The Physics of Large Scale Structure andNew Results from the Sloan Digital Sky Survey

Beth Reid ICC Barcelona

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 Verde

David SpergelSDSS TEAM

arXiv:0907.1659arXiv:0907.1660*Colloborators: Will Percival*

Daniel EisensteinLicia Verde

David SpergelSDSS 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

OutlineOutline

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 PerturbationsThe Physics of LSS: Primordial Density Perturbations

WMAP3+SDSS MAIN

bh2, mh2/rh2 = 1+zeq well-constrained by CMB peak height ratios.

During radiation domination, perturbations inside the particle horizon are suppressed: keq = (2mHo

2 zeq)1/2 ~ 0.01 Mpc-1 [e.g., Eisenstein & Hu, 98]

Other important scale: sound horizon at the drag epoch rs

bh2, mh2/rh2 = 1+zeq well-constrained by CMB peak height ratios.

During radiation domination, perturbations inside the particle horizon are suppressed: keq = (2mHo

2 zeq)1/2 ~ 0.01 Mpc-1 [e.g., Eisenstein & Hu, 98]

Other important scale: sound horizon at the drag epoch rs

Physics of LSS: CDM, baryons, photons, neutrinos IPhysics of LSS: CDM, baryons, photons, neutrinos I

Completely negligible

Effective number of relativistic species; 3.04 for std neutrinos

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BAOBAO

For those of you who think in Real space

Courtesy of D. Eisenstein

BAO

For those of you who think in Fourier space

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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 IIPhysics of LSS: CDM, baryons, photons, neutrinos II

Superhorizon during radiation domination

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Massive neutrinos m<~ 1 eV become non-relativistic AFTER recombination and suppress power on small scales

Massive neutrinos m<~ 1 eV become non-relativistic AFTER recombination and suppress power on small scales

Physics of LSS: CDM, baryons, photons, neutrinos IIIPhysics of LSS: CDM, baryons, photons, neutrinos III

Courtesy of W. Hu

WMAP5 almost fixes* the expected Plin(k) in Mpc-1 through 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.

WMAP5 almost fixes* the expected Plin(k) in Mpc-1 through 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.

Physics of LSS: SummaryPhysics 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“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 rs/DV(zi)

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)

BAO in SDSS DR7 + 2dFGRS power spectraBAO in SDSS DR7 + 2dFGRS power spectra

Percival et al. (2009, arXiv:0907.1660)Percival et al. (2009, arXiv:0907.1660)

SDSS DR7 BAO results:modeling the distance-redshift relation

SDSS DR7 BAO results:modeling the distance-redshift relation

Percival et al. (2009, arXiv:0907.1660)Percival et al. (2009, arXiv:0907.1660)

Parameterize distance-redshift relation by smooth fit: can then be used to constrain multiple sets of models with smooth 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

For SDSS+2dFGRS analysis, choose nodes at z=0.2 and z=0.35, for fit to DV

BAO in SDSS DR7 + 2dFGRS power spectraBAO 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

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:0907.1660)Percival et al. (2009, arXiv:0907.1660)

Comparing BAO constraints against different dataComparing BAO constraints against different data

ΛCDM models with curvature flat wCDM models

Union supernovae

WMAP 5year

BAO Constraint on rs(zd)/DV(0.275)

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Cosmological ConstraintsCosmological Constraints

ΛCDM models with curvature flat wCDM models

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WMAP 5year

rs(zd)/DV(0.2) & rs(zd)/DV(0.35)

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

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

Modeling Pgal(k): ChallengesModeling Pgal(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 space Redshift spacez

“Finger-of-God” (FOG)

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From:Tegmark et al 04

Interlude: the Halo ModelInterlude: the Halo Model

Galaxy formation from first principles is HARD!

Linear bias model insufficient!gal = bgal m Pgal(k) = bgal

2 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

Galaxy formation from first principles is HARD!

Linear bias model insufficient!gal = bgal m Pgal(k) = bgal

2 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

Luminous Red GalaxiesLuminous 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

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

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Luminous Red GalaxiesLuminous 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

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

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Statistical power compromised by QNL

at k < 0.09

DR7: What’s new?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!

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)Reid et al. (2009, arXiv:0907.1659)

Phalo(k) ResultsPhalo(k) Results

Constrains turnover (mh2 DV) and BAO scale (rs/DV) Constrains turnover (mh2 DV) and BAO scale (rs/DV)

mh2 (ns/0.96)1.2= 0.141 ± 0.011DV(z=0.35) = 1380 ± 67 Mpc

mh2 (ns/0.96)1.2= 0.141 ± 0.011DV(z=0.35) = 1380 ± 67 Mpc

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WMAP+Phalo(k) Constraints: Neutrinos in CDMWMAP+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

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)Reid et al. (2009, arXiv:0907.1659)

Summary & ProspectsSummary & 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!

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!

Near future…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

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

BAO reconstructionBAO 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)

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)

Redshift space distortionsRedshift space distortions

In linear theory, modes are amplified along the LOS by peculiar velocities: In linear theory, modes are amplified along the LOS by peculiar velocities:

Okumura et al., arXiv:0711.3640

Song and Percival, arXiv:0807.0810