Cosmology with Galaxy Correlations from Photometric Redshift Surveys

1
Cosmology with Galaxy Correlations from
Photometric Redshift Surveys

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

2
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

3
Why Very Large Scales?

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

4
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

5
Photo-z Errors
Dotted lines measured galaxy power spectrum
(PS), including photo-z suppression and redshift
distortion Solid line matter PS Circles
reconstructed matter PS with a simple estimator,
can be improved, also subject to galaxy
clustering bias errors and errors in cosmological
parameters, may be improved with a better
estimator Dashed line matter PS with linear
redshift distortion The larger the rms photo-z
error the more suppression on the PS The
subscripts l n enumerate spherical harmonic
modes

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

Zhan et al. (astro-ph/0508119)
6
All-sky dust IR emission, centered at north
sough galactic poles. Note the structures and the
low dust at high latitudes.
Schlegel, Finkbeiner, Davis (1998)
7
Dust Extinction
only modes in the histogram contribute to the PS
measurement at k0.02h/Mpc

• 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.

Zhan et al. (astro-ph/0508119)
8
Galaxy Bias
Constant bias when binned in luminosity
Tegmark et al. (2004)
9
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

Zhan et al. (astro-ph/0508119)
10
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)

Zhan et al. (astro-ph/0508119)
11
Very-Large-Scale Power Spectrum WMAP
Bridle et al. (2003)
20 errors on largest scales.
12
BAO as a Standard Ruler
Angular diameter distance Hubble parameter
RS150 Mpc
(Sound horizon at recombination)
(Angular radial scales)
13
Standard Sphere (AlcockPaczynski Test)
AP test is weak Constraints mostly from BAO as
standard ruler
14
Detections SDSS LRGs
Luminous red galaxies, still noisy
Eisenstein et al. (2005)
15
Detections 2dFGRS
noisy
Cole et al. (2005)
16
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)
Shot noise is amplified by the photo-z
suppression when recovering PS(k,m). P(k)
decreases toward small scales (kgt0.03h/Mpc), so
at high k3 the amplified shot noise may not be
tolerable and the modes have to be discarded.
17
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).
18
Prospects Angular Diameter Distance

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

s1000 1000 sq deg spectroscopic survey up to
z3 note that WFMOS is 2000 sq deg at zlt1.3 and
300 sq deg at 2.5ltzlt3 distance error
proportional to sqrt(sigma_z) 0.1n(r) for
sub-sampling
19
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.

20
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)
21
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 useful
  self-calibration of photo-z bias.

Zhan Knox (astro-ph/0509260)
22
LSST Constraints on w0 and wa BAO
Zhan Knox (astro-ph/0509260)
23
LSST Constraints on w0 and wa Weak Lensing
Ma, Hu, Huterer (2005) Ma (private
communication)
24
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.

Zhan Knox (astro-ph/0509260)
25
CMB LSST BAO Shear Tomography
26
CMB LSST BAO Shear Tomography
27
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!
28
Curvature? The Need for High-z Data
29
Curvature? The Need for High-z Data
30
Curvature? The Need for High-z Data
31
Curvature? The Need for High-z Data

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

1000 sq deg spectroscopic survey w0wa degrades
quite a bit if no high-z data even worse if WK
is to be inferred.
32
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).