Angular Correlation Function from sample covariance with BOSS and eBOSS LRG

Abstract

The Baryon Acoustic Oscillations (BAO) are one of the most used probes to understand the accelerated expansion of the Universe. Traditional methods rely on fiducial model information within their statistical analysis, which may be a problem when constraining different families of models. The aim of this work is to provide a method that constrains $\theta_{BAO}$ through a model-independent and compare parameter estimation of the angular correlation function polynomial approach, using the covariance matrix from the galaxy sample from thin redshift bins, with the usual mock sample covariance matrix. We proposed a different approach to finding the BAO angular feature revisiting previous work in the literature, we take the bias between the correlation function between the bins and the whole sample. We used widths of $\delta z = 0.002$ separation for all samples as the basis for a sample covariance matrix weighted by the statistical importance of the redshift bin. We propose a different weighting scheme based only on random pair counting. We also propose an alternate shift parameter based only on the data. Each sample belongs to the Sloan Digital Sky Survey Luminous Red Galaxies (LRG): BOSS1, BOSS2, and eBOSS, with effective redshift $z_{eff}$: 0.35, 0.51, 0.71, respectively, and different numbers of bins with 50, 100, and 200 respectively. In addition, we correct the angular separation from the polynomial fit ($\theta_{fit}$) that encodes the BAO feature with a bias function obtained by comparing each bin correlation function with the correlation function of the whole set. We also tested the same correction choosing the bin at $z_{eff}$ and found that for eBOSS $\theta_{BAO}$ is in $1 \sigma$ agreement with the Planck 18 model. BOSS1 and BOSS2 $\theta_{BAO}$ agreed in $1\sigma$ with the Pantheon+ & S$H_0$ES Flat$\Lambda$CDM model, in tension with Planck 18.Comment: 18 page