Cosmological Constraints from the Clustering of the Sloan Digital Sky Survey DR7 Luminous Red Galaxies

TL;DR

This paper develops and applies a halo-density-field approach to SDSS DR7 LRG clustering, reconstructing the halo field to closely trace the underlying matter power spectrum up to $k\le0.2\,h\,\mathrm{Mpc}^{-1}$. The authors calibrate a physically motivated model for $P_{halo}(k,\mathbf{p})$ using extensive N-body mocks, account for non-linear BAO damping, non-linear growth, and halo bias, and incorporate systematic nuisance parameters with controlled priors. They obtain LRG-alone constraints on $\Omega_m h^2$ and $D_V(0.35)$, and, when combined with WMAP5 and Union SN data, deliver tight bounds on $\Omega_m$, $H_0$, $\Omega_k$, and $w$, with additional competitive limits on $\sum m_\nu$ and $N_{eff}$. The results demonstrate the power of full-shape information from the halo power spectrum in breaking degeneracies and providing robust, cross-validated cosmological constraints, setting a framework for analyzing future, larger redshift surveys.

Abstract

We present the power spectrum of the reconstructed halo density field derived from a sample of Luminous Red Galaxies (LRGs) from the Sloan Digital Sky Survey Seventh Data Release (DR7). The halo power spectrum has a direct connection to the underlying dark matter power for k <= 0.2 h/Mpc, well into the quasi-linear regime. This enables us to use a factor of ~8 more modes in the cosmological analysis than an analysis with kmax = 0.1 h/Mpc, as was adopted in the SDSS team analysis of the DR4 LRG sample (Tegmark et al. 2006). The observed halo power spectrum for 0.02 < k < 0.2 h/Mpc is well-fit by our model: chi^2 = 39.6 for 40 degrees of freedom for the best fit LCDM model. We find Ω_m h^2 * (n_s/0.96)^0.13 = 0.141^{+0.009}_{-0.012} for a power law primordial power spectrum with spectral index n_s and Ω_b h^2 = 0.02265 fixed, consistent with CMB measurements. The halo power spectrum also constrains the ratio of the comoving sound horizon at the baryon-drag epoch to an effective distance to z=0.35: r_s/D_V(0.35) = 0.1097^{+0.0039}_{-0.0042}. Combining the halo power spectrum measurement with the WMAP 5 year results, for the flat LCDM model we find Ω_m = 0.289 +/- 0.019 and H_0 = 69.4 +/- 1.6 km/s/Mpc. Allowing for massive neutrinos in LCDM, we find \sum m_ν < 0.62 eV at the 95% confidence level. If we instead consider the effective number of relativistic species Neff as a free parameter, we find Neff = 4.8^{+1.8}_{-1.7}. Combining also with the Kowalski et al. (2008) supernova sample, we find Ω_{tot} = 1.011 +/- 0.009 and w = -0.99 +/- 0.11 for an open cosmology with constant dark energy equation of state w.

Figures (19)

• Figure 1: Fits to the redshift distributions for the LRG selection used in this work (solid curves) and the zehavi/etal:2005a$-23.2 < M_g < -21.2$ sample used in tegmark/etal:2006 (dashed curves). Upper panel: $n(z)$ vs redshift in units of $10^{-4}$ ($h^{-1}$ Mpc)$^{-3}$Lower panel: $N(<z) = \int dz n(z) dV/dz$ (arbitrary overall normalization).
• Figure 2: Top panel: Measured $\hat{P}_{halo}(k)$ bandpowers. Error bars indicate $\sqrt{C_{ii}}$ (Eq. \ref{['covdefn']}). Middle panel: Correlations between data values calculated using Log-normal catalogues, assuming our fiducial cosmological model. Bottom panel: The normalized window function for each of our binned power spectrum values with $0.02<k<0.2 \,h\,{\rm Mpc}^{-1}$. Each curve shows the relative contribution from the underlying power spectrum as a function of $k$ to the measured power spectrum data. The normalisation is such that the area under each curve is unity. For clarity we only plot curves for every other band power.
• Figure 3: Upper left panel: Power spectra for the fiducial cosmology. The solid curve is $P_{\rm lin}(k)$ and the dashed curve is $P_{\rm nw}(k) r_{\rm halofit}$, the non-linear power spectrum from halofit using $P_{\rm nw}(k)$ as the input. Upper right panel: $P_{\rm lin}(k)/P_{\rm nw}(k)$. Bottom left panel: $P_{DM}(k)/P_{damp}(k, \sigma_m)$ measured in $N$-body simulation snapshots at $z_{MID}$, reported in reid/spergel/bode:2008, compared with the smooth correction predicted by halofit, $r_{\rm halofit}$. Bottom right panel: $r_{\rm halofit}$ at {$z_{NEAR}$, $z_{MID}$, $z_{FAR}$} = {0.235, 0.342, 0.421}.
• Figure 4: BAO-damping times polynomial fits to $P_{halo}(k,{\bf p}_{fid})/P_{lin}(k,{\bf p}_{fid})$ for our mock NEAR, MID, and FAR LRG reconstructed halo density field subsamples in reid/spergel/bode:2008; {$z_{NEAR}$, $z_{MID}$, $z_{FAR}$} = {0.235, 0.342, 0.421}. The smooth component of these fits (dashed curves) enter our model $P_{halo}(k, {\bf p})$ through Eqns. (\ref{['eq:bias']}), while the amplitude of the BAO suppression $\sigma^2_{halo}$ enters in Eqn. \ref{['eq:Pdamp']}. Lower right panel: Ratio of the shape of the smooth components for the NEAR and FAR redshift subsamples to the MID redshift subsample.
• Figure 5: Constraints from the LRG DR7 $\hat{P}_{halo}(k)$ for a $\Lambda$CDM model with $\Omega_b h^2 = 0.02265$ and $n_s = 0.960$ fixed. The dotted contours show $\Delta \chi^2 = 2.3$ and 6.0 contours for the $\hat{P}_{halo}(k)$ fit to a no-wiggles model. The solid contours indicate $\Delta \chi^2 = 2.3$, 6.0, and 9.3 contours for $k_{max} =0.2 \,h\,{\rm Mpc}^{-1}$ and our fiducial $P_{halo}(k,{\bf p})$ model. The three dashed lines show the best-fitting and $\pm 1\sigma$ values $r_s/D_V(0.35) = 0.1097 \pm 0.0036$ from P09.