EUCLID galaxy clustering and weak lensing at high redshift

Transcription

1 EUCLID galaxy clustering and weak lensing at high redshift Luca Amendola INAF/Osservatorio Astronomico di Roma

2 Observations are converging to an unexpected universe

3 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

4 DE checklist What do we need to test DE? 1) observations at z~1 2) observations involving background and perturbations 3) independent, complementary probes

5 Why z~1 probes at z=0 and z=1000

6 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

7 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)

8 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

9 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 Acquaviva et al Schimd et al L.A., Kunz &Sapone 2007 Bean et al Hu et al Tsujikawa 2007 Lue et al. 2004; Koyama et al see L. A., C. Charmousis, S. Davis 2006

10 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[ 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 Wang et al Bernardeau 2002 L.A Linder 2006

11 Growth of fluctuations as a measure of modified gravity Scalar Tensor γm 1 0.5β2 g=δ/a Di Porto & L.A. 2007

12 Present constraints on gamma s d log δ /d log a Viel et al. 2004,2006; McDonald et al. 2004; Tegmark et al. 2004

13 Present constraints on gamma sfit γm 1 η =0.6±0.4 LCDM DGP C. Di Porto & L.A. PRD 2007

14 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

15 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

16 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

17 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 , 5 years duration, half sky an imaging mission in several bands optical+nir (>1 billion galaxies) a spectroscopic survey: galaxy redshifts a pan european collaboration current PIs: A. Refregier (DUNE), A. Cimatti (SPACE)

18 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

19 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

20 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

21 The power of WL

22 Details, details FM, parameters in Modified Gravity:

23 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

24 Fisher matrix Tegmark, Hu, Jain... DUNE baseline: 20,000 deg2, 35 galaxies/amin2, <z>=0.9, photo z s, l_max=10000

25 Forecasts for WL L.A., M. Kunz, D. Sapone JCAP 2008

26 Forecasts for WL Marginalization over the modified gravity parameters does not spoil errors on standard parameters L.A., M. Kunz, D. Sapone 2007

27 Weak lensing measures Dark Gravity DGP Phenomenological DE DGP Σ0 LCDM Weak lensing tomography over half sky L.A., M. Kunz, D. Sapone arxiv:

28 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.

29 Non linearity in WL ell_max=1000,3000,10000 Weak lensing tomography over half sky

30 Non linearity in BAO Matarrese & Pietroni 2007

31 Clustering measures Dark Gravity Guzzo et al Galaxy clustering at 0<z<2 over half sky...if you know the bias to 1%

32 Combining P(k) with WL Weak lensing/ BAO over half sky

33 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...