to evaluate the projection effect on the expected 2PCF, $\xi_E$. For this, consider a sample of cosmic objects in a thin redshift bin $z \in [z_1, z_2]$, that is, $z_1 \simeq z_2$. Because of this, $\xi_E^{z_1}(s) \simeq \xi_E^{z_2}(s) \simeq  \xi_E^{\bar{z}}(s)$, where $\overline{z} \equiv (z_{1}+z_{2})/2$. Therefore, one can obtain the expected 2PACF, $\omega_E^{\bar{z}}(\theta)$, as a projection of the expected 2PCF, $\xi_E^{\bar{z}}(s)$, in that redshift shell $$\begin{aligned}
\omega_E^{\bar{z}}(\theta)=\int_{0}^{\infty}dz_{1}\, \phi(z_{1})
\int_{0}^{\infty}dz_{2}\, \phi(z_{2})\, \xi_E^{\bar{z}}(s) \, ,
\label{eq4}\end{aligned}$$ where $\phi$ is the top-hat selection function which should be normalized to 1, $s$ is the 3D separation between pairs, and for a spatially flat Robertson-Walker metric is calculated using the relation: $s = \sqrt{\zeta^2(z_1)+\zeta^2(z_2)-2\zeta(z_1)\zeta(z_2) \cos{\theta}}$, where $\theta$ is the angular separation between those pairs, and $\zeta(z_i)$ is the comoving radial distance to the quasar with redshift $z_i$, obtained using a cosmological model. The expected 2PCF is given by $$\begin{aligned}
\xi_E^{\bar{z}}(s)=\int_{0}^{\infty}\frac{dk}{2\pi^{2}}\,k^{2}\,j_{0}(ks)\,P(k,\overline{z}) \, ,\end{aligned}$$ where $j_{0}$ and $P(k,\overline{z})$ are the spherical Bessel function of zero order and the matter power spectrum, respectively. To calculate the matter power spectrum one needs to assume a cosmological model, and this is the model dependence step mentioned in section \[sec1\]. However, as we shall confirm in section \[IVc\], for the features of 