EUCLID galaxy clustering and weak lensing at high redshift Luca Amendola INAF/Osservatorio Astronomico di Roma
Observations are converging to an unexpected universe
The dark energy problem F g μν 1 R μν g μν R= 8π GT μν 2 gravity 8π GTμν φ matter tot 1 cluster 0. 3 Solution: modify either the Matter sector DE or the Gravity sector MG
DE checklist What do we need to test DE? 1) observations at z~1 2) observations involving background and perturbations 3) independent, complementary probes
Why z~1 probes at z=0 and z=1000
Why background+perturbations The background expansion only probes H(z) The (linear) perturbations probe first order quantities ds2 =a2 [ 1 2φ dt2 1 2ψ dx 2 +dy 2 +dz2 ] Full metric reconstruction at first order H z φ k,z ψ k,z
Why independent probes a) systematics: because we need to test systematics like volutionary effects in SN Ia or biasing effects in the baryon acoustic oscillations b) theory: because in all generality we need to measure two free functions at pert. level (in addition to H(z) at background level)
Two free functions ds 2 =a2 [ 1 2φ dt2 1 2ψ dx 2 +dy 2 +dz2 ] An equivalent choice for the free functions is modified Poisson equation anisotropic stress k 2 φ= 4π Ga2 Q k,a ρm δm φ ψ η k,a = ψ
Two free functions standard gravity scalar tensor models Q k,a =1 η k,a =0 G 2 F+F'2 Q a = FGcav,0 2F 3F ' 2 η a = f(r) DGP coupled Gauss Bonnet F'2 F+F'2 k2 k2 m G a2 R a2 R Q a =, η a = FGcav,0 k2 k2 1 3m 2 1 2m 2 a R a R 1 4m Q a =1 1 ; β= 1 2 Hr c wde 3β 2 η a = 3β 1 Q a =... η a =... Boisseau et al. 2000 Acquaviva et al. 2004 Schimd et al. 2004 L.A., Kunz &Sapone 2007 Bean et al. 2006 Hu et al. 2006 Tsujikawa 2007 Lue et al. 2004; Koyama et al. 2006 see L. A., C. Charmousis, S. Davis 2006
Growth of fluctuations as a measure of modified gravity H' δk '' 1 δk ' 4π GQ k,a ρδ k=0 H Instead of Q k,a good fit we parametrize LCDM γ= 0.55 γ= 0.55[1 0. 05 w 1 ] DE γ= 0.67 DGP ST γm 1 0.5β 2 γ 0.55 is an indication of modified gravity d log δ = m a γ d log a γ=const DGP Peebles 1980 Lahav et al. 1991 Wang et al. 1999 Bernardeau 2002 L.A. 2004 Linder 2006
Growth of fluctuations as a measure of modified gravity Scalar Tensor γm 1 0.5β2 g=δ/a Di Porto & L.A. 2007
Present constraints on gamma s d log δ /d log a Viel et al. 2004,2006; McDonald et al. 2004; Tegmark et al. 2004
Present constraints on gamma sfit γm 1 η =0.6±0.4 LCDM DGP C. Di Porto & L.A. PRD 2007
Observables Correlation of galaxy positions: galaxy clustering 2 Pgal k,z =b Pmatt k,z bψ Correlation of galaxy ellipticities: galaxy weak lensing Pellipt k,z Φ+Ψ 2 Correlation of galaxy velocities: galaxy peculiar field Ψ' 2 Ppec. vel. k,z Ψb 2
Peculiar velocities Correlation of galaxy velocities: galaxy peculiar field v x δz =δ r H0 x 2 2 Pz= 1 +βμ Pr redshift distortion parameter Ψ' β= Ψb Guzzo et al. 2008
The EUCLID theorem Correlation of galaxy positions: galaxy clustering Pgal k,z =b2 Pmatt k,z bψ 2 Ψ' 2 Ppec. vel. k,z Ψb Pellipt k,z Φ+Ψ 2 Correlation of galaxy velocities: galaxy peculiar field Correlation of galaxy ellipticities: galaxy weak lensing THE EUCLID THEOREM: reconstructing Ψ,Φ,b in k,z requires An imaging tomographic survey: and a spectroscopic survey: Pellipt. k,z Pgal k,z, k,z
EUCLID a satellite mission that merges DUNE and SPACE proposals one of 4 mission selected by ESA Cosmic Vision in 2007 final selection 2011 launch 2015 2020, 5 years duration, half sky an imaging mission in several bands optical+nir (>1 billion galaxies) a spectroscopic survey: 500.000.000 galaxy redshifts a pan european collaboration current PIs: A. Refregier (DUNE), A. Cimatti (SPACE)
Requirements for Weak Lensing Statistical Requirements: a 20,000 deg2 survey at high galactic latitude ( b >30 deg) sample of at least 35 galaxies/amin2 usable for weak lensing (SNR[Sext]>7, FWHM>1.2 FWHM[PSF]) with a median z~1 and an rms shear error per galaxy of σγ=0.35 (or equivalent combination) a PSF FWHM smaller than 0.23 to be competitive with ground based surveys photometric redshifts to derive 3 redshift bins over the survey area (from ground based observations) Systematics Requirements: Survey scanned in compact regions <20 on a side, with 10% overlap between adjacent stripes a precision in the measurement of the shear after deconvolution of the PSF better than about 0.1%. This can be achieved with a PSF with a FWHM of 0.23, an ellipticity e <6% with an uncertainty after calibration of δe <0.1%. good image quality: low cosmic ray levels, reduced stray light, linear and stable CPS Review CCDs, achromatic optics CNES Paris
Science from DUNE/EUCLID Primary goal: Cosmology with WL and SNe Measurement of the evolution of the dark energy equation of state (w,w ) from z=0 to ~1 Statistics of the dark matter distribution (power spectrum, high order correlation functions Reconstruction of the primordial power spectrum (constraints on inflation) Cross correlation with CMB (Planck) Search for correlations of Galaxy shear with ISW effect, SZ effect, CMB lensing Search for DE spatial fluctuations on large scales Study of Dark Matter Haloes: Mass selected halo catalogues (about 80,000 haloes) with multi λ follow up (X ray, SZ, optical) halo mass calibration Strong lensing: probe the inner profiles of haloes Galaxy formation: Galaxy bias with galaxy galaxy and shear galaxy correlation functions Galaxy clustering with high resolution morphology Core Collapse supernovae: constraints on the history of star formation up to z~1 CPS Review CNES Paris
Weak Lensing Power Spectrum Tomography The power of WL DUNE baseline: 20,000 deg2, 35 galaxies/amin2, ground based photometry for photo z s, 3 year WL survey WL power spectrum for each z bin z>1 z<1 CPS Review CNES Paris Redshift bins from photo z s
The power of WL
Details, details FM, parameters in Modified Gravity:
Probing gravity with weak lensing In General Relativity, lensing is caused Φ=φ+ψ by the lensing potential and this is related to the matter perturbations via Poisson s equation. Therefore the lensing signal depends on two modified gravity functions { η Σ=Q 1 2 η k,a in the WL power spectrum H0 ℓ η Pell ℓ = dzf z; m,λ,etc Q 1 P m z,k = 2 r z and in the growth function Pm z,k =D z,q 2 Pm z= 0, k
Fisher matrix Tegmark, Hu, Jain... DUNE baseline: 20,000 deg2, 35 galaxies/amin2, <z>=0.9, photo z s, l_max=10000
Forecasts for WL L.A., M. Kunz, D. Sapone JCAP 2008
Forecasts for WL Marginalization over the modified gravity parameters does not spoil errors on standard parameters L.A., M. Kunz, D. Sapone 2007
Weak lensing measures Dark Gravity DGP Phenomenological DE DGP Σ0 LCDM Weak lensing tomography over half sky L.A., M. Kunz, D. Sapone arxiv:0704.2421
Weak lensing measures Dark Gravity scalar tensor model 1 1 ξφ2 R 2 Weak lensing tomography over half sky V. Acquaviva, L.A., C. Baccigalupi, in prep.
Non linearity in WL ell_max=1000,3000,10000 Weak lensing tomography over half sky
Non linearity in BAO Matarrese & Pietroni 2007
Clustering measures Dark Gravity Guzzo et al. 2008 Galaxy clustering at 0<z<2 over half sky...if you know the bias to 1%
Combining P(k) with WL Weak lensing/ BAO over half sky
Conclusions Two solutions to the DE mismatch: either add dark energy or dark gravity The high precision data of present and near future allow to test for dark energy/gravity It is crucial to combine background and perturbations A full reconstruction to first order requires imaging and spectroscopy EUCLID is a good bet...