Luca Amendola INAF/Osservatorio Astronomico di Roma

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

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

3. SAIT 2008 Observations are converging… …to anunexpected universe

4. SAIT 2008 The dark energy problem gravity matter Solution: modify eitherthe Matter sector DE orthe Gravity sector MG

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

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

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

8. Simplest MG (I) : DGP (Dvali, Gabadadze, Porrati 2000)‏ • 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 brane gravity leakage SAIT 2008

9. Simplest MG (II): f(R)‏ Simplest MG (II): f(R) The simplest modification of Einstein’s gravity: f(R)‏ eg higher order corrections • 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 SAIT 2008

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

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

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

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

14. SAIT 2008 The power of the m(r) method REJECTED REJECTED REJECTED REJECTED 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 standard DE phantom DE L.A., S. Tsujikawa, 2007

17. DE observations checklist What do we need to test DE?1) observations at z~12) observations involving background and perturbations3) independent, complementary probes SAIT 2008

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

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

20. 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) SAIT 2008

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

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

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

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

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

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

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

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. 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 =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. 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. 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 Redshift bins from photo-z’s z>1 z<1

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 { in the WL power spectrum and in the growth function

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

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

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

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...