,000deg2 total
• Deep multi-band photometry (also time domain)
• Crucial complement to Euclid
• Very challenging big data application
• US-led with international partners; 


discussing ODF at the moment

Large Synoptic Survey Telescope

Summary & Outlook

• Tension between CMB and most low-z LSS

measurements (KV450). Systematics? New physics??

• Very exciting times:
• KiDS+VIKING ~1000deg2 now, 1350deg2 2019.
• DES has tripled area and doubled depth.
• HSC gearing up for second data release.
• Prepare with today’s data for Euclid/LSST.
• Find decisive answer on fundamental questions about


DE, DM, neutrino mass, (inflation), etc.