Munich 2008 Luca Amendola INAF/Osservatorio Astronomico di Roma The dark side of gravity

Munich 2008 Why DE/MG is interesting How to observe it g

Munich 2008 Observations are converging… …to an unexpected universe

Munich 2008 Classifying the unknown a) change the equations i.e. add new matter field (DE) or modify gravity (MG) b) change the metric i.e. inhomogeneous non-linear effects, void models, etc Standard cosmology: GR gravitational equations + FRW metric

Munich 2008 Which are the effects of modified gravity at background linear level ? non-linear { } Modified gravity

Munich 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 !

Munich 2008 How to hide modified gravity (in the solar system) L.A., C. Charmousis, S. Davis, PRD 2008, arXiv Generalized Brans-Dicke- Gauss-Bonnet Lagrangian Solution in static spherical symmetry in a linearized PPN metric with Conclusion: there are solutions which look “Einsteinian” but are not…

Munich 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)

Munich 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 MG in 4D: f(R) Simplest MG (II): f(R)

Munich 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 λ Adelberger et al. 2005

Munich 2008 The fourfold way out of local gravity { depend on time depend on space depend on local density depend on species

Munich 2008 Sound horizon in R+R - n model L.A., D. Polarski, S. Tsujikawa, PRL 98, , astro-ph/ Turner, Carroll, Capozziello etc in the Matter Era !

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

Munich 2008 MG in the background (JF) An autonomous dynamical system characteristic function

Munich 2008 MG in the background ΩKΩK ΩPΩP ΩγΩγ

Munich 2008 Classification of f(R) solutions deSitter acceleration, w = -1 General acceleration, any w For all f(R) theories: wrong matter era (t 1/2 ) good matter era (t 2/3 ) for m≥0

Munich 2008 The power of the m(r) method REJECTED

Munich 2008 The triangle of viable trajectories cosmologically viable trajectories Notice that in the triangle m>0 L.A., D. Polarski, S. Tsujikawa 2007 PRD astro-ph/

Munich 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 Navarro & Van Acoyelen 2006; Faraoni 2006; Bean et al. 2006; Chiba et al. 2006; Hu, Sawicky 2007; Mota et al. 2006;....

Munich 2008 c LGC+Cosmology Take for instance the ΛCDM clone Applying the criteria of LGC and background cosmology i.e. ΛCDM to an incredible precision

Munich 2008 What background hides perturbations reveal The background expansion only probes H(z) The (linear) perturbations probe first-order quantities Full metric reconstruction at first order requires 3 functions

Munich 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 (most of what follows in collaboration with M. Kunz, D. Sapone)

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

Munich 2008 Reconstruction of the metric Correlation of galaxy positions: galaxy clustering Correlation of galaxy ellipticities: galaxy weak lensing

Munich 2008 Peculiar velocities Correlation of galaxy velocities: galaxy peculiar field Guzzo et al redshift distortion parameter  =0.70±0. 2

Munich 2008 The Euclid theorem We can measure 3 combinations and we have 2 theoretical relations… Observables:Conservation equations: Theorem: lensing+galaxy clustering allows to measure all (total matter) perturbation variables at first order without assuming any particular gravity theory 5 unknown variables:

Munich 2008 The Euclid theorem We can measure 3 combinations and we have 2 theoretical relations… Observables:Conservation equations: Theorem: lensing+galaxy clustering allows to measure all (total matter) perturbation variables at first order without assuming any particular gravity theory 5 unknown variables:

Munich 2008 The Euclid theorem From these we can estimate deviations from Einstein’s gravity:

Munich 2008 Euclid A geometrical probe of the universe proposed for Cosmic Vision =+ All-sky optical imaging for gravitational lensing All-sky near-IR spectra to H=22 for BAO

Munich 2008 Weak lensing Weak lensing tomography over half sky LCDM DGP L.A., M. Kunz, D. Sapone arXiv: DiPorto & L.A Euclid forecastPresent constraints

Munich 2008 Power spectrum Galaxy clustering at 0<z<2 over half sky....if you know the bias to 1%

Munich 2008 Non-linearity in BAO Matarrese & Pietroni 2007

Munich 2008 Poster advertisement See poster by Miguel Quartin… Quercellini, Quartin & LA, arXiv LTB void model Garcia-Bellido & Haugbolle 2008 Cosmic parallax

Munich 2008 Conclusions  Two solutions to the DE mismatch: either add “dark energy” or “dark gravity”  High-precision next generation cosmological observations are the best tool to test for modifications of gravity  It is crucial to combine background and perturbations  A full reconstruction to first order requires imaging and spectroscopy: Euclid

Munich 2008 Luca Amendola INAF/Osservatorio Astronomico di Roma The bright side of Munich

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

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

Munich 2008 Non-linearity in BAO Matarrese & Pietroni 2007

Munich 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...

Munich 2008 References L.A., Phys. Rev. D62, , 2000; Basics: L.A., Phys. Rev. D62, , 2000; L.A., Phys. Rev. Lett. 86,196,2001; CMB: L.A., Phys. Rev. Lett. 86,196,2001; L.A. & D. Tocchini-Valentini, PRD66, , 2002 Bias: L.A. & D. Tocchini-Valentini, PRD66, , 2002 astro-ph/ , Phys Rev 2003 WMAP: astro-ph/ , Phys Rev 2003 : A. Maccio’ et al N-body: A. Maccio’ et al Dilatonic dark energy: L.A., M. Gasperini, D. Tocchini-Valentini, C. Ungarelli, Phys. Rev. D67, , 2003

Munich 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 Semboloni et al Astier et al. 2005