1. Cosmology with Galaxy Correlations from Photometric Redshift Surveys
Hu Zhan UC Davis in 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
1/12/2006
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3. Why Very Large Scales? Cross-check for CMB Primordial power spectrum
Probing inflation
Consistency test for cosmological constraints from smaller scales
1/12/2006
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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
1/12/2006
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5. Large Synoptic Survey Telescope The
8.4-meter primary
10 deg2 FOV
3 billion pixels µm
Large Synoptic Survey Telescope
The
23,000 deg2 survey area
V = 26.5 mag
Billions of galaxies up to z ~ 3
1/12/2006
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6. Photo-z Errors Spherical harmonic basis
Subject to errors in galaxy bias, photometry, cosmology…
Reconstruction at high k can be improved
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
Zhan et al (astro-ph/ )
1/12/2006
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7. Schlegel, Finkbeiner, & Davis (1998)
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)
1/12/2006
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8. 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.
only modes in the histogram contribute to the PS measurement at k=0.02h/Mpc
1/12/2006
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9. Galaxy Bias Constant bias when binned in luminosity
Tegmark et al. (2004)
1/12/2006
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10. Statistical Errors of the Power Spectrum
Binning: Dk = 0.05 k
Survey volume with zmax=1 is roughly 1/9 of that with zmax=2.5
LSST: complimentary to CMB
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11. 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)
1/12/2006
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12. Very-Large-Scale Power Spectrum: WMAP
~20% errors on largest scales.
Bridle et al. (2003)
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13. (Angular & radial scales)
BAO as a Standard Ruler
+ RS~150 Mpc
Angular diameter distance & Hubble parameter
(Sound horizon at recombination)
RS = c Dz/H = Dq D
(Angular & radial scales)
1/12/2006
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14. Standard Sphere (Alcock—Paczynski Test)
Dq D
c Dz/H
c Dz/H = Dq D
 HD
Wrong HD!
Observer
A—P test is weak, Constraints mostly from BAO as standard ruler
It is a weak test.
1/12/2006
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15. Detections: SDSS LRGs Luminous red galaxies, still noisy
Eisenstein et al. (2005)
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16. Detections: 2dFGRS
Cole et al. (2005)
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17. BAO Surveys
Blake & Bridle (2005)
+ DES, JEDI, LSST, SNAP… Almost every proposed dark energy survey plans to measure BAO.
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18. Reduction of Modes due to Photo-z Errors
1/10 modes left!
Shot noise is amplified by the photo-z suppression when recovering PS(k,m). P(k) decreases toward small scales (k>0.03h/Mpc), so at high k3 the amplified shot noise may not be tolerable and the modes have to be discarded.
Glazebrook & Blake (2005)
Spectroscopic survey k < 0.2 h-1Mpc
Photo-z survey sz = 0.03 (1+z)
1/12/2006
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19. Prospects: Power Spectrum
LSST: 0.2<z<3, 7 redshift bins. Spectroscopic survey can use finer bins, very hard to get spectra at 1.3<z<2.5.
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).
1/12/2006
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20. Prospects: Angular Diameter Distance
~ 1% distance errors
~ scales with √sz
CMB priors & WK=0
s1000 = 1000 sq deg spectroscopic survey up to z=3; note that WFMOS is 2000 sq deg at z<1.3 and 300 sq deg at 2.5<z<3; distance error proportional to sqrt(sigma_z); 0.1n(r) for sub-sampling
1/12/2006
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21. 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.
1/12/2006
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22. 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 & WK=0
Zhan & Knox (astro-ph/ )
1/12/2006
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23. 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.
1/12/2006
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24. LSST Constraints on w0 and wa: BAO
Zhan & Knox (astro-ph/ )
1/12/2006
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25. LSST Constraints on w0 and wa: Weak Lensing
Ma, Hu, & Huterer (2005); Ma (private communication)
1/12/2006
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26. Comparison CMB priors & WK=0
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.
LSST WL is from Song & Knox (2004). BAO is from Zhan & Knox (2005) SNe is from Knox, Albrecht, & Song (2005)
1/12/2006
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27. CMB + LSST BAO “+” Shear Tomography
0.2<z<3, 7bins, same as before, rms photo-z error is a little larger, but the priors on photo-z rms and bias are stronger. omegam is the physical matter density.
1/12/2006
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28. CMB + LSST BAO “+” Shear Tomography
1/12/2006
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29. 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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30. Curvature? The Need for High-z Data
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31. Curvature? The Need for High-z Data
1/12/2006
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32. Curvature? The Need for High-z Data
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33. 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
1000 sq deg spectroscopic survey: w0—wa degrades quite a bit if no high-z data; even worse if WK is unknown.
1/12/2006
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34. 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).
1/12/2006
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