Angular Correlation Function from sample covariance with BOSS and eBOSS LRG

TL;DR

This paper introduces a model-independent method to measure the BAO angular scale using sample covariance matrices from galaxy surveys, validated with mocks, and compares results with Planck 2018 and other cosmological data.

Contribution

It proposes a novel approach to constrain the BAO angular scale without relying on fiducial models, using covariance matrices from galaxy samples across different surveys and redshifts.

Findings

eBOSS $ heta_{BAO}$ agrees with Planck 18 within 1 sigma

Sample covariances are noisier at lower redshifts due to nonlinear effects

Results align with Planck 18 and Pantheon + SH0ES when using the bin at $z_{eff}$.

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. This work aims to provide a method that constrains $\theta_{BAO}$ through a model-independent approach using the covariance matrix from the galaxy sample from thin redshift bins, later validated with a mock sample covariance matrix. 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. Each sample belongs to the Sloan Digital Sky Survey: BOSS1, BOSS2, and eBOSS, with effective redshift $z_{eff}$: 0.35, 0.51, 0.71, and different numbers of bins with 50, 100, and 200. To get $\theta_{BAO}$, we correct the angular separation from the polynomial fit ($\theta_{fit}$) by comparing each bin correlation function with the correlation function of the whole set, a parameter named $\tilde{\alpha}$. We also tested such correction by choosing the bin at $z_{eff}$ and found that for eBOSS $\theta_{BAO}$ is in $1 \sigma$ agreement with the Planck 18 model. Finally, we found that the sample covariances are noisy compared to the mocks for lower $z$ samples, something expected due to nonlinear effects. Such noise impact can be seen in the parameter constraints but does not affect the eBOSS covariance sample. It is shown that mocks' results do tend to its chosen fiducial cosmology $\theta_{BAO}$. BOSS1 and BOSS2 showed agreement with Planck 18 and an agreement with Pantheon + S$H_0$ES when $\tilde{\alpha}$ is based on the bin $z=z_{eff}$.