1. SAIT 2008 Luca Amendola INAF/Osservatorio Astronomico di Roma The dark side of gravity

2. SAIT 2008 Why DE is interesting How to observe it g

3. SAIT 2008 Observations are converging… …to an unexpected universe

4. SAIT 2008 gravity matter Solution: modify either the Matter sector or the Gravity sector DE MG The dark energy problem

5. SAIT 2008 Can we detect traces of modified gravity at background linear level ? non-linear { } Modified gravity

6. SAIT 2008 What is gravity ? A universal force in 4D mediated by a massless tensor field What is modified gravity ? What is modified gravity ? A non-universal force in nD mediated by (possibly massive) tensor, vector and scalar fields What is modified gravity?

7. SAIT 2008 Cosmology and modified gravity in laboratory in the solar system at astrophysical scales at cosmological scales } very limited time/space/energy scales; only baryons complicated by non-linear/non- gravitational effects unlimited scales; mostly linear processes; baryons, dark matter, dark energy ! Cosmology and modified gravity

8. SAIT 2008 L = crossover scale: 5D gravity dominates at low energy/late times/large scales 4D gravity recovered at high energy/early times/small scales 5D Minkowski bulk: infinite volume extra dimension gravity leakage brane (Dvali, Gabadadze, Porrati 2000)‏ Simplest MG (I) : DGP

9. SAIT 2008 f(R) models are simple and self-contained (no need of potentials) easy to produce acceleration (first inflationary model) high-energy corrections to gravity likely to introduce higher- order terms particular case of scalar-tensor and extra-dimensional theory eg higher order corrections The simplest modification of Einstein’s gravity: f(R)‏ Simplest MG (II): f(R)‏ Simplest MG (II): f(R)

10. SAIT 2008 Is this already ruled out by local gravity? (on a local minimum) α λ Is MG already ruled out by local gravity ? Yukawa correction to Newton’s potential

11. SAIT 2008 From dark energy to dark force From dark energy to dark force rad mat field rad mat field  MDE today instead of !! In Jordan frame: From Dark Energy to Dark Force L.A., D. Polarski, S. Tsujikawa, PRL 98, 131302, astro-ph/0603173

12. SAIT 2008 A recipe to modify gravity Can we find f(R) models that work? A recipe for modified gravity

13. SAIT 2008 The m,r plane The dynamics becomes 1-dimensional ! The qualitative behavior of any f(R) model can be understood by looking at the geometrical properties of the m,r plot m(r) curve crit. line acceleration matter era deSitter L.A., D. Polarski, S. Tsujikawa, PRD, astro-ph/0612180 The m,r plane

14. SAIT 2008 The power of the m(r) method REJECTED

15. SAIT 2008 The triangle of viable trajectories There exist only two kinds of cosmologically viable trajectories

16. SAIT 2008 A theorem on phantom crossing Theorem: for all viable f(R) models  there is a phantom crossing of  there is a singularity of  both occur typically at low z when phantom DE standard DE L.A., S. Tsujikawa, 2007

17. SAIT 2008 What do we need to test DE? 1) observations at z~1 2) observations involving background and perturbations 3) independent, complementary probes DE observations checklist

18. SAIT 2008 Why z~1 probes at z=0 and z=1000

19. SAIT 2008 Why background+perturbations The background expansion only probes H(z) The (linear) perturbations probe first-order quantities Full metric reconstruction at first order

20. SAIT 2008 Why independent probes a) systematics: because we need to test systematics like evolutionary effects in SN Ia, biasing effects in the baryon acoustic oscillations, intrinsic alignments in lensing, etc. b) theory: because in all generality we need to measure two free functions at pert. level (in addition to H(z) at background level)

21. SAIT 2008 Two free functions At the linear perturbation level and sub-horizon scales, a modified gravity model will  modify Poisson’s equation  induce an anisotropic stress

22. SAIT 2008 MG at the linear level  scalar-tensor models  standard gravity  DGP  f(R) Lue et al. 2004; Koyama et al. 2006 Bean et al. 2006 Hu et al. 2006 Tsujikawa 2007  coupled Gauss-Bonnet see L. A., C. Charmousis, S. Davis 2006 Boisseau et al. 2000 Acquaviva et al. 2004 Schimd et al. 2004 L.A., Kunz &Sapone 2007

23. SAIT 2008 Growth of fluctuations as a measure of modified gravity we parametrize Instead of LCDM DE DGP ST is an indication of modified gravity good fit Peebles 1980 Lahav et al. 1991 Wang et al. 1999 Bernardeau 2002 L.A. 2004 Linder 2006 Di Porto & L.A. 2007

24. SAIT 2008 Present constraints on gamma Viel et al. 2004,2006; McDonald et al. 2004; Tegmark et al. 2004 Present constraints on gamma

25. SAIT 2008 Present constraints on gamma C. Di Porto & L.A. Phys.Rev. 2007 DGP LCDM

26. SAIT 2008 Observables Correlation of galaxy positions: galaxy clustering Correlation of galaxy ellipticities: galaxy weak lensing Correlation of galaxy velocities: galaxy peculiar field

27. SAIT 2008 Peculiar velocities Correlation of galaxy velocities: galaxy peculiar field Guzzo et al. 2008 redshift distortion parameter

28. SAIT 2008 The EUCLID theorem reconstructing in k,z requires An imaging tomographic survey and a spectroscopic survey: THE EUCLID THEOREM: Correlation of galaxy positions: galaxy clustering Correlation of galaxy ellipticities: galaxy weak lensing Correlation of galaxy velocities: galaxy peculiar field

29. SAIT 2008 DUNE x SPACE = 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

30. 30CPS Review CNES Paris Requirements for Weak Lensing Statistical Requirements: a 20,000 deg 2 survey at high galactic latitude (|b|>30  deg) sample of at least 35 galaxies/amin 2 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  =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 |  e|<0.1%. good image quality: low cosmic ray levels, reduced stray light, linear and stable CCDs, achromatic optics Photometric redshifts with precision ∆z<0.1 in a subset of the survey to place limits on the intrinsic correlations of galaxy shapes (from ground based observations)‏

31. 31CPS Review 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- 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 Fundamental tests: – Test of gravitational instability paradigm – Dark Energy clustering – Distinguish dark energy from modification of gravity

32. 32CPS Review CNES Paris Weak Lensing Power Spectrum Tomography DUNE baseline: 20,000 deg 2, 35 galaxies/amin 2, ground-based photometry for photo-z’s, 3 year WL survey z>1 z<1 Redshift bins from photo-z’s WL power spectrum for each z-bin The power of WL

33. SAIT 2008 The power of WL

34. SAIT 2008 Probing gravity with weak lensing In General Relativity, lensing is caused 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 and in the growth function in the WL power spectrum {

35. SAIT 2008 Forecasts for Weak Lensing L.A., M. Kunz, D. Sapone JCAP 2007 Marginalization over the modified gravity parameters does not spoil errors on standard parameters

36. SAIT 2008 Weak lensing measures Dark Gravity DGPPhenomenological DE Weak lensing tomography over half sky LCDM DGP L.A., M. Kunz, D. Sapone arXiv:0704.2421

37. SAIT 2008 Non-linearity in WL Weak lensing tomography over half sky ell_max=1000,3000,10000

38. SAIT 2008 Non-linearity in BAO Matarrese & Pietroni 2007

39. SAIT 2008 Clustering measures Dark Gravity Galaxy clustering at 0<z<2 over half sky....if you know the bias to 1%

40. SAIT 2008 Combining P(k) with WL Weak lensing/ BAO over half sky

41. SAIT 2008 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  Let EUCLID fly...