though the redshifts for template cluster galaxies are replaced by the systematic redshift of the cluster. Galaxies fainter the an estimated magnitude of -20 were removed from the sample as those showed significant deviations from a linear TF relation. In order to get a cleaner TF sample we select only objects with inclination $i > 45^\circ$ to ease problems with inclination corrections. All this leaves us with a sample of 2859 galaxies with redshifts less than $100\hmpc$. The effective depth of the sample defined as the error weighted mean redshift of galaxies is $\sim 40\hmpc$.

We will refer with $\Lambda$CDM7 to the $\Lambda$CDM cosmological model with the WMAP7 best fit parameters [@wmap7] for a flat Universe, i.e. the total mass density parameter $\Omega_m=0.266$, baryonic density parameter $\Omega_b=0.0449$, a Hubble constant $h=0.71$ in units of $100\kms {\rm Mpc}^{-1}$, a scalar spectral index $n_s=0.963$, and $\sigma_8=0.8$ for the rms of linear density fluctuations in spheres of $8\hmpc$. Throughout the paper, variants of $\Lambda$CDM7 with different $\Omega_m$ and $\sigma_8$ will be considered. All other parameters will be fixed at their WMAP7 values.

The outline of the paper is as follows. Details of the  method are described in §\[sec:ace\], while the more standard Maximum 