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Geometric Dark Energy Probes and Consistency with CDM

This talk discusses the scale and gauge dependence of the general relativistic growth of perturbations and explores the consistency of different datasets with cold dark matter (CDM) and standard rulers. It also addresses potential conflicts of CDM with data and presents recent constraints using geometric dark energy probes.

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Geometric Dark Energy Probes and Consistency with CDM

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  1. Open page Beyond the Sub-Hubble approximation for the General Relativistic Growth of Perturbations: Scale and Gauge Dependence of δ(z) L. Perivolaropouloshttp://leandros.physics.uoi.gr Department of Physics University of Ioannina

  2. Structure of Talk Review Geometric Dark Energy Probes and Recent Constraints Introduction: Potential Conflicts of ΛCDM with Data Sub-Hubble approximation, k>0.01h Mpc-1 Dynamical Probe δ(z):GR + Newtonian Gauge Beyond Sub-Hubble: Linear GR, k<0.01h Mpc-1 Growth Rate Gauge Dependence of δm(a) Conclusion

  3. Geometric Probes: Recent SnIa Datasets Q1: What is the Figure of Merit of each dataset? Q2: What is the consistency of each dataset with ΛCDM? Q3: What is the consistency of each dataset with Standard Rulers? J. C. Bueno Sanchez, S. Nesseris, LP, JCAP 0911:029,2009, 0908.2636

  4. Figures of Merit The Figure of Merit:Inverse area of the 2σ CPL parameter contour.A measure of the effectiveness of the dataset in constraining the given parameters. GOLD06 SNLS ESSENCE UNION CONSTITUTION WMAP5+SDSS5 WMAP5+SDSS7

  5. Figures of Merit The Figure of Merit:Inverse area of the 2σ CPL parameter contour.A measure of the effectiveness of the dataset in constraining the given parameters. SDSS5 Percival et. al. SDSS7 Percival et. al.

  6. Consistency with ΛCDM Trajectories of Best Fit Parameter Point ESSENCE+SNLS+HST data Ω0m=0.24 SNLS 1yr data The trajectories of SNLS and Constitution clearly closer to ΛCDM for most values of Ω0m Gold06 is the furthest from ΛCDM for most values of Ω0m Q: What about the σ-distance (dσ) from ΛCDM?

  7. The σ-distance to ΛCDM ESSENCE+SNLS+HST data Trajectories of Best Fit Parameter Point Consistency with ΛCDM Ranking:

  8. The σ-distance to Standard Rulers ESSENCE+SNLS+HST Trajectories of Best Fit Parameter Point Consistency with Standard Rulers Ranking:

  9. Puzzles for ΛCDM From LP, 0811.4684 Large Scale Velocity Flows - Predicted: On scale larger than 50 h-1Mpc Dipole Flows of 110km/sec or less. - Observed: Dipole Flows of more than 400km/sec on scales 50 h-1Mpc or larger. - Probability of Consistency:1% R. Watkins et. al. , 0809.4041 Cluster and Galaxy Halo Profiles: - Predicted: Shallow, low-concentration mass profiles - Observed: Highly concentrated, dense halos - Probability of Consistency:3-5% Broadhurst et. al. ,ApJ 685, L5, 2008, 0805.2617, S. Basilakos, J.C. Bueno Sanchez, LP., 0908.1333, PRD, 80, 043530, 2009. Bright High z SnIa: - Predicted: Distance Modulus of High z SnIa close to best fit ΛCDM - Observed: Dist. Modulus of High z SnIa lower (brighter) than best fit ΛCDM - Probability of Consistency for Union and Gold06:3-6% LP and A. Shafielloo , PRD 79, 123502, 2009, 0811.2802 The Emptiness of Voids: - Predicted: Many small dark matter halos should reside in voids. - Observed: Smaller voids (10Mpc) look very empty (too few dwarf galaxies) - Probability of Consistency:3-5% P.J.E. Peebles , astro-ph/0101127, Klypin et. al. APJ, 522, 82, 1999, astro-ph/9901240

  10. Dynamical Probe: Growth in General Relativity (Newtonian Gauge, Sub-Hubble scales) Perturbed Metric: Linear Einstein equations: Generalized Poisson: Poisson equation Sub-horizon scale approximation=Newtonian Result

  11. Growth in General Relativity (Newtonian Gauge) Perturbed Metric: Linear Einstein equations: Generalized Poisson: better approximation Dent, Dutta, Phys.Rev.D79:063516,2009

  12. Why do we need a better approximation? Comoving Hubble scale at early times when most growth occurs is much smaller At recombination commoving Hubble scale ~100 Mpc Hubble scale 100Mpc Recombination Sub-Hubble approximation is hardly valid at early times when most growth occurs!

  13. Modified Effective Gravitational Potential Generalized Poisson: Fourier Space Coordinate Space Yukawa potential with a Hubble scale cutoff

  14. Growth in Modified Gravity Conservation of matter stress energy tensor Modified Poisson: to be compared with

  15. The Growth Factor Define the growth factor as approximate standard solution approximate scale dependent solution Dent, Dutta, LP, Phys.Rev.D80:023514,2009.

  16. Comparison of Solutions Dent, Dutta, LP, Phys.Rev.D80:023514,2009.

  17. Dynamical Dark Energy Use dynamical dark energy parametrization: Trial growth parametrization: Best fit to numerical GR solution: Variation as scales changes

  18. Accuracy of Scale Dependent Parametrization (ΛCDM)

  19. Accuracy of Scale Dependent Parametrization (DDE)

  20. Gauge Modes: The Synchronous Gauge Line element in synchronous gauge: Growth equation in synchronous gauge: (matter local rest frame everywhere) Exact result. No scale dependence!! (can not pick up Hubble scale effects) Growth equation in newtonian gauge: (time slicing of isotropic expansion) Scale dependence.(can pick up Hubble scale effects) Line element in conformal Newtonian gauge: Q: What is the proper gauge to use when comparing with observations?

  21. Gauge Dependent Power Spectra Hubble Scale H0 at z=0 Power Spectrum at z=0Newtonian Gauge Power Spectrum at z=0Synchronous Gauge Near the horizon power spectra in the two gauges differ significantly. Comoving line of sight distance1/r(z) Yoo, Fitzpatrick, Zaldarriaga, Phys.Rev.D80:083514,2009. 0907.0707

  22. What are the Observable Gauge Invariant Perturbations? Need an observable gauge invariant replacement of δm. General Perturbed Metric: Some benefits of Newtonian gauge: The gauge invariant perturbation δGI : reduces to δmΝ in the Newtonian gauge (B=E=0). The gauge invariant potential ϕ obeys a scale dependent Poisson equation reduces to Φ in the Newtonian gauge (B=E=0).

  23. SUMMARY The consistency of ΛCDM with geometric probes of accelerating expansion is very good and it appears to be further improving with time. There are a few puzzling potential conflicts of ΛCDM withspecific cosmological data mainly related with dynamical large scale structure probes. On scales larger than about 100h-1Mpcthe sub-Hubble approximation for the growth rate of perturbations δ(z) needs to be improved by a scale dependent factor in the Newtonian gauge. The growth rate of of perturbations δ(z) depends on the gauge considered and this dependence becomes important on scales larger than about 100h-1Mpc .

  24. Observable Gauge Invariant Perturbations The predicted observable (gauge invariant) matter perturbations depend on the gauge dependent perturbations, on the perturbed metric and on other observables Yoo, Fitzpatrick, Zaldarriaga, 0907.0707

  25. What are the Observable Gauge Invariant Perturbations? Need an observable gauge invariant replacement of δm. Example: The observed redshift of a source is not directly connected to the scale factor at the time of emission due to the perturbed FRW metric δzdepends on peculiar velocity of source and metric perturbations Yoo, Fitzpatrick, Zaldarriaga, 0907.0707Phys.Rev.D80:083514,2009 Observed redshift Gauge invariant Q: What is the dynamical equation for the evolution of the gauge invariant perturbation? Matter density at source Mean matter density at observed redshift z

  26. 2σ Contours of Recent Datasets GOLD06 SNLS ESSENCE UNION CONSTITUTION WMAP5+SDSS5 WMAP5+SDSS7

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