Clustering tomography: measuring cosmological distances through angular clustering in thin redshift shells

We test the cosmological implications of studying galaxy clustering using a tomographic approach, by computing the galaxy two-point angular correlation function $\omega(\theta)$ in thin redshift shells using a spectroscopic-redshift galaxy survey. The advantages of this procedure are that it is not necessary to assume a fiducial cosmology in order to convert measured angular positions and redshifts into distances, and that it gives several (less accurate) measurements of the angular diameter distance $D_\rm{A}(z)$ instead of only one (more precise) measurement of the effective average distance $D_\rm{V}(z)$, which results in better constraints on the expansion history of the Universe. We test our model for $\omega(\theta)$ and its covariance matrix against a set of mock galaxy catalogues and show that this technique is able to extract unbiased cosmological constraints. Also, assuming the best-fit $\Lambda$CDM cosmology from the cosmic microwave background measurements from the Planck satellite, we forecast the result of applying this tomographic approach to the final Baryon Oscillation Spectroscopic Survey catalogue in combination with Planck for three flat cosmological models, and compare them with the expected results of the isotropic baryon acoustic oscillation (BAO) measurements post-reconstruction on the same galaxy catalogue combined with Planck. While BAOs are more accurate for constraining cosmological parameters for the standard $\Lambda$CDM model, the tomographic technique gives better results when we allow the dark energy equation of state $w_{DE}$ to deviate from $-1$, resulting in a performance similar to BAOs in the case of a constant value of $w_{DE}$, and a moderate improvement in the case of a time-dependent value of $w_{DE}$, increasing the value of the Figure-of-Merit in the $w_0-w_a$ plane up to $15\%$.