1. Bologna 2007 of gravity Luca Amendola INAF/Osservatorio Astronomico di Roma The dark side

2. Bologna 2007 Observations are converging… …to an unexpected universe

3. Bologna 2007 The dark energy problem gravity matter Solution: modify either the Matter sector or the Gravity sector...but remember : DE MG

4. Bologna 2007 Modified matter Problem: All the matter particles we know possess an effective interaction range that is much smaller the cosmological ones the effective pressure is always positive ! Solution: add new forms of matter with strong interaction/self-interaction the effective pressure can be large and negative Dark Energy=scalar fields, generalized perfect fluids etc

5. Bologna 2007 Can we detect traces of modified gravity at background linear level ? non-linear { } Modified gravity

6. Bologna 2007 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

7. Bologna 2007 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 !

8. Bologna 2007 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)

9. Bologna 2007 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)

10. Bologna 2007 f(R) is popular....

11. Bologna 2007 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

12. Bologna 2007 Dark Fog The trouble with f(R): it’s Fourth Order Gravity (FOG) ! Higher order equations introduce: new solutions (acceleration ?) new instabilities (is the universe stable?)

13. Bologna 2007 The simplest case In Einstein Frame Turner, Carroll, Capozziello etc. 2003

14. Bologna 2007 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:

15. Bologna 2007 Sound horizon in R+R n model...and by the way L.A., D. Polarski, S. Tsujikawa, PRL 98, 131302, astro-ph/0603173

16. Bologna 2007  cl) WMAP and the coupling  Planck:  L.A., C. Quercellini et al. 2003

17. Bologna 2007 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

18. Bologna 2007 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

19. Bologna 2007 The power of the m(r) method REJECTED

20. Bologna 2007 The triangle of viable trajectories There exist only two kinds of cosmologically viable trajectories Notice that in the triangle m>0

21. Bologna 2007 Constraints on viable trajectories Cosmological constraints Constraint from the matter expansion: CMB peak requires m(past)<0.1 Constraint from accelerated expansion: SN require m(present)<0.1

22. Bologna 2007 Viable trajectories are cool ! Viable trajectories have a very peculiar effective equation of state Define w DE implicitely as We find Theorem: diverges if grows in the past, i.e. if Corollary: all viable f(R) cosmologies possess a divergent L.A., S. Tsujikawa, 2007

23. Bologna 2007 Phantom crossing Conclusions: 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

24. Bologna 2007 Crossing/singularity as signatures of modified gravity The same phenomenon occurs for  DGP (Alam et al 2005)  Scalar,Vector, Tensor models (Libanov et al. 2007)  and in the Riess et al. (2004) dataset !! Nesseris Perivolaropoulos 2005

25. Bologna 2007...but don’t forget the Local Gravity Constraints... However, if we apply naively the LGC at the present epoch.

26. Bologna 2007 relaxing the Local Gravity Constraints ? However, the mass depends 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;....

27. Bologna 2007 LGC+Cosmology Take for instance the ΛCDM clone Applying the criteria of LGC and Cosmology i.e. ΛCDM to an incredible precision

28. Bologna 2007 However... perturbations

29. Bologna 2007 MG at the linear level At the linear perturbation level and sub-horizon scales, a modified gravity model will  modify Poisson’s equation  induce an anisotropic stress  modify the growth of perturbations

30. Bologna 2007 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

31. Bologna 2007 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

32. Bologna 2007 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 the two modified gravity functions and in the growth function in the WL power spectrum

33. Bologna 2007 Growth of fluctuations A good fit to the linear growth of fluctuations is where LCDM DE DGP ST we parametrize Instead of Peebles 1980 Lahav et al. 1991 Wang et al. 1999 Bernardeau et al. 2002 L.A. 2004 Linder 2006

34. Bologna 2007 Weak lensing measures Dark Gravity DGPPhenomenological DE Weak lensing tomography over half sky LCDM DGP L.A., M. Kunz, D. Sapone arXiv:0704.2421

35. Bologna 2007 Weak lensing measures Dark Gravity scalar-tensor model Weak lensing tomography over half sky V. Acquaviva, L.A., C. Baccigalupi, in prep.

36. Bologna 2007 Weak lensing measures Dark Gravity Marginalizing over modified gravity parameters FOM

37. Bologna 2007 Non-linearity N-Body simulations Higher-order perturbation theory Maccio’ et al. 2004 Jain et al. 2006.... Kamionkowski et al. 2000 Gaztanaga et al. 2003 Freese et al. 2002 Makler et al. 2004 Lue et al. 2004 L.A. & C. Quercellini 2004....

38. Bologna 2007 N-body simulations in MG Two effects: DM mass is varying, G is different for baryons and DM mbmb mcmc Dark energy/dark matter coupling

39. Bologna 2007 N-body simulations A. Maccio’, L.A.,C. Quercellini, S. Bonometto, R. Mainini 2004 Λ β=0.15 β=0.25

40. Bologna 2007 N-body simulations β=0.15 β=0.25

41. Bologna 2007 N-body simulations: halo profiles β-dependent behaviour towards the halo center. Higher β: smaller r c

42. Bologna 2007 Conclusions: the teachings of DE  There is much more than meets the eyes in the Universe  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  It is crucial to combine background and perturbations  Weak Lensing is a good bet...(to be continued)

43. Bologna 2007

44. An ultra-light scalar field Abundance Mass L.A. & R. Barbieri 2005 Adopting a PNGB potential Hubble size Galactic size

45. Bologna 2007 Dark energy as scalar gravity Einstein frame Jordan frame

46. Bologna 2007 An extra gravity Newtonian limit: the scalar interaction generates an attractive extra-gravity Yukawa term in real space

47. Bologna 2007 Understanding dark energy Let him who seeks continue seeking until he finds. When he finds, he will become troubled. When he becomes troubled, he will be astonished Coptic Gospel of Thomas

48. Bologna 2007

49. An ultra-light scalar field Abundance Mass L.A. & R. Barbieri 2005 Adopting a PGB potential Hubble size Galactic size