M. Vargas-Magaña, Julian. E. Bautista, J. -Ch. Hamilton, N. G. Busca, É. Aubourg, A. Labatie, J. -M. Le Goff, Stephanie Escoffier, Marc Manera, Cameron K. McBride, Donald P. Schneider, Christopher N. A. Willmer
Measuring the two-point correlation function of the galaxies in the Universe gives access to the underlying dark matter distribution, which is related to cosmological parameters and to the physics of the primordial Universe. The estimation of the correlation function for current galaxy surveys makes use of the Landy-Szalay estimator, which is supposed to reach minimal variance. This is only true, however for a vanishing correlation function. We study the Landy-Szalay estimator when these conditions are not fulfilled and propose a new estimator that provides the smallest variance for a given survey geometry. Our estimator is a linear combination of ratios between pair-counts of data and/or random catalogues (DD, RR and DR). The optimal combination for a given geometry is determined by using log-normal mock catalogues. The resulting estimator is biased in a model dependent way, but we propose a simple iterative procedure to obtain an unbiased model independent estimator. Using various sets of simulated data (log-normal, second-order LPT and N-Body), we obtain a 20-25% gain on the error bars on the two-point correlation function for the SDSS geometry and $\Lambda$CDM correlation function. When applied on to SDSS data (DR7 and DR9), we achieve a similar gain on the correlation functions which translates in a 10-15% improvement on the estimation of the densities of matter, $\Omega_m$, and dark energy, $\Omega_\Lambda$ in open LCDM model. The constraints derived from DR7 data with our estimator are similar to those obtained with the DR9 data and the Landy-Szalay estimator which covers a volume twice larger and with a density three times higher.
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http://arxiv.org/abs/1211.6211
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