1. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 Light Bending as a probe for Geometric Dark Energy Alessandro Gruppuso (INAF/IASF, Bologna) In collaboration with Fabio Finelli & Matteo Galaverni (INAF/IASF, Bologna) EDEN in Paris: 7th-9th December 2005, LPNHE, Paris France

2. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 Plan of the Talk Introduction Light Bending as a preferred general relativistic test to distinguish between a Cosmological Constant and other Dark Energy models Focus on Geometric Dark Energy models Analytic Results Applications to Astrophysical sets-up Conclusions

3. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 Introduction Supernova and WMAP observations provide clear evidence that the CDM model is not suitable to describe our universe. A Cosmological Term Λ is the simplest explanation for the mismatch between theory and observation But its value is completely at odd with naive estimate of the vacuum energy of quantum fluctuations! (fine- tuning!)

4. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 2nd way: modify LHS i.e. changing the Einstein Tensor (DGP model, Weyl Gravity,…) Introduction Are there alternatives to Λ? Or otherwise stated: How modify Einstein Equations in order to be compatible with observations? 1st way: modify RHS i.e. considering an additional field such that p/ρ < -1/3 (quintessence models,…) Dynamical Dark Energy models Geometric Dark Energy models

5. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 Introduction Up to now observational data have not been able to discriminate between ΛCDM model and other Dark Energy models (both geometric and dynamical) The aim of this talk is to analyze DE effects at astrophysical level (for systems that are decoupled from the cosmological expansion)

6. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 Introduction   does not deflect light Light Bending! The importance of DE effects in Astrophysical tests is already known. In particular the perihelion precession of Mars in DGP model is found to be close to the sensitivity of the next experiments. Dvali, Gruzinov & Zaldarriaga PRD (2003) Lue & Strakman PRD (2003) Lue astro-ph/0510068 (2005)

7. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 Light Bending   does not deflect light observersource mass

8. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 Light Bending Why is it preferred among general relativistic tests? Schwarzschild solution in presence of    does not deflect light  drops out!!!

9. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 Light Bending   does not deflect light  does not deflect light!!! In agreement with Islam PLA (1983)

10. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 Focus on Geometric DE models Consider a metric of the following form A solution of this kind come from gDE and DGP model Dvali, Gabadadze & Porrati PLB (2000) In DGP theory there is a maximum scale (Vainshtein scale) and Weyl gravity Mannheim & Kazanas ApJ (1989)

11. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 Focus on Geometric DE models Therefore at scales much smaller than cosmological ones, there are some deviation from Schwarzschild results (Cluster of Galaxies!) Cosmological Scale Critical Scale A parametrization of this kind introduces two scales In DGP model this coincides with Vainshtein radius.

12. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 Analityc Results F.Finelli, M.Galaverni & A.G. (2005)

13. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 DGP model This is why the deflection of light in this model is not rigorously vanishing! is the crossover scale between 4D and 5D behaviour In contrast with Lue & Starkman PRD (2003)

14. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 DGP model Since has to be positive in order to describe at cosmological level the recent acceleration of the universe, then the sign of is positive.

15. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 DGP model In which astrophysical system the contribution is the largest? Since (and is constrained by cosmology to be of the order of 5 Gpc) we found that it is the largest for Cluster of galaxies.

16. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 DGP model For a Cluster we find with (,, ). analytic expression is checked to be good at 0.03%

17. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 DGP model Total = Schw1 + Schw2 + DE 1st order Schwarzschild 1st + 2nd order Schwarzschild Total = Schw1 + Schw2 + DE

18. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 Weyl gravity when is much larger than 1 Edery and Paranjape PRD (1998)

19. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 Weyl gravity can be positive or negative depending on the sign of. As in DGP case the contribution is the largest for the largest astrophysical system (i.e.: cluster of galaxies)

20. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 Weyl gravity For a cluster we find With (, )

21. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 Weyl gravity 1st order Schwarzschild 1st + 2nd order Schwarzschild Total = Schw1 + Schw2 + DE

22. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 Conclusions Light Bending is studied in a static spherically symmetric space time non asymptotically flat ( ). These terms cannot be parametrized in the usual PPN approach! This kind of solution is justified in the context of gDE models but it might be that also dDE models are included in the parametrized metric Since Λ does not deflect light, it is a preferred test for the study of DE models in astrophysical context

23. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 Conclusions In both cases the DE contribution to light deflection is much greater than Schw one at higher orders In both cases the main deviation from Λ is given by Cluster of Galaxies. In DGP model we have a small effect with respect to Weyl gravity for two reasons 1) The coefficient is smaller and 2) the geometric factor is smaller.

24. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 DGP model sun gal g.gal cluster

25. Light Bending as a probe of Geometric Dark Energy modelsEDEN, Paris December 8,2005 Weyl gravity sun gal g.gal cluster