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of gravity

Luca Amendola INAF/Osservatorio Astronomico di Roma. of gravity. The dark side. Observations are converging …. …to an un expected universe. Modified gravity. Can we detect traces of modified gravity at. background linear level ? non-linear. {. }.

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of gravity

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

  2. Portsmouth 2008 Observationsareconverging… …to anunexpected universe

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

  4. 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 Portsmouth 2008

  5. 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 ! Portsmouth 2008

  6. 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 Portsmouth 2008

  7. Simplest MG (II): f(R) Let’s start with one of the simplest MG model: 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 Portsmouth 2008

  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 α (on a local minimum) λ

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

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

  11. Portsmouth 2008 Sound horizon in R+Rn 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 For all f(R) theories, define the characteristic curve: deSitter acceleration, w = -1 General acceleration, any w wrongmatter era (t1/2) goodmatter era (t2/3) for m≥0 The problem is: can we go from matter to acceleration?

  15. Portsmouth 2008 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

  16. Portsmouth 2008 The power of the m(r) method REJECTED REJECTED REJECTED REJECTED 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 standard DE phantom 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 • 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

  24. Parametrized MG: 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/matter Portsmouth 2008

  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 LCDM DGP C. Di Porto & L.A. 2007

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

  28. Portsmouth 2008 Probing gravity with weak lensing Statistical measure of shear pattern, ~1% distortion Background sources Dark matter halos Observer Radial distances depend on geometry of Universe 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 { in the WL power spectrum and in the growth function

  30. Portsmouth 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

  31. Portsmouth 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

  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 =1000,3000,10000 Weak lensing tomography over half sky

  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 Hoekstra et al. 2005 Semboloni et al. 2005 Weak Lensing First results From CFHT Legacy Survey with Megacam (w=constant and other priors assumed) Type Ia Super- novae Astier et al. 2005

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