equation (\[eq4\]) for the case of $\delta z=0$. Next, one applies the same procedure but considering $\delta z = 0.05$, which is the thickness of the redshift shell used in the actual measurement, to find $\theta_{E}^{\delta z}$. Then, the BAO angular scale, $\theta_{\mbox{\footnotesize\sc bao}}$, is given by $$\theta_{\mbox{\footnotesize\sc bao}}(\overline{z}) \,=\, \theta_{\mbox{\footnotesize\sc fit}}(\overline{z}) 
+ \Delta \theta(\overline{z}, \delta z) \, \theta_{\mbox{\footnotesize\sc fit}}(\overline{z}) \, ,$$ where $\Delta \theta(\overline{z}, \delta z) \equiv (\theta_{E}^{0} - \theta_{E}^{\delta z})/\theta_{E}^{0}$, that is, computing the expected values $\theta_{E}^{0}$ and $\theta_{E}^{\delta z}$, we perform the shift in the measured value $\theta_{\mbox{\footnotesize\sc fit}}(\overline{z})$ to find the BAO angular scale $\theta_{\mbox{\footnotesize\sc bao}}(\overline{z})$.

This numerical analysis assumes six cosmological parameters: the baryon density $\omega_b \equiv \Omega_b h^2$, the cold dark matter density $\omega_c \equiv \Omega_c h^2$, the ratio between the sound horizon and the angular diameter distance to decoupling $\Theta$, the optical depth to reionization $\tau$, the overall normalization of the primordial power spectrum $A_s$, and the tilted scalar spectral index $n_s$. As a reference model we use $\omega_b = 0.0226,\, \omega_c = 0.112,\, 100\, \Theta=1.04,\, \tau=0.09,\, 10^{9}\,A_s = 2.2,\, 
n_s = 0.96$, and $h$ is the Hubble constant in unit of $ 100\, km\,s^{-1}\,Mpc^{-1}$. We also assume flatness and, for neutrinos, the 