Cosmological parameter constraints from SDSS luminous red galaxies: a new treatment of large-scale clustering

Abstract

We apply a new model for the spherically averaged correlation function at large pair separations to the measurement of the clustering of luminous red galaxies (LRGs) made from the SDSS by Cabre and Gaztanaga(2009). Our model takes into account the form of the BAO peak and the large scale shape of the correlation function. We perform a Monte Carlo Markov chain analysis for different combinations of datasets and for different parameter sets. When used in combination with a compilation of the latest CMB measurements, the LRG clustering and the latest supernovae results give constraints on cosmological parameters which are comparable and in remarkably good agreement, resolving the tension reported in some studies. The best fitting model in the context of a flat, Lambda-CDM cosmology is specified by Omega_m=0.261+-0.013, Omega_b=0.044+-0.001, n_s=0.96+-0.01, H_0=71.6+-1.2 km/s/Mpc and sigma_8=0.80+-0.02. If we allow the time-independent dark energy equation of state parameter to vary, we find results consistent with a cosmological constant at the 5% level using all data sets: w_DE=-0.97+-0.05. The large scale structure measurements by themselves can constrain the dark energy equation of state parameter to w_DE=-1.05+-0.15, independently of CMB or supernovae data. We do not find convincing evidence for an evolving equation of state. We provide a set of "extended distance priors" that contain the most relevant information from the CMB power spectrum and the shape of the LRG correlation function which can be used to constrain dark energy models and spatial curvature. Our model should provide an accurate description of the clustering even in much larger, forthcoming surveys, such as those planned with NASA's JDEM or ESA's Euclid mission.

Figures (17)

• Figure 1: The spherically averaged correlation function of LRGs in redshift space. Circles with errorbars show the correlation function used in this paper. The shaded region shows the dispersion in the correlation function obtained when using the new MANGLE mask of Swanson et al. (2008) with different completeness fractions. The dotted line shows the result for the north stripe of DR6. We have also calculated the correlation function for the new DR7 (solid line), estimated using a random catalog generated from a smoothed version of the selection function. The dashed line shows the estimate from DR7 without smoothing. The measurement from Eisenstein et al. (2005) is shown using triangles; note these authors had fewer LRGs and used broader bins.
• Figure 2: Normalized covariance matrix estimated from 216 mocks LRG samples. Here we test the covariance between the monopole correlation (horizontal axis) and the radial (LOS) correlation (vertical axis). The correlation is only important on small scales and is negligible (less than 10%) for the scales of interest here ($>40\,h^{-1}\,{\rm Mpc}$).
• Figure 3: The correlation function of dark matter halos in redshift space measured in an ensemble of 50 large-volume N-body simulations (with total volume of $\sim 105\,h^{-3}\, {\rm Gpc}^3$). The error bars correspond to the error on the mean of the ensemble and are obtained from the scatter among the $50$ realizations. The best fitting parametric model used in this work, Eq. (\ref{['eq:xi_model']}), is shown by the solid blue line (note the fit takes into account the covariance between the bins). The dashed line corresponds to setting $A_{\rm MC}=0$ and highlights the importance of this term in matching the shape of the correlation function at $r < 80\,h^{-1}\,{\rm Mpc}$. The scaling uses $r_{\rm BAO}=102 h^{-1}$Mpc.
• Figure 4: The impact of a mismatch in cosmology on the form of the correlation function. The upper panel shows the difference between the correlation functions measured assuming different fiducial cosmologies ($\Lambda$CDM models with varying $\Omega_{\rm m}$) from that obtained assuming $\Omega_{\rm m}=0.25$. The lower panel shows the same comparison after applying the scale shift of Eq. (\ref{['eq:cor_fact']}) to take into account the change in the value of $\Omega_{\rm m}$.
• Figure 5: The dependence of the constraints on cosmological parameters on the minimum pair separation, $r_{\rm min}$, included in the correlation function measurement. The points show the mean value of the likelihood for each parameter and the error bars show the 68% CL.