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L. Perivolaropoulos http://leandros.physics.uoi.gr Department of Physics University of Ioannina

Open page. Reconstruction of Scalar-Tensor Theories from the Hubble Expansion History. L. Perivolaropoulos http://leandros.physics.uoi.gr Department of Physics University of Ioannina. Main Points. Dark Energy Equation of State w(z) may be crossing the w=-1 line.

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L. Perivolaropoulos http://leandros.physics.uoi.gr Department of Physics University of Ioannina

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  1. Open page Reconstruction of Scalar-Tensor Theories from the Hubble Expansion History L. Perivolaropouloshttp://leandros.physics.uoi.gr Department of Physics University of Ioannina

  2. Main Points Dark Energy Equation of State w(z) may be crossing the w=-1 line Minimally Coupled Quintessence is inconsistent with such crossing Scalar Tensor Quintessence is consistent with w=-1 crossing L.P. accepted in JCAP (2005)

  3. Best Fit Parametrizations Almost 2σ better than ΛCDM Crossing Phantom Divide w=-1 Gold Dataset (157 SNeIa): Riess et. al. 2004

  4. Basic Question What theory produces the features of best parametrizations?

  5. Minimally Coupled Scalar: No w=-1 crossing Homogeneous Minimally Coupled Scalar: +: Quintessence -: Phantom Equation of State: To cross the w=-1 line the kinetic energy term must change sign (impossible for single phantom or quintessence field) Generalization for k-essence:

  6. Non-minimal Coupling: Scalar Tensor Theories Non-minimal Coupling Rescale Φ Theory Defined by Minimal Coupling

  7. Why Scalar-Tensor Theories? 1. Fundamental theories involving extra dimensions to unify gravity reduce to scalar-tensor theories (string theory-dilaton, Kaluza-Klein,...) 2. The evolution of Fundamental Constants is an appealing idea (eg Dirac large number hypothesis) 3. Scalar Tensor theories are consistent with an equation of state w(z) crossing the w=-1 line

  8. Why Not Scalar-Tensor Theories Sringent Observational Constraints: Solar System: Cosmology:

  9. The Reconstruction Method Usual Research Approach: Too many Models! Problem: The Reconstruction Approach More Efficient Approach

  10. Cosmological Evolution in Scalar-Tensor Theories Vary ST action in flat FRW background assuming perfect fluid: +

  11. Reconstruction Equations Convert t to z, solve for U and Φ': where positive energy of gravitons Constraints: Is there a theory satisfying the constraints and crossing the w=-1 line? Q:

  12. Special Case: F(z)=1 (Minimal Coupling) Use in reconstruction equations to get: Constraint: The constraint is equivalent to w(z) > -1:

  13. Special Case: F(z)=1 (Minimal Coupling) Use in reconstruction equations to get: Simplest Reconstruction Example: Cosmological Constant

  14. Non-Minimal Coupling: Previous Results For U(z)=0 there is no acceptable F(z)>0 in 0<z<2 consistent with the H(z) obtained even from a flat LCDM model.

  15. Reconstruction from Polynomial Best Fit H(z) Polynomial Parametrization for H(z) Prior: Best Fit to Gold SnIa dataset Q.: Is there a set Φ(z), F(z),U(z) consistent with the constraints that predicts the best fit w(z) crossing the w=-1 line? Crossing w=-1 line Can not be reproduced by any single field minimally coupled theory

  16. Steps for Reconstructing F(Φ), U(Φ) from H(z) 1 2 • Use trial Φ(z) to solve (2) for F(z) with F'(z=0)=0, F(z=0)=1. • Select Φ(z)such that F(z)>0 for all z (need Φ'(z) small). • Use the resulting f(z) and the best fit q(z) in (1) to find U(z). • Invert Φ(z)to find z(Φ). • Sustitute z(Φ) in F(z) and U(z) to find F(Φ) and U(Φ).

  17. Results G(z)~1/F(z) decreases at recent times thus boosting accelerating expansion Minimum: Generic feature

  18. Results F(Φ) U(Φ) Minimum: Generic feature Φ Φ

  19. Drawbacks of Analysis H(z) is not sufficient to fix unambigously F(z), U(z) and Φ(z) (more data are needed eg δm(z)) Evolving Newton's constant G(z) implies evolving absolute magnitude M(G(z)) for SnIa. (best fit H(z) must be rederived fiting M(z) with new parameters)

  20. Resolution By Fitting M(G(z))-H(z) with SnIa data we at the same time fit for F(z)-H(z)! Using both the fitted F(z) and H(z) in the Reconstruction, the ambiguity Disappears! No additional data are needed! Φ'(z) and U(z) are uniquely determined just from SnIa data

  21. Implementation (S. Nesseris, LP in progress) SnIa peak luminosity: SnIa Absolute Magnitude Evolution: SnIa Apparent Magnitude: with: Parametrizations:

  22. Results

  23. Results Φ'2changes sign!

  24. SUMMARY • An observationally viable scalar tensor theory that predicts an H(z)-w(z) crossing the w=-1 line was explicitly reconstructed. • The reconstructed theory is not uniquely determined from H(z). • The SnIa data can be utilized to simulatneously fit for bothH(z) and the Newton's constant G(z) in the context of scalar tensor theories. This can lead to a uniquely defined reconstruction process.

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