Left: isocontours of the function displaying the relative variation in the galaxy clustering ratio (with respect to the best-fitting value deduced from the analysis of SDSS DR7 data) induced by a wrong choice of the distance-redshift conversion model (i.e. a wrong guess of the cosmological parameters [Ω_m,Ω_X]). The galaxy clustering ratio is reconstructed on the scales (R,r) = (14,42)  h^-1 Mpc, and its expression is approximated well by Eq. (25). The best-fitting cosmology inferred from the analysis of SDSS DR7 data is Ω_m = 0.28, Ω_X = 0.45, w = −1.2. The isocontours measure the strength of the AP geometric distortions. Right: relative variation in the mass clustering ratio that results from computing the power spectrum in the wrong cosmology.