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The Physics of Large Scale Structure and New Results from the Sloan Digital Sky Survey Beth Reid ICC Barcelona. arXiv:0907.1659 arXiv:0907.1660* Colloborators: Will Percival* Daniel Eisenstein Licia Verde David Spergel SDSS TEAM. Outline.

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  1. The Physics of Large Scale Structure andNew Results from the Sloan Digital Sky Survey Beth Reid ICC Barcelona arXiv:0907.1659arXiv:0907.1660*Colloborators: Will Percival*Daniel EisensteinLicia VerdeDavid SpergelSDSS TEAM

  2. Outline • Physics of Large Scale Structure (LSS): lineary theory • The “theory” of observing LSS • Real world complications: galaxy redshift surveys to cosmological parameters • SDSS DR7: New Results • The Near Future of LSS

  3. The Physics of LSS: Primordial Density Perturbations • Either parameterized like this: • Or reconstructed using a “minimally-parametric smoothing spline technique” (LV and HP, JCAP 0807:009, 2008) • Contains information about the inflationary potential WMAP3+SDSS MAIN

  4. Physics of LSS: CDM, baryons, photons, neutrinos I Effective number of relativistic species; 3.04 for std neutrinos Completely negligible • bh2, mh2/rh2 = 1+zeq well-constrained by CMB peak height ratios. • During radiation domination, perturbations inside the particle horizon are suppressed: keq = (2mHo2 zeq)1/2 ~ 0.01 Mpc-1 [e.g., Eisenstein & Hu, 98] • Other important scale: sound horizon at the drag epoch rs Eisenstein et al. (2005) ApJ 633, 560 k (h/Mpc)

  5. BAO For those of you who think in Real space Courtesy of D. Eisenstein

  6. BAO Observe photons Photons coupled to baryons “See” dark matter If baryons are ~1/6 of the dark matter these baryonic oscillations should leave some imprint in the dark matter distribution (gravity is the coupling) Courtesy L Verde For those of you who think in Fourier space

  7. Physics of LSS: CDM, baryons, photons, neutrinos II • Linear matter power spectrum P(k) depends on the primordial fluctuations and CMB-era physics, represented by a transfer function T(k). Thereafter, the shape is fixed and the amplitude grows via the growth factor D(z) • Cosmological probes span a range of scales and cosmic times Superhorizon during radiation domination Tegmark et al. (2004), ApJ 606, 702 keq

  8. Physics of LSS: CDM, baryons, photons, neutrinos III • Massive neutrinos  m<~ 1 eV become non-relativistic AFTER recombination and suppress power on small scales Courtesy of W. Hu

  9. Physics of LSS: Summary • WMAP5 almost fixes* the expected Plin(k) in Mpc-1through c h2 (6%) and b h2 (3%), independent of CMB (and thus curvature and DE). • In the minimal model (Neff = 3.04, m= 0), entire P(k) shape acts as a “std ruler” and provides an impressive consistency check -- same physics that generates the CMB at z=1100 also determines clustering at low z. BAO turnover scale

  10. “Theory” of Observing LSS: Geometry • We measure , z; need a model to convert to co-moving coordinates. • Transverse: Along LOS: • Spherically averaged, isotropic pairs constrain • Redshift Space Distortions -- later, time permitting

  11. BAO in SDSS DR7 + 2dFGRS power spectra • Combine 2dFGRS, SDSS DR7 LRG and Main Galaxies • Assume a fiducial distance-redshift relation and measure spherically-averaged P(k) in redshift slices • Fit spectra with model comprising smooth fit × damped BAO • To first order, isotropically distributed pairs depend on • Absorb cosmological dependence of the distance-redshift relation into the window function applied to the model P(k) • Report model-independent constraint on rs/DV(zi) Percival et al. (2009, arXiv:0907.1660)

  12. SDSS DR7 BAO results:modeling the distance-redshift relation Parameterize distance-redshift relation by smooth fit: can then be used to constrain multiple sets of models with smooth distance-redshift relation For SDSS+2dFGRS analysis, choose nodes at z=0.2 and z=0.35, for fit to DV Percival et al. (2009, arXiv:0907.1660)

  13. results can be written as independent constraints on a distance measure to z=0.275 and a tilt around this consistent with ΛCDM models at 1.1σ when combined with WMAP5 Reduced discrepancy compared with DR5 analysis more data revised error analysis (allow for non-Gaussian likelihood) more redshift slices analyzed improved modeling of LRG redshift distribution BAO in SDSS DR7 + 2dFGRS power spectra Percival et al. (2009, arXiv:0907.1660)

  14. Comparing BAO constraints against different data flat wCDM models ΛCDM models with curvature Percival et al. (2009: arXiv:0907.1660) Percival et al. (2009: arXiv:0907.1660) Union supernovae WMAP 5year BAO Constraint on rs(zd)/DV(0.275)

  15. Cosmological Constraints flat wCDM models ΛCDM models with curvature Percival et al. (2009: arXiv:0907.1660) Percival et al. (2009: arXiv:0907.1660) WMAP5+BAO CDM: m = 0.278 ± 0.018, H0 = 70.1 ± 1.5 WMAP5+BAO+SN wCDM + curvature: tot = 1.006 ± 0.008, w = -0.97 ± 0.10 Union supernovae WMAP 5year rs(zd)/DV(0.2) & rs(zd)/DV(0.35)

  16. Modeling Pgal(k): Challenges • density field goes nonlinear • uncertainty in the mapping between galaxy and matter density fields • galaxy positions observed in redshift space “Finger-of-God” (FOG) Real space Redshift space z

  17. From: Tegmark et al 04

  18. Interlude: the Halo Model • Galaxy formation from first principles is HARD! • Linear bias model insufficient! • gal = bgal m Pgal(k) = bgal2 Pm(k) • Halo Model Key Assumptions: • Galaxies only form/reside in halos • N-body simulations can determine the statistical properties of halos • Halo mass entirely determines key galaxy properties • Provides a non-linear, cosmology-dependent model and framework in which to quantify systematic errors

  19. Luminous Red Galaxies • DR5 analysis: huge deviations from Plin(k) • nP ~ 1 to probe largest effective volume • Occupy most massive halos large FOG features • Shot noise correction important Tegmark et al. (2006, PRD 74 123507) Tegmark et al. (2006, PRD 74 123507)

  20. Luminous Red Galaxies • DR5 analysis: huge deviations from Plin(k) • nP ~ 1 to probe largest effective volume • Occupy most massive halos large FOG features • Shot noise correction important Tegmark et al. (2006, PRD 74 123507) Statistical power compromised by QNL at k < 0.09

  21. DR7: What’s new? • nLRG small find “one-halo” groups with high fidelity • Provides observational constraint on FOGs and “one-halo” excess shot noise • NEW METHOD TO RECONSTRUCT HALO DENSITY FIELD • Better tracer of underlying matter P(k) • Replace heuristic nonlinear model (Tegmark et al. 2006 DR5) with cosmology-dependent, nonlinear model calibrated on accurate mock catalogs and with better understood, smaller modeling systematics • Increase kmax = 0.2 h/Mpc; 8x more modes! Reid et al. (2009, arXiv:0907.1659)

  22. Phalo(k) Results • Constrains turnover (mh2 DV) and BAO scale (rs/DV) mh2 (ns/0.96)1.2= 0.141 ± 0.011 DV(z=0.35) = 1380 ± 67 Mpc

  23. WMAP+Phalo(k) Constraints: Neutrinos in CDM • Phalo(k) constraints tighter than P09 BAO-only • Massive neutrinos suppress P(k) • WMAP5:  m< 1.3 eV (95% confidence) • WMAP5+LRG:  m< 0.62 eV • WMAP5+BAO:  m< 0.78 eV • Effective number of relativistic species Nrel alters turnover and BAO scales differently • WMAP5: Nrel = 3.046 preferred to Nrel = 0 with > 99.5% confidence • WMAP5+LRG: Nrel = 4.8 ± 1.8 Reid et al. (2009, arXiv:0907.1659)

  24. Summary & Prospects • BAOs provide tightest geometrical constraints • consistent with ΛCDM models at 1.1σ when combined with WMAP5 • improved error analysis, n(z) modeling, etc. • DR7 P(k) improvement: We use reconstructed halo density field in cosmological analysis • Halo model provides a framework for quantifying systematic uncertainties • Result: 8x more modes, improved neutrino constraints compared with BAO-only analysis • Likelihood code available here: • http://lambda.gsfc.nasa.gov/toolbox/lrgdr/ • Shape information comes “for free” in a BAO survey!

  25. Near future… • BAO reconstruction (Eisenstein, Seo, Sirko, Spergel 2007, Seo et al. 2009) • Fitting for the BAO in two dimensions: get DA(z) and H(z) [ask Christian] • Extend halo model modeling to redshift space distortions to constrain growth of structure and test GR or dark coupling (e.g., Song and Percival 2008) • Constraining primordial non-Gaussianity with LSS [ask Licia] • Technical challenge -- extract P(k), BAO, & redshift distortion information simultaneously, and understand the covariance matrix

  26. BAO reconstruction • In linear theory, velocity and density fields are simply related. • Main idea: compute velocity field from measured density field, and move particles back to their initial conditions using the Zel’dovich approximation • It works amazingly well: • reduces the “damping” of the BAO at low redshifts (Eisenstein et al. 2007, and thereafter) • removes the small systematic shift of the BAO to below the cosmic variance limit, <0.05% (Seo et al. 2009 for DM, galaxies in prep)

  27. Redshift space distortions • In linear theory, modes are amplified along the LOS by peculiar velocities: Song and Percival, arXiv:0807.0810 Okumura et al., arXiv:0711.3640

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