Influence of photometric galaxies redshift distribution in BAO estimation

In the present study, we use the DES Y3 catalog of LRG to incorporate the realistic galaxies' redshift Probability Distribution Function(PDF) into the correlation function cosmological model. We used four different photo-z estimators ANNz2, BPZ, ENF, and DNF to compare how they affect the BAO feature constraint. Moreover, each algorithm included two sample selections based on distinct PDF shapes; one where the PDFs are nearly Gaussian and another opting for the least noisy PDFs with a pronounced peak. Following a parametrised model, we estimated the shift parameter $\alpha$ for the ANNz2 three cuts and the DNF full samples. We found that the BAO from ANNz2 Gaussian sample selection is closer to the fiducial Planck 18 $\Lambda$CDM model. Later, we computed the correlation function $\xi_perp(z_p)$ by getting the bin pairs transversal to each other using CAMB. The kernel window function is the $f(z|z_p)$ which is the selection of the PDF value when the photometric redshift is nearly the same as the spectroscopic redshift estimated by the matched spectroscopic sample. For compatible z eff, we concluded that the shape of the galaxy redshift PDF could shift the BAO feature position either by including the PDF in the model or not. We also learnt that, given the same spectroscopic sample, ANNz2 estimator with its respective selection samples outperforms other estimators for most parameters examined. When the dark energy equation of state parameter, $w_0$, is considered, DNF emerges as the optimal algorithm, provided it has sufficient statistical data. Our analysis recommends that upcoming photo-z survey collaborations incorporate multiple photo-z estimation algorithms in their cosmological inference process; this approach will facilitate comprehension of systematic effects on various parameters.