1. 6-band Survey: ugrizy 320–1050 nm
Cosmology with Galaxy Correlations from the Large Synoptic Survey Telescope Hu Zhan (UC Davis)
Deep and wide photometric redshift surveys are useful probes of the large-scale structure of the universe. The proposed survey of the Large Synoptic Survey Telescope (LSST) will enable us to measure the galaxy power spectrum on very large scales that are not yet accessible to current galaxy surveys. One may use such large-scale galaxy power spectrum to probe possible features in the primordial power spectrum. On smaller scales, baryon acoustic oscillations (BAO) will be readily detectable with LSST and be utilized to achieve percent level measurements of the angular diameter distance as a function of redshift. Meanwhile, if the distribution of photometric redshift errors is accurately quantified as required by weak lensing, then LSST will also be able to measure the Hubble parameter with a comparable accuracy. This will allow LSST BAO to place tight constraints on dark energy equation of state parameters that are competitive with those from LSST weak lensing shear tomography.
Very-Large-Scale Matter Power Spectrum
Baryon Acoustic Oscillations
The matter power spectrum on very large scales is of great interest because it can be cleanly used to infer the power spectrum of primordial fluctuations. The primordial power spectrum is one of our only handles on the mechanism that led to the fluctuations that are responsible for the diversity of structures we see in the universe today.
The acoustic waves that give rise to the peaks in the CMB temperature fluctuations also generate a small excess in the galaxy two-point correlation function at roughly 150 Mpc, corresponding to oscillating features in the power spectrum known as baryon acoustic oscillations (BAO). Since the co-moving scales of these features do not change after recombination, BAO can be used as a CMB-calibrated standard ruler to measure the angular diameter distance D and Hubble parameter H and to constrain dark energy (see e.g. Eisenstein, Hu, & Tegmark 1998). Photo-z errors can inflate the uncertainties in H, if one does not know the photo-z error distribution.
Figure 3 Baryon acoustic oscillations in LSST galaxy power spectra.
Figure 1 Statistical errors of the matter power spectrum from the LSST survey. The solid lines represent the fiducial model power spectrum, while the dotted lines are the power spectrum generated by a step inflation potential (Peiris et al. 2003).
In the context of inflation, probing larger scales means probing inflation at an earlier epoch. Larger scales exited the fixed-size horizon earlier and thus had more time to expand. Reaching back to these earlier epochs may provide us with valuable clues about inflation (e.g. Zhan et al. 2006).
Exploring these large scales is perhaps the best way, other than precision measurement of CMB polarization on large angular scales, to test the claims of statistical anisotropy in the WMAP temperature maps.
The Need to Know the Photo-z Error Distribution Accurately
The Hubble parameter is a direct measure of the cosmic expansion rate and, hence, crucial for constraining dark energy equation of state (EOS) parameters. Photo-z surveys cannot measure H accurately through BAO. However, since the photo-z suppression to the power spectrum is exponentially sensitive to H (for Gaussian errors, ), one can achieve tight constraints on H with accurate knowledge of the photo-z error distribution (Zhan & Knox 2005, astro-ph/ ). This will enable LSST BAO to place tight constraints on dark energy equation of state parameters that are competitive with those from LSST shear power spectra.
In reality, photo-z errors are not Gaussian. Therefore, to achieve the constraints, one must quantify the probability distribution of photo-z errors accurately.
Reconstructing the Matter Power Spectrum
Figure 2 A simple estimator of the matter power spectrum. Dotted lines are redshift space galaxy power spectra with photo-z errors sz = sz0 (1 + z). The reconstructions are performed for sz0 = Arrows indicate errors due to a 30% under-estimation of the galaxy bias growth rate.
Photometric redshift (photo-z) errors severely suppress the observed galaxy power spectrum. A smaller rms photo-z error leads to a better reconstruction.
An incorrect model of galaxy bias evol-ution can alter the shape of the recon-structed power spectrum. But, the bias may not be the dominant error, because it can be determination to percent level through a joint analysis of shear and galaxy correlations (Hu & Jain 2004).
A moderate error (~10%) in the fiducial cosmological model does not severely degrade the reconstruction.
The reconstruction on smaller scales can be improved with better estimators.
Other challenges: photometry errors, extinction, redshift distortion…
Figure 4 Left panel: Improvement of the constraints on w0 and wa with strengthening priors on the rms photo-z error, where the dark energy EOS is parametrized as w(z)=w0+wa(1-a). Note that the rms itself is not so crucial as the uncertainties of the rms. Right panel: The importance of high-z data in the presence of an unknown curvature.
The Large Synoptic Survey Telescope
6-band Survey: ugrizy 320–1050 nm
Coverage: 20,000 deg2, 0.2 arcsec / pixel
FOV: 10 deg2
Depth: 26.5 AB (24.5 in u)
24 AB mag in 15 seconds
3 billion galaxies with color redshifts
200,000 Type Ia supernovae
100,000 Shear-selected galaxy clusters
Curvature: the Need for High-z Data
For LSST BAO with the flatness assumption, high-z data (z >1.4 in Fig. 4) do not provide much additional constraint on dark energy EOS parameters w0 and wa, but it is crucial if one includes curvature as a free parameter (for SNe, see Weller & Albrecht 2001; Linder 2005). This is because curvature is somewhat degenerate with dark energy. For example, it is indistinguishable from dark energy of w = -1/3 in terms of D & H. The curvature term WK evolves as (1 + z)2, so one can constrain it better with high-z data [in this case, s (WK) = ±10-3], assuming that dark energy evolves much slower, and restore the constraints on w0 and wa.