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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:

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Presentation on theme: "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:"— Presentation transcript:

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

2  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  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 Outline

3  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  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 The Physics of LSS: Primordial Density Perturbations WMAP3+SDSS MAIN

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

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

6 BAO For those of you who think in Fourier space Photons coupled to baryons 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) Observe photons “See” dark matter Courtesy L Verde

7  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  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 Physics of LSS: CDM, baryons, photons, neutrinos II Superhorizon during radiation domination k eq Tegmark et al. (2004), ApJ 606, 702

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

9  WMAP5 almost fixes* the expected P lin (k) in Mpc -1 through  c h 2 (6%) and  b h 2 (3%), independent of  CMB (and thus curvature and DE).  In the minimal model (N eff = 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.  WMAP5 almost fixes* the expected P lin (k) in Mpc -1 through  c h 2 (6%) and  b h 2 (3%), independent of  CMB (and thus curvature and DE).  In the minimal model (N eff = 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. Physics of LSS: Summary turnover scale BAO

10  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  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 “Theory” of Observing LSS: Geometry

11  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 r s /D V (z i )  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 r s /D V (z i ) BAO in SDSS DR7 + 2dFGRS power spectra Percival et al. (2009, arXiv: )

12 SDSS DR7 BAO results: modeling the distance-redshift relation Percival et al. (2009, arXiv: ) 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 D V

13 BAO in SDSS DR7 + 2dFGRS power spectra  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 Percival et al. (2009, arXiv: )

14 Comparing BAO constraints against different data ΛCDM models with curvature flat wCDM models Union supernovae WMAP 5year BAO Constraint on r s (z d )/D V (0.275) Percival et al. (2009: arXiv: )

15 Cosmological Constraints ΛCDM models with curvature flat wCDM models Percival et al. (2009: arXiv: ) Union supernovae WMAP 5year r s (z d )/D V (0.2) & r s (z d )/D V (0.35) WMAP5+BAO  CDM:  m = ± 0.018, H 0 = 70.1 ± 1.5 WMAP5+BAO+SN wCDM + curvature:  tot = ± 0.008, w = ± 0.10 WMAP5+BAO  CDM:  m = ± 0.018, H 0 = 70.1 ± 1.5 WMAP5+BAO+SN wCDM + curvature:  tot = ± 0.008, w = ± 0.10

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

17 From: Tegmark et al 04

18 Interlude: the Halo Model  Galaxy formation from first principles is HARD!  Linear bias model insufficient! –  gal = b gal  m P gal (k) = b gal 2 P m (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  Galaxy formation from first principles is HARD!  Linear bias model insufficient! –  gal = b gal  m P gal (k) = b gal 2 P m (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 P lin (k)  nP ~ 1 to probe largest effective volume – Occupy most massive halos large FOG features – Shot noise correction important  DR5 analysis: huge deviations from P lin (k)  nP ~ 1 to probe largest effective volume – Occupy most massive halos large FOG features – Shot noise correction important Tegmark et al. (2006, PRD )

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

21 DR7: What’s new?  n LRG 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 DR5) with cosmology-dependent, nonlinear model calibrated on accurate mock catalogs and with better understood, smaller modeling systematics –Increase k max = 0.2 h/Mpc; 8x more modes!  n LRG 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 DR5) with cosmology-dependent, nonlinear model calibrated on accurate mock catalogs and with better understood, smaller modeling systematics –Increase k max = 0.2 h/Mpc; 8x more modes! Reid et al. (2009, arXiv: )

22 P halo (k) Results  Constrains turnover (  m h 2 D V ) and BAO scale (r s /D V )   m h 2 (n s /0.96) 1.2 = ± D V (z=0.35) = 1380 ± 67 Mpc   m h 2 (n s /0.96) 1.2 = ± D V (z=0.35) = 1380 ± 67 Mpc

23 WMAP+P halo (k) Constraints: Neutrinos in  CDM  P halo (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 N rel alters turnover and BAO scales differently – WMAP5: N rel = preferred to N rel = 0 with > 99.5% confidence – WMAP5+LRG: N rel = 4.8 ± 1.8  P halo (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 N rel alters turnover and BAO scales differently – WMAP5: N rel = preferred to N rel = 0 with > 99.5% confidence – WMAP5+LRG: N rel = 4.8 ± 1.8 Reid et al. (2009, arXiv: )

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: –  Shape information comes “for free” in a BAO survey!  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: –  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 D A (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  BAO reconstruction (Eisenstein, Seo, Sirko, Spergel 2007, Seo et al. 2009)  Fitting for the BAO in two dimensions: get D A (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 for DM, galaxies in prep)  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 for DM, galaxies in prep)

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


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