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L. Perivolaropoulos Department of Physics University of Ioannina Open page

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Talk Made in Corfu-Greece Summer 2006

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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 Extended Gravity Theories (DGP, Scalar Tensor etc) predict unique signatures in the perturbations growth rate Boisseau, Esposito-Farese, Polarski, Starobinsky 2000 LP 2005

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Directly Observable Dark Energy (Inferred) No Yes Flat Friedmann Equation Not Consistent

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

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(from large scale structure observations) Friedman eqn I: Friedman eqn II:

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SNLS Truncated Gold Gold Sample S. Nesseris, L.P. Phys. Rev. D72:123519, 2005 astro-ph/

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

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All best fit parameterizations cross the phantom divide at z~0.25 The parametrization with the best χ 2 is oscillating Lazkoz, Nesseris, LP 2005

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Espana-Bonet, Ruiz-Lapuente astro-ph/ Wang, Lovelace 2001 Huterer, Starkman 2003 Saini 2003 Wang, Tegmark 2005 Espana-Bonet, Ruiz-Lapuente 2005 Q: Do other SnIa data confirm this trend?

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Trunc. Gold (140 points, z<1) Full Gold (157 points, z<1.7)SNLS (115 points z<1) SNLS data show no trend for crossing the phantom divide w=-1! S. Nesseris, L.P. Phys. Rev. D72:123519, 2005 astro-ph/

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Definition:

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Q: Does R contain all the info about H(z) in the CMB Spectrum?

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CMB Spectrum practically unaffected All the useful H(z) related info coming from the CMB spectrum is contained in R.

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

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What theory produces crossing of the w=-1?

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+: Quintessence -: Phantom To cross the w=-1 line the kinetic energy term must change sign (impossible for single phantom or quintessence field) Generalization for k-essence:

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Non-minimal Coupling

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Minimum: Generic feature F(Φ) ΦΦ U(Φ) L.P. astro-ph/ , JCAP 0510:001,2005, S. Nesseris, L.P. astro-ph/ , Phys.Rev.D73:103511,2006 JCAP 0511:010,2005

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

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ΛCDM (SnIa best fit, Ω m =0.26 ) DGP SnIa best fit + Flat Constraint Scalar Tensor (α=-0.5, Ω m =0.26 ) Flat Matter Only Verde et. al. MNRAS 2002 Hawkins et. al. MNRAS 2003

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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

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SnIa peak luminosity: SnIa Absolute Magnitude Evolution: SnIa Apparent Magnitude: with: Parametrizations:

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Growth Factor: Models degenerate in ISW are also degenerate in linear growth factor.

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Hubble free luminosity Distance Apparent Magnitude: χ 2 depends on M: where Minimize:

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Gold SampleSNLS Uniform Analysis of Data (light curves) by one Group Combination of Data from Various Instruments Use of a single ground based instrument (megaprime of CFH 3.6m telescope) Redshift Range 0

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smoothing scale Wang, Lovelace 2001 Huterer, Starkman 2003 Saini 2003 Wang, Tegmark 2005 Espana-Bonet, Ruiz-Lapuente 2005

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

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from Max Tegmark's home page

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Effective Scale: Correlation function:

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Minimize: Assume:

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Global Mass Fraction vs Baryon Gas Mass fraction: Isothermal Gas Model: Hydrostatic Equilibrium: Define Cluster Baryon Gas Mass fraction:

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Cluster Baryon Gas Mass fraction: Connect to Global Mass fraction: Define: Observed Data SCDMLCDM

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Minimize: Assume:

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Growth Factor: Growth Factor Evolution (Linear-Fourier Space): General Relativity:

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Verde et. al. MNRAS 2002 Hawkins et. al. MNRAS 2003

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Minimize: Assume:

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positive energy of gravitons

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For U(z)=0 there is no acceptable F(z)>0 in 0

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SNLS Truncated Gold Full Gold S. Nesseris, L.P. Phys. Rev. D72:123519, 2005 astro-ph/ Minimize:

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

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