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Light Bending as a probe for Geometric Dark Energy

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

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Light Bending as a probe for Geometric Dark Energy

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

  2. 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 Plan of the Talk

  3. 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!) Introduction

  4. Are there alternatives to Λ? Or otherwise stated: How modify Einstein Equations in order to be compatible with observations? Introduction • 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 • 2nd way: modify LHS i.e. changing the Einstein Tensor (DGP model, Weyl Gravity,…)

  5. Up to now observational data have not been able to discriminate between ΛCDM model and other Dark Energy models(both geometric and dynamical) Introduction The aim of this talk is to analyze DE effects at astrophysical level (for systems that are decoupled from the cosmological expansion)

  6. Introduction 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) •   does not deflect light Lue astro-ph/0510068 (2005) Light Bending! •   does not deflect light

  7. Light Bending observer source mass •   does not deflect light •   does not deflect light

  8. Why is it preferred among general relativistic tests? Light Bending Schwarzschild solution in presence of  •   does not deflect light •   does not deflect light  drops out!!!

  9. Light Bending  does not deflect light!!! •   does not deflect light In agreement with Islam PLA (1983) •   does not deflect light

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

  11. Focus on Geometric DE models A parametrization of this kind introduces two scales Cosmological Scale Critical Scale In DGP model this coincides with Vainshtein radius. Therefore at scales much smaller than cosmological ones, there are some deviation from Schwarzschild results (Cluster of Galaxies!)

  12. Analityc Results F.Finelli, M.Galaverni & A.G. (2005)

  13. DGP model is the crossover scale between 4D and 5D behaviour This is why the deflection of light in this model is not rigorously vanishing! In contrast with Lue & Starkman PRD (2003)

  14. Since has to be positive in order to describe at cosmological level the recent acceleration of the universe, then the sign of is positive. DGP model

  15. 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. DGP model

  16. For a Cluster we find with ( , , ) . analytic expression is checked to be good at 0.03% DGP model

  17. DGP model Total = Schw1 + Schw2 + DE 1st order Schwarzschild Total = Schw1 + Schw2 + DE 1st + 2nd order Schwarzschild

  18. Weyl gravity when is much larger than 1 Edery and Paranjape PRD (1998)

  19. 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) Weyl gravity

  20. For a cluster we find With ( , ) Weyl gravity

  21. Weyl gravity Total = Schw1 + Schw2 + DE 1st order Schwarzschild Total = Schw1 + Schw2 + DE Total = Schw1 + Schw2 + DE 1st + 2nd order Schwarzschild

  22. 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 Conclusions

  23. 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. Conclusions

  24. DGP model

  25. Weyl gravity

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