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

2. Portsmouth 2008 Observations are converging… …to an unexpected universe

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

4. Portsmouth 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

5. Portsmouth 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 !

6. Portsmouth 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 Simplest MG (I): DGP (Dvali, Gabadadze, Porrati 2000)

7. Portsmouth 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 Let’s start with one of the simplest MG model: f(R) Simplest MG (II): f(R)

8. Portsmouth 2008 Is this already ruled out by local gravity? is a scalar-tensor theory with Brans-Dicke parameter ω=0 or a coupled dark energy model with coupling β=1/2 (on a local minimum) α λ

9. Portsmouth 2008 The simplest case In Einstein Frame Turner, Carroll, Capozziello etc. 2003

10. Portsmouth 2008 R-1/R model : the φ MDE R-1/R model : the φ MDE rad mat field rad mat field  MDE today Caution: Plots in the Einstein frame! instead of !! In Jordan frame:

11. Portsmouth 2008 Sound horizon in R+R n model L.A., D. Polarski, S. Tsujikawa, PRL 98, 131302, astro-ph/0603173

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

13. Portsmouth 2008 MG in the background (JF) An autonomous dynamical system characteristic function

14. Portsmouth 2008 Classification of f(R) solutions deSitter acceleration, w = -1 General acceleration, any w For all f(R) theories, define the characteristic curve: The problem is: can we go from matter to acceleration? wrong matter era (t 1/2 ) good matter era (t 2/3 ) for m≥0

15. Portsmouth 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

16. Portsmouth 2008 The power of the m(r) method REJECTED

17. Portsmouth 2008 The triangle of viable trajectories There exist only two kinds of cosmologically viable trajectories Notice that in the triangle m>0

18. Portsmouth 2008 A theorem on viable models 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

19. Portsmouth 2008 Local Gravity Constraints are very tight Depending on the local field configuration depending on the experiment: laboratory, solar system, galaxy see eg. Nojiri & Odintsov 2003; Brookfield et al. 2006 Navarro & Van Acoyelen 2006; Faraoni 2006; Bean et al. 2006; Chiba et al. 2006; Hu, Sawicky 2007;....

20. Portsmouth 2008 LGC+Cosmology Take for instance the ΛCDM clone Applying the criteria of LGC and Cosmology i.e. ΛCDM to an incredible precision

21. Portsmouth 2008 However... perturbations

22. Portsmouth 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

23. Portsmouth 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

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

25. Portsmouth 2008 Present constraints on gamma Viel et al. 2004,2006; McDonald et al. 2004; Tegmark et al. 2004

26. Portsmouth 2008 Present constraints on gamma C. Di Porto & L.A. 2007 DGP LCDM

27. Portsmouth 2008 Two MG observables Correlation of galaxy positions: galaxy clustering Correlation of galaxy ellipticities: galaxy weak lensing

28. Portsmouth 2008 Observer Dark matter halos Background sources Radial distances depend on geometry of Universe Probing gravity with weak lensing Statistical measure of shear pattern, ~1% distortion Foreground mass distribution depends on growth/distribution of structure

29. Portsmouth 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 {

30. Portsmouth 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

31. Portsmouth 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

32. Portsmouth 2008 Weak lensing measures Dark Gravity scalar-tensor model Weak lensing tomography over half sky V. Acquaviva, L.A., C. Baccigalupi, in prep.

33. Portsmouth 2008 Non-linearity in WL Weak lensing tomography over half sky =1000,3000,10000

34. Portsmouth 2008 Non-linearity in BAO Matarrese & Pietroni 2007

35. Portsmouth 2008 Conclusions: the teachings of DE  Two solutions to the DE mismatch: either add “dark energy” or “dark gravity”  The high precision data of present and near-future observations allow to test for dark energy/gravity  New MG parameters: γ,Σ  A general reconstruction of the first order metric requires galaxy correlation and galaxy shear  Let EUCLID fly...

36. Portsmouth 2008 Current Observational Status: CFHTLS First results From CFHT Legacy Survey with Megacam (w=constant and other priors assumed) Weak Lensing Type Ia Super- novae Hoekstra et al. 2005 Semboloni et al. 2005 Astier et al. 2005