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

Open page. Crossing the Phantom Divide: Observational Status and Theoretical Implications. L. Perivolaropoulos http://leandros.physics.uoi.gr Department of Physics University of Ioannina. Talk Made in Corfu-Greece Summer 2006. Main Points.

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

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  1. Open page Crossing the Phantom Divide: Observational Status and Theoretical Implications L. Perivolaropouloshttp://leandros.physics.uoi.gr Department of Physics University of Ioannina

  2. Talk Made in Corfu-Greece Summer 2006

  3. Main Points Dark Energy Probes include-SnIa (Gold sample and SNLS), -CMB shift parameter (WMAP 3-year), -Baryon Acoustic Oscillation Peak in LSS surveys,-Cluster gas mass fraction, -Linear growth rate from 2dF (z=0.15) Some of these probes mildly favor an evolving w(z) crossing the phantom divide w=-1 over ΛCDM Minimally Coupled Quintessence is inconsistent with such crossing Scalar Tensor Quintessence is consistent with w=-1 crossing Boisseau, Esposito-Farese, Polarski, Starobinsky 2000LP 2005 Extended Gravity Theories (DGP, Scalar Tensor etc) predict unique signatures in the perturbations growth rate

  4. The Dark Energy Puzzle Friedmann Equation Flat General Relativity DirectlyObservable Dark Energy(Inferred) DirectlyObservable Not Consistent Q: Is GR the correct theory on the Largest Scales? What is the Correct Theory? No Yes What are the properties of the dark energy? What microphysical theory can reproduce these properties?

  5. Observed Hubble Diagram from Spergel et. al. 2006 z~0.5: Acceleration starts 157 SnIa Q: What causes this accelerating expansion? Flat

  6. Negative Pressure Acceleration from Friedman eqn I: Dark Energy Evolution: Friedman eqn II: Best Fit ? (from large scale structure observations)

  7. Fitting the Cosmological Constant Friedman Equation Observations Theory Theory- -Observations Compare:

  8. Comparative analysis for LCDM SNLS TruncatedGold GoldSample Flat SCDM (Ωm=1) rulled out at more than 10σ Gold dataset mildly favors closed universe S. Nesseris, L.P. Phys. Rev. D72:123519, 2005 astro-ph/0511040 Data Consistent at 95% Q: Can we get better fits?

  9. Strategy: Parametrize H(z)-w(z)

  10. Parametrizations Constant w Weller-Albrecht 2002 Chevalier-Polarski 2001, Linder 2003 Sahni et. al. 2003 Huterer-Cooray 2004 Nesseris-LP 2004 Pogosian et. al. 2005

  11. Best Fit Parametrizations (Gold Sample) • All best fit parameterizations cross the phantom divide at z~0.25 • The parametrization with the best χ2is oscillating Crossing Phantom Divide w=-1 Lazkoz, Nesseris, LP 2005

  12. Best Fit (Uncorrelated Gold)

  13. Non-Parametric approach (smooth data using kernel function) Espana-Bonet, Ruiz-Lapuenteastro-ph/0503210 Wang, Lovelace 2001Huterer, Starkman 2003Saini 2003Wang, Tegmark 2005Espana-Bonet, Ruiz-Lapuente 2005 Q: Do other SnIa data confirm this trend?

  14. Comparison with SNLS Trunc. Gold (140 points, z<1) SNLS (115 points z<1) Full Gold (157 points, z<1.7) SNLS data show no trend for crossing the phantom divide w=-1! S. Nesseris, L.P. Phys. Rev. D72:123519, 2005 astro-ph/0511040 Q: What do other cosmological data favor?

  15. CMB Tests: The Shift Parameter Definition:

  16. Evaluating the Shift Parameter Q: Does R contain all the info about H(z) in the CMB Spectrum?

  17. Vary H(z) with fixed R CMB Spectrum practically unaffected All the useful H(z) related info coming fromthe CMB spectrum is contained in R.

  18. Best Fits for w(z) Gold dataset Riess -et. al. (2004) SNLS dataset Astier -et. al. (2005) Other data: CMB, BAO, LSS, Clusters Other data: CMB, BAO, LSS, Clusters S. Nesseris, L.P.in prep. Gold dataset Riess -et. al. (2004) SNLS dataset Astier -et. al. (2005) Other data: CMB, BAO, LSS, Clusters Minimize: Wang, Mukherjee 2006 Eisenstein et. al. 2005 2dF:Verde et. al. MNRAS 2002 Allen et. al. 2004

  19. Parameter Contours

  20. Basic Question What theory produces crossing of the w=-1?

  21. 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:

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

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

  24. JCAP 0511:010,2005 Crossing w=-1 line Reconstruction from Best Fit to Gold Dataset L.P. astro-ph/0504582, JCAP 0510:001,2005, S. Nesseris, L.P. astro-ph/0602053, Phys.Rev.D73:103511,2006 F(Φ) U(Φ) Minimum: Generic feature Φ Φ

  25. Other Signature: Growth Factor Growth Factor: Growth Factor Evolution (Linear-Fourier Space): General Relativity: Koyama and Maartens (2006) DGP: Boisseau, Esposito-Farese, Polarski Staroninski (2000)Uzan (2006) Scalar Tensor: Modified Poisson: Sealfon et. al. (2004)

  26. Compare with Data (2dF) Flat Matter Only ΛCDM (SnIa best fit, Ωm=0.26) Scalar Tensor (α=-0.5, Ωm=0.26) DGP SnIa best fit+Flat Constraint Verde et. al. MNRAS 2002Hawkins et. al. MNRAS 2003 Future Prospect: Decrease Error Bars

  27. SUMMARY • Interesting probes of the dark energy evolution include: - SnIa (Gold sample, SNLS) - CMB shift parameter - Baryon Acoustic Oscillations (BAO) Peak of LSS correlation (z=0.35) - Clusters X-ray gas mass fraction - Growth rate of perturbations at z=0.15 (from 2dFGRS) • All recent data indicate that w(z) is close to -1. Thus w(z) may be crossing the w=-1 line. • Minimally Coupled Scalar predicts no crossing of w=-1 line • Scalar Tensor Theories are consistent with crossing of w=-1 • Extended Gravity Theories (DGP, Scalar Tensor etc) predict unique signatures in the growth rate of cosmological perturbations

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

  29. Implementation SnIa peak luminosity: SnIa Absolute Magnitude Evolution: SnIa Apparent Magnitude: with: Parametrizations:

  30. Perurbation Growth Factor and ISW effect Models degenerate in ISW are also degenerate in linear growth factor. Growth Factor:

  31. Dealing with the Absolute Magnitude M Hubble free luminosity Distance Apparent Magnitude: χ2depends on M: where Minimize:

  32. SnIa Datasets

  33. Strategy II:Smooth d(z) smoothing scale Wang, Lovelace 2001Huterer, Starkman 2003Saini 2003Wang, Tegmark 2005Espana-Bonet, Ruiz-Lapuente 2005

  34. Error Estimation: Fisher Matrix Fisher Matrix: Covariance Matrix Parameter Estimation: w(z) plot with error regions:

  35. Cosmic Perturbations and Hubble Expansion from Max Tegmark's home page

  36. Other Probes II: Baryon Acoustic Peak Effective Scale: Correlation function:

  37. CMB Shift + BAO Peak Constraints Assume: Minimize:

  38. Other Probes III: Clusters (Mass Fraction) Define Cluster Baryon Gas Mass fraction: Global Mass Fraction vs Baryon Gas Mass fraction: Isothermal Gas Model: Hydrostatic Equilibrium:

  39. Other Probes III: Clusters (Mass Fraction) Cluster Baryon Gas Mass fraction: Observed Connect to Global Mass fraction: Define: Data SCDM LCDM

  40. Other Probes III: Clusters (Mass Fraction) Assume: Minimize:

  41. Effect of Cluster Data (Minimal)

  42. Other Probes IV: Growth of Perturbations Growth Factor: Growth Factor Evolution (Linear-Fourier Space): General Relativity:

  43. Compare with Data (2dF) Verde et. al. MNRAS 2002Hawkins et. al. MNRAS 2003 Future Prospect: Decrease Error Bars

  44. Growth Rate Constraints (Minimal) Assume: Minimize:

  45. 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:

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

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

  48. 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.

  49. Comparative analysis for LCDM SNLS TruncatedGold FullGold S. Nesseris, L.P. Phys. Rev. D72:123519, 2005 astro-ph/0511040 Data Consistent at 95% Minimize: Gold dataset favors closed universe Flat SCDM (Ωm=1) rulled out at more than 10σ Q: Can we get better fits?

  50. Error Estimation: Fisher Matrix Fisher Matrix: Covariance Matrix Parameter Estimation: w(z) plot with error regions:

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