3D-Radial galaxy correlation function

Abstract

Tests of cosmological models via measurements of galaxy correlations will require increasing modeling accuracy, given the high precision of measurements promised by forthcoming galaxy surveys. In this work we investigate the biases introduced in parameter estimation when using different approximations in the modeling of the galaxy two point correlation function. We study this for two example surveys, with different binning strategies, for measurements of the Primordial non-Gaussianity parameter $f_{\mathrm{NL}}$ and the growth rate of structures $\gamma$. We then investigate the same issue for the nDGP model, to see if results will change for a different cosmological model. Our results show that failing to properly account for radial and angular separation between galaxies will induce a considerable shift in parameters best fit estimates, the bias being larger for thicker redshift bins. When accounting for radial evolution within the bins by integrating over z, such shifts are reduced but still present. We then introduce a new hybrid model, which we call 3D radial, where we neglect the purely wide angle terms, but include a proper 3D modeling of the system by including radial modes. Using this model, we show that biases are greatly reduced, making it an accurate formalism to be safely used for forthcoming galaxy surveys. This moreover confirms other recent findings on the importance of including radial modes to accurately model the galaxy correlation function.