Cosmological implications from the full shape of the large-scale power spectrum of the SDSS DR7 luminous red galaxies

TL;DR

The paper constrains cosmology by modeling the full shape of the large-scale power spectrum from ~9×10^4 SDSS DR7 LRGs, using a Renormalized Perturbation Theory–inspired framework to describe mildly nonlinear bias and redshift-space effects. By combining with CMB, Union2 SNIa, and a precise $H_0$ prior, it yields tight constraints on flat and non-flat $\Lambda$CDM and its extensions, notably showing consistency with a cosmological constant and negligible curvature. The analysis demonstrates that the full $P(k)$ information reduces parameter degeneracies and improves constraints beyond BAO alone, validating the approach for upcoming larger surveys. The results underscore the need for accurate modeling of nonlinearities and survey window effects to exploit the full information content of future galaxy surveys.

Abstract

We obtain cosmological constraints from a measurement of the spherically averaged power spectrum (PS) of the distribution of about 90000 luminous red galaxies (LRGs) across 7646 deg2 in the Northern Galactic Cap from the DR7 of the SDSS. The errors and mode correlations are estimated thanks to the 160 LasDamas mock catalogues, created in order to simulate the same galaxies and to have the same selection as the data. We apply a model, that can accurately describe the full shape of the PS with the use of a small number of free parameters. Using the LRG PS, in combination with the latest measurement of the temperature and polarisation anisotropy in the cosmic microwave background (CMB), the luminosity-distance relation from the largest available type 1a supernovae (SNIa) dataset and a precise determination of the local Hubble parameter, we obtain cosmological constraints for five different parameter spaces. When all the four experiments are combined, the flat LCDM model is characterised by Omega_M=0.259+-0.016, Omega_b=0.045+-0.001, n_s=0.963+-0.011, sigma_8=0.802+-0.021 and h=0.712+-0.014. When we consider curvature as a free parameter, we do not detect deviations from flatness: Omega_k=(1.6+-5.4)*10^{-3}, when only CMB and the LRG PS are used; the inclusion of the other two experiments do not improve this result. Considering the dark energy equation of state w_DE as time independent, we measure w_DE=-1.025+-0.065, for a flat geometry, w_DE=-0.981+-0.083 otherwise. When describing w_DE through a linear function of the scale factor, our results do not evidence any time evolution. In the next few years new experiments will allow to measure the clustering of galaxies with a precision much higher than achievable today. Models like the one used here will be a valuable tool in order to achieve the full potentials of the observations and obtain unbiased constraints on the cosmological parameters.

Figures (26)

• Figure 1: Spline fit to the redshift distribution of the LRGs (dot-dashed line) and the original and modified $n(z)$ of the mock catalogues (dashed and solid lines, respectively)
• Figure 2: LRGs power spectrum (blue dots connected with solid line) and corresponding 1-$\sigma$ error bars from the mock catalogues (shaded area). The green dashed and the red solid lines show, respectively, the linear and model power spectra computed using the mean value of the cosmological parameters of the $\Lambda$CDM cosmology show in the last column of Table \ref{['tab:1D_LCDM']}.
• Figure 3: Panel a): power spectra of Figure \ref{['fig:meas_powersp']} divided by a linear power spectrum without BAOs Eisenstein_98. Panel b): rows of the window matrix corresponding to the $k$-bands of the measured LRG power spectrum. For clarity only one every third row is shown.
• Figure 4: Panel a): mean power spectrum (blue dots connected by solid line) with 1-$\sigma$ variance (blue shaded area) from the mock catalogues. The linear and model power spectra, convolved with the window function, are shown with green dashed and red solid lines, respectively. Panel b): same power spectra divided by a linear power spectrum without BAOs Eisenstein_98.
• Figure 5: Correlation matrix computed from the LasDamas mock catalogues.