Outline. Weak gravitational lensing. Modified gravity theories. Conclusions. Next future missions and surveys

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1 Stefano Camera CAUSTIC Cosmology Group, A. Avogadro Dept. of General Physics, Univ. of Turin, Turin National Institute for Nuclear Physics (INFN), Sect. of Turin, Turin In collaboration with A. Diaferio, D. Bertacca, N. Bartolo, S. Matarrese (Padua Univ. and INFN), T.D. Kitching, A.F. Heavens (Edinburgh Univ. and IfA), V.F. Cardone (Molise Univ. and INFN)

2 Outline Weak gravitational lensing Next future missions and surveys Modified gravity theories Unified DM and DE models Brane world cosmologies Modified action theories Conclusions

3 Kravtsov & Klypin Weak gravita/onal lensing S. Camera PPC 2010: IV International Workshop on the Interconnections Between Particle Physics and Cosmology Torino, July 12th 16th, 2010

4 Weak gravita/onal lensing Distorsion tensor: ( κ + Re[γ] Im[γ] ψ ij Im[γ] κ Re[γ] ) = χ χ(z) radial comoving distance W[χ(z)] window function [ ] Φ= Ψ Newtonian potential (in General Relativity) 0 [ ] Ψ Φ dχ χ W (χ ) 2,ij Linear theory of scalar perturbations: ds 2 = (1 + 2Φ)dt 2 + a 2 (t) (1 + 2Ψ)dx 2

5 Weak gravita/onal lensing 3D shear signal!4 C γγ (k1, k2 ;!) = 2 π!" 2 Φk (χi ) W (χi )j" (ki χi )P Φ (k, 0) dχi dk k 2 i (0) Φ ki i=1 Limber s approximation!4 C γγ (!) = 4! W 2 (χ) Φ dχ P χ6 " #!,χ χ S. Camera PPC 2010: IV International Workshop on the Interconnections Between Particle Physics and Cosmology Torino, July 12th 16th, 2010

6 Weak gravita/onal lensing The Dark Energy Survey (DES) is designed to probe the origin of the accelerating universe and help uncover the nature of dark energy by measuring the 14 billion year history of cosmic expansion with high precision. DES will create a catalogue of over 300 million galaxies looking for shear effects. The effect of lensing will depend upon how clumped the distribution of DM is and upon the distances to the lensing structure and the object being lensed. Euclid is an ESA mission to map the geometry of the dark Universe. The mission will investigate the distance redshift relationship and the evolution of cosmic structures by measuring shapes and redshifts of galaxies and galaxy clusters out to a look back time of 10 billion years. It will therefore cover the entire period over which DE played a significant role in accelerating the expansion of the Universe.

7 Modified gravity theories L = R 16πG + L m/r + L DM + Λ 8πG Unified DM and DE models Brane world cosmologies Modified action theories DM and DE as two aspects of one exotic dark fluid Accelerated expansion via leakage of gravity into extra dimensions DE (and even DM) as curvature effects L = R 16πG + L m/r + L UDM L = R(n) 16πG (n) + R(4) 16πG + L m/r + L DM L = f(r) 16πG + L m/r [+L DM ]

8 Unified DM and DE models In Unified Dark Matter (UDM) models there is only one exotic component, a scalar field which can mimic both DM and DE: H(z) =H 0 Ω m (1 + z) 3 + Ω r (1 + z) 4 + Ω Λ c s 2 (z) = ρ UDM (z) =ρ DM (z)+ρ Λ Ω Λ c 2 Ω Λ + (1 c 2 ) Ω DM (1 + z) 3 Grativational potential in ΛCDM and UDM models at different scales and for different values of c SC, Bertacca, Diaferio, Bartolo & Matarrese (2009)

9 Unified DM and DE models SC, Kitching, Heavens, Bertacca & Diaferio (2010) 3D shear signal in ΛCDM and UDM models for a Euclidlike survey

10 Unified DM and DE models Expected marginal e r r o r s o n U D M parameters from a Euclid like survey SC, Kitching, Heavens, Bertacca & Diaferio (2010)

11 Brane world cosmologies In the Dvali Gabadadze Porrati (DGP) model and its extensions the Universe is a 4D brane embedded i n an h i g h e r dimensional bulk. ] H 2 = H 0 ( Ω m (1 + z) 3 + Ω r (1 + z) 4 + Ω Λ ) [ ] Ψ Φ 2 =4πG (k, a)ρ 2 Growth factor in ΛCDM and extended DGP models for different values of r c and α Kobayashi & Tashiro (2009)

12 Brane world cosmologies SC, Diaferio & Cardone (in prep.) Shear power spectra for ΛCDM, DGP and extended DGP models compared with Euclid and DES errorbars

13 Modified ac/on theories In f(r) ( theories, the Hilbert Einstein Lagrangian is replaced by a more general function of Ricci s scalar: ] w curv Λ = = [ ] L HE = 1 (R +2Λ) 16πG H 2 = H 0 ( Ω m (1 + z) 3 + Ω r (1 + z) 4 + Ω Λ ) [ ) Rf,RR + (Ṙf,RRR Ṙ Hf,R (f Rf,R /2) 3HṘf,RR Equation of state parameter in two viable f(r) theories Cardone, SC & Diaferio (2009)

14 Conclusions The concordance cosmological model reproduces current observational data excellently; however it presents some problems (e.g. DM and DE) Modified gravity theories furnish viable alternatives to DM and/or DE by modifying the behaviour and the nature of gravity Weak gravitational lensing can powerfully investigate the LSS of the Universe, thus constraining the nature of DM & DE and of the gravitational interaction

15 Thanks