Baryon Acoustic Oscillations from galaxy surveys

Abstract: We conducted a review of the fundamental aspects of describing and detecting the Baryon Acoustic Oscillation (BAO) feature in galaxy surveys, emphasizing the optimal tools for constraining this probe based on the type of observation. Additionally, we included new results with two spectroscopic datasets to determine the best-fit model for the power spectrum, $P(k)$. Using the framework described in a previous analysis, we applied this to a different sub-sample of the BOSS survey, specifically galaxies with redshifts $0.3<z<0.65$. We also examined the eBOSS dataset with redshifts $0.6<z<1.0$, adjusting the number of parameters in the traditional polynomial fit to account for the higher redshift range. Our results showed that the dilation scale parameter $\alpha$ derived from the BOSS dataset had smaller error bars compared to the eBOSS dataset, attributable to the larger number of luminous red galaxies (LRGs) in the BOSS sample. We also compared our findings with other surveys such as WiggleZ, DES Y6, and DESI III, noting that photometric surveys typically yield larger error bars due to their lower precision. The DESI III results were in good agreement with ours within $1\sigma$, with most bins close to unity. The variation of $\alpha$ with respect to the redshift is an unresolved issue in the field, appearing in both three-dimensional and angular tomographic analyses.