Cosmology with Galaxy Correlations from Photometric Redshift Surveys

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Cosmology with Galaxy Correlations from
Photometric Redshift Surveys

• Hu ZhanUC Davisin collaboration with Lloyd
  Knox, Tony Tyson, and Vera Margoniner

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Outline

• Power spectrum on very large scales
  (k 10-3 h Mpc-1)
• Baryon acoustic oscillations (BAO) on large
  scales (k 10-1 h Mpc-1)
• LSST dark energy constraints CMB BAO Weak
  lensing
• Curvature the need for high-z data

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Why Very Large Scales?

• Cross-check for CMB
• Primordial power spectrum
• Probing inflation
• Consistency test for cosmological constraints
  from smaller scales

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Challenges

• Photometric redshift errors
• Suppress the power
• Boost the shot noise ? reduce number of modes
• Photometry errors (e.g. dust extinction)
• Lead to spurious power
• Contribute to photo-z errors
• Galaxy bias
• Alters the amplitude and shape of the PS
• Redshift distortion
• Evolution within the survey volume

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• 8.4-meter primary
• 10 deg2 FOV
• 3 billion pixels
• 0.3 - 1 µm

• 23,000 deg2 survey area
• V 26.5 mag
• Billions of galaxies up to z 3

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Photo-z Errors

• Spherical harmonic basis
• Subject to errors in galaxy bias, photometry,
  cosmology
• Reconstruction at high k can be improved

Zhan et al. (astro-ph/0508119)
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Schlegel, Finkbeiner, Davis (1998)
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Dust Extinction

• Left axis fractional rms fluctuations of galaxy
  counts within a Gaussian window of size q.
• Right normalized mode counts for a given k.
• LSST galaxy surface density can calibrate
  photometry errors.

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Galaxy Bias
Constant bias when binned in luminosity
Tegmark et al. (2004)
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Statistical Errors of the Power Spectrum

• Binning Dk 0.05 k
• Survey volume with zmax1 is roughly 1/9 of that
  with zmax2.5
• LSST complimentary to CMB

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Very-Large-Scale Power Spectrum LSST

• Binning Dk 0.16 k
• Inner error bars cubic geometric outer ones
  spherical harmonic mode counting
• Dotted lines caused by a step inflation
  potential that fits WMAP data (Peiris et al.
  2003)

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Very-Large-Scale Power Spectrum WMAP
Bridle et al. (2003)
20 errors on largest scales.
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BAO as a Standard Ruler
Angular diameter distance Hubble parameter
RS150 Mpc
(Sound horizon at recombination)
RS c Dz/H Dq D
(Angular radial scales)
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Standard Sphere (AlcockPaczynski Test)
It is a weak test.
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Detections SDSS LRGs
Eisenstein et al. (2005)
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Detections 2dFGRS
Cole et al. (2005)
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BAO Surveys
DES, JEDI, LSST, SNAP Almost every proposed
dark energy survey plans to measure BAO.
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Reduction of Modes due to Photo-z Errors
1/10 modes left!
Glazebrook Blake (2005)
Spectroscopic survey k lt 0.2 h-1Mpc
Photo-z survey sz 0.03 (1z)
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Prospects Power Spectrum
Errors are dominated by sample variance (volume)
at low-z and shot noise (number density) at
high-z. For photo-z surveys, sz reduces the
number of modes. See also Blake Bridle (2005).
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Prospects Angular Diameter Distance

• 1 distance errors
• scales with vsz
• CMB priors WK0

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Recovering the Hubble Parameter

• Photo-z errors (in the line-of-sight direction)
  introduce a strong feature in the power spectrum
• Exponentially sensitive to the Hubble parameter
• Knowledge of the photo-z error distribution is
  crucial for recovering H from photometric BAO
  surveys.

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Constraints on the Hubble Parameter

• Constraints on the Hubble parameter as a function
  of the prior on the rms error of photo-zs.
• Precision on sz controls the errors on H.
• CMB priors WK0

Zhan Knox (astro-ph/0509260)
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Self-Calibration of Photo-z Bias

• Constraints on the photo-z bias as a function of
  the prior on the rms.
• Tight constraints on D H provide a useful
  consistency test of photo-z bias.

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LSST Constraints on w0 and wa BAO
Zhan Knox (astro-ph/0509260)
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LSST Constraints on w0 and wa Weak Lensing
Ma, Hu, Huterer (2005) Ma (private
communication)
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Comparison

• CMB priors WK0
• Weak lensing shear tomography assumes that
  photo-z errors are known perfectly.
• BAO constraints are competitive.
• A large rms photo-z error is tolerable the key
  is the uncertainty in sz.

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CMB LSST BAO Shear Tomography
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CMB LSST BAO Shear Tomography
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CMB LSST BAO Shear Tomography
Unrealistic because 1) we have not accounted for
the shear-galaxy correlation (Hu Jain 2004), 2)
photo-z errors are known perfectly in WL. This is
a limiting case!
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Curvature? The Need for High-z Data
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Curvature? The Need for High-z Data
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Curvature? The Need for High-z Data
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Curvature? The Need for High-z Data

• CMB priors
• High-z data not critical if WK is fixed
• High-z data crucial if WK unknown
• Behavior of the constraints depends on the survey
  and redshift errors
• See also Weller Albrecht (2001) and Linder
  (2005) for discussions on SNe data

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Summary

• Deep and wide photo-z surveys such as the LSST
  survey can be a valuable probe of possible
  features in the matter power spectrum on very
  large scales.
• LSST can measure the angular diameter distance to
  percent level through BAO as well as weak lensing
  shear tomography.
• Photo-z errors introduce a new feature in the
  galaxy power spectrum that enables us to measure
  the Hubble parameter, H. However, the errors of H
  depend highly on our knowledge of the error
  distribution of photo-zs.
• Consequently, photo-z BAO (weak lensing as well)
  constraints on dark energy equation of state
  parameters are sensitive to how accurately we
  know the photo-z error distribution.
• Given the same priors on photo-z errors, photo-z
  BAO is competitive with weak lensing shear
  tomography.
• To relax the flatness prior, high-z data are
  crucial.
• Nonlinearities are not negligible. One must
  precisely calibrate the power spectrum in real
  and redshift spaces with N-body simulations (e.g.
  Seo Eisenstein 2003, 2005 Scoccimarro 2004
  Linder White 2005 Springel et al. 2005).