Cosmological Constraints from the Clustering of the Sloan Digital Sky Survey DR7 Luminous Red Galaxies (0907.1659v2)

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 \Omega_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 \Omega_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 \Omega_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_{\nu} < 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 \Omega_{tot} = 1.011 +/- 0.009 and w = -0.99 +/- 0.11 for an open cosmology with constant dark energy equation of state w.

• The paper refines cosmological constraints by reconstructing the halo density field to leverage eight times more modes than previous analyses.
• The paper fits a ΛCDM model to the power spectrum, yielding precise estimates such as Ωm h²(nₛ/0.96)⁰.¹³ ≈ 0.141 and rₛ/DV(0.35) ≈ 0.11.
• The paper combines SDSS DR7 data with WMAP5 results to tighten bounds on H₀, Ωm, neutrino masses, and the effective number of relativistic species.

Cosmological Constraints from the SDSS DR7 Luminous Red Galaxies

The paper by Reid et al. presents a detailed analysis of the cosmological implications derived from the clustering of luminous red galaxies (LRGs) as observed in the Sloan Digital Sky Survey Data Release 7 (SDSS DR7). The key focus of the paper is to utilize the power spectrum of the LRGs to extract significant cosmological parameters with improved precision and accuracy. This work enhances previous analyses by leveraging the increased volume and superior quality of the DR7 dataset, enabling a more in-depth exploration into the quasi-linear regime beyond previous constraints.

Power Spectrum Analysis

The researchers reconstructed the halo density field from the DR7 LRG sample to mitigate the non-linear distortions and shot noise effects prevalent in galaxy clustering data. The analysis shows that the reconstructed halo power spectrum is closely aligned with the underlying dark matter distribution for scales with wave numbers $0.02 < k < 0.2 \; h$ Mpc$^{-1}$. This allows the authors to utilize approximately eight times more modes in the cosmological analysis than previous studies restricted to $k_{max} = 0.1 \; h \, \text{Mpc}^{-1}$.

The power spectrum measurement was fitted using a $\Lambda$CDM cosmological model, yielding notable constraints such as $$\Omega_m h^2 (n_s/0.96)^{0.13} = 0.141^{+0.009}_{-0.012}$$. This result is in excellent agreement with existing Cosmic Microwave Background (CMB) measurements, reinforcing the consistency of the standard cosmological model. Additionally, the analysis derives $r_s/D_V(0.35) = 0.1097^{+0.0039}_{-0.0042}$, constraining the ratio of the sound horizon at the baryon-drag epoch to an effective distance at redshift $z=0.35$.

Combined Cosmological Constraints

By integrating the halo power spectrum data with WMAP 5-year results, the paper provides even tighter bounds on the cosmological parameters, specifically obtaining $\Omega_m = 0.289 \pm 0.019$ and $H_0 = 69.4 \pm 1.6 \, \text{km/s/Mpc}$ when assuming a flat $\Lambda$CDM universe. Allowing for massive neutrinos yields the constraint $\sum m_{\nu} < 0.62 \, \text{eV}$ at 95% confidence level, which signifies a considerable improvement over constraints derived from the CMB alone. Furthermore, when considering the effective number of relativistic species as a free parameter, the paper derives $N_{eff} = 4.8^{+1.8}_{-1.7}$, suggesting potential deviations from the standard model expectation of $N_{eff} = 3.04$.

Comparison with a no-wiggles model highlights the significance of baryon acoustic oscillations (BAO) in breaking the degeneracies inherent in cosmological distance measurements, thereby tightening constraints on key parameters such as $D_V(0.35)$. Additionally, the paper demonstrates the robustness of the results against various systematics and modeling uncertainties, including the treatment of redshift space distortions (RSD) and the approximation of galaxy bias.

Broader Implications and Future Prospects

The work represents a crucial contribution to precision cosmology, offering refined constraints on the parameters governing the universe’s expansion and composition. The analytical enhancements, particularly those concerning the halo model and the incorporation of additional statistical power, set a high standard for future large-scale structure surveys. These results are pivotal in providing independent verification of the $\Lambda$CDM paradigm and may serve as a foundation for interpreting more complex or extended cosmological models.

The developments elucidated in this paper hold promise not only for the continued refinement of cosmological parameters but also in the methodological approaches to survey analysis, serving as a template for forthcoming projects such as the Dark Energy Spectroscopic Instrument (DESI) and the Euclid mission. The techniques showcased are poised to underpin analyses aiming to further unravel the intricacies of dark matter, dark energy, and other fundamental cosmological phenomena.