Cosmological Weak Gravitational Lensing Hendrik Hildebrandt - Ruhr-Universität Bochum
Credit: LSST
Λ CDM Cosmological Constant / Vacuum Energy / Dark Energy Credit: Planck
Gravitational light deflection Credit: Michael Sachs
Gravitational lens MASS
Optical lens
Gravitational lens analogue Spherical abberation!
Weak lensing Mellier (1999) ✏ = ✏ ( s ) + g D ✏ ( s ) E h ✏ i = + h g i = h g i
Dark matter in the bullet cluster separated from the hot X-ray gas Credit: NASA, ESA, and D. Clowe
Dark matter maps
Cosmic shear Sensitive to: • Matter distribution • Geometry Observables: • Ellipticities • Photo- z Statistical measurement of many galaxies Wittman et al. (2000)
2pt shear correlation functions ξ + ( ϑ ) ξ − ( ϑ ) 10 -4 Shear correlation 10 -5 10 -6 10 -7 1 10 100 Kilbinger et al. (2013) ϑ [arcmin] Very directly related to the matter power spectrum P δ .
Observation -> theory ξ ± ( θ ) = ⟨ γ t γ t ⟩ ( θ ) ± ⟨ γ × γ × ⟩ ( θ ) � ∞ � ∞ d ℓ ℓ d ℓ ℓ ξ + ( θ ) = 2 π J 0 ( ℓθ ) P κ ( ℓ ) ; ξ − ( θ ) = 2 π J 4 ( ℓθ ) P κ ( ℓ ) 0 0 � χ h P κ ( ℓ ) = 9 H 4 0 Ω 2 d χ g 2 ( χ ) � � ℓ m a 2 ( χ ) P δ f K ( χ ) , χ 4 c 4 0 � χ h d χ ′ p χ ( χ ′ ) f K ( χ ′ − χ ) g ( χ ) = f K ( χ ′ ) χ
Cosmological constraints • Measure amount of clustered matter • S 8 = σ 8 ( Ω m /0.3) 0.5 Kilbinger et al. (2013)
S 8 results over the years 1 . 1 COSMOS 100 deg 2 CFHTLS/CFHTLenS SDSS-Stripe82 1 . 0 DLS SDSS-DR7 CMB 0 . 9 σ 8 ( Ω m / 0 . 3) α 0 . 8 0 . 7 0 . 6 0 . 5 2006 2008 2010 2012 2014 year Kilbinger (2015)
Dark energy e.o.s. w = p / ρ ; w ( a ) = w 0 + w a (1- a ) ; a = 1/(1+ z ) Joudaki et al. (2017b)
Massive neutrinos Joudaki et al. (2017b)
Warm dark matter − 4 10 l(l+1)C l /2 ! m WDM >2.5keV with Euclid m WDM = 250 eV − 5 m WDM = 500 eV 10 m WDM = 1 keV CDM 0.1 2 3 4 10 10 10 multipole, l Markovi č et al. (2011)
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
HSC: Hyper-Suprime Cam Survey KiDS: Kilo Degree Survey DES: Dark Energy Survey
KiDS-450 CFHTLenS (MID J16) 1.2 WMAP9+ACT+SPT Planck15 1 1.0 σ 8 0.8 0.6 0.1 0.2 0.3 0.4 Ω m
KiDS-450 CFHTLenS (MID J16) 1.2 WMAP9+ACT+SPT Planck15 2 1.0 σ 8 0.8 0.6 0.1 0.2 0.3 0.4 Ω m
KiDS-450 CFHTLenS (MID J16) 1.2 WMAP9+ACT+SPT Planck15 3 1.0 σ 8 0.8 0.6 0.1 0.2 0.3 0.4 Ω m
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KiDS-450 KiDS-450 1.2 0.88 CFHTLenS (MID J16) WMAP9+ACT+SPT σ 8 ( Ω m / 0.3) 0.5 Planck15 1.0 0.80 σ 8 0.8 0.72 0.6 0.64 0.16 0.24 0.32 0.40 0.16 0.24 0.32 0.40 Ω m Ω m Hildebrandt et al. (2017)
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 1.50 KiDS-450 ( w 0 w a CDM) KiDS-450 5.0 Planck 2015 ( w 0 w a CDM) Planck 2015 KiDS ( Λ CDM) JLA 2014 1.25 KiDS+Planck 2.5 Planck ( Λ CDM) KiDS+Planck+ H 0 σ 8 w a 1.00 0.0 0.75 − 2.5 − 5.0 0.1 0.2 0.3 0.4 − 2.4 − 1.8 − 1.2 − 0.6 0.0 Ω m Joudaki et al. (2017b) w 0 • Resolves tension between KiDS and Planck. • Only extension that is moderately favoured by the data. • Resolves tension between Riess et al. (2016) and Planck.
Sum of neutrino masses Σ m ν < 4eV (95% CL) from KiDS-450 alone Joudaki et al. (2017b)
VIKING@VISTA • Same footprint as KiDS. • Already finished (1350deg 2 ). • ZYJHK s images. • 5 σ depths of 21.2 ( K s ) 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 = σ 8 ( Ω m /0.3) 0.5 Hildebrandt et al. (2018)
Cosmological constraints = σ 8 ( Ω m /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 w 0 to <2% and w a to <10% • Measure γ (growth factor ~0.5) to <0.02 • Constrain Σ m ν to <0.03eV • PS slope ~3x better than Planck • Lots of legacy science (NIR, deep fields, “all-sky” cross-correlations) • Open huge parameter space
Large Synoptic Survey Telescope • 8.4m optical wide-field imaging telescope • Huge camera, rapid survey speed, 18,000deg 2 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
Summary & Outlook • Tension between CMB and most low-z LSS measurements (KV450). Systematics? New physics?? • Very exciting times: • KiDS+VIKING ~1000deg 2 now, 1350deg 2 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.
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