L. Perivolaropoulos Department of Physics University of Ioannina Open page

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

3 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, Q1: What is the Figure of Merit of each dataset?

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. SNLS ESSENCE GOLD06 UNION CONSTITUTION WMAP5+SDSS5WMAP5+SDSS7

5 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 SDSS7 Percival et. al.

6 ESSENCE+SNLS+HST data SNLS 1yr data Trajectories of Best Fit Parameter Point The trajectories of SNLS and Constitution clearly closer to ΛCDM for most values of Ω 0m Gold06 is the furthest from ΛCDM for most values of Ω 0m Q: What about the σ-distance (d σ ) from ΛCDM? Ω 0m =0.24

7 ESSENCE+SNLS+HST data Trajectories of Best Fit Parameter Point Consistency with ΛCDM Ranking:

8 Consistency with Standard Rulers Ranking: ESSENCE+SNLS+HST Trajectories of Best Fit Parameter Point

9 Large Scale Velocity Flows - Predicted: On scale larger than 50 h -1 Mpc Dipole Flows of 110km/sec or less. - Observed: Dipole Flows of more than 400km/sec on scales 50 h -1 Mpc or larger. - Probability of Consistency: 1% Cluster and Galaxy Halo Profiles: - Predicted: Shallow, low-concentration mass profiles - Observed: Highly concentrated, dense halos - Probability of Consistency: 3-5% 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% 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% From LP, R. Watkins et. al., Broadhurst et. al.,ApJ 685, L5, 2008, , S. Basilakos, J.C. Bueno Sanchez, LP., , PRD, 80, , LP and A. Shafielloo, PRD 79, , 2009, P.J.E. Peebles, astro-ph/ , Klypin et. al. APJ, 522, 82, 1999, astro-ph/

10 Perturbed Metric: Linear Einstein equations:Generalized Poisson: Poisson equation Sub-horizon scale approximation=Newtonian Result

11 Perturbed Metric: Linear Einstein equations:Generalized Poisson: better approximation Dent, Dutta, Phys.Rev.D79:063516,2009

Comoving Hubble scale at early times when most growth occurs is much smaller Sub-Hubble approximation is hardly valid at early times when most growth occurs! At recombination commoving Hubble scale ~100 Mpc Recombination Hubble scale 100Mpc

13 Generalized Poisson: Fourier Space Coordinate Space Yukawa potential with a Hubble scale cutoff

14 Conservation of matter stress energy tensorModified Poisson: to be compared with

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

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

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

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

Hubble Scale H 0 at z=0 Power Spectrum at z=0 Newtonian Gauge Power Spectrum at z=0 Synchronous Gauge Near the horizon power spectra in the two gauges differ significantly. Comoving line of sight distance 1/r(z) Yoo, Fitzpatrick, Zaldarriaga, Phys.Rev.D80:083514,

Need an observable gauge invariant replacement of δ m. The gauge invariant perturbation δ GI : Some benefits of Newtonian gauge: reduces to δ mΝ in the Newtonian gauge (B=E=0). The gauge invariant potential ϕ obeys a scale dependent Poisson equation General Perturbed Metric: reduces to Φ in the Newtonian gauge (B=E=0).

23 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 with specific cosmological data mainly related with dynamical large scale structure probes. On scales larger than about 100h -1 Mpc the 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 -1 Mpc.

24 The predicted observable (gauge invariant) matter perturbations depend on the gauge dependent perturbations, on the perturbed metric and on other observables Yoo, Fitzpatrick, Zaldarriaga,

25 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 Yoo, Fitzpatrick, Zaldarriaga, Phys.Rev.D80:083514,2009 Matter density at source Mean matter density at observed redshift z Gauge invariant δz depends on peculiar velocity of source and metric perturbations Observed redshift Need an observable gauge invariant replacement of δ m. Q: What is the dynamical equation for the evolution of the gauge invariant perturbation? Example:

26 SNLS ESSENCE GOLD06 UNION CONSTITUTION WMAP5+SDSS5WMAP5+SDSS7