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

 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

 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

  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

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

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

 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

 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

 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

 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

 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: )

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

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: )

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: )

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

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)

From: Tegmark et al 04

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

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 )

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

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: )

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

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: )

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!

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

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)

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