Angular Correlation Function from sample covariance with BOSS and eBOSS LRG

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

When did cosmic acceleration start? How fast was the transition?

Cosmic acceleration is investigated through a kink-like expression for the deceleration parameter (q). The new parametrization depends on the initial (q_i) and final (q_f) values of q, on the redshift of the transition from deceleration to acceleration (z_{t}) and the width of such transition (\tau). We show that although supernovae (SN) observations (Gold182 and SNLS data samples) indicate, at high confidence, that a transition occurred in the past (z_{t}>0) they do not, by themselves, impose strong constraints on the maximum value of z_{t}. However, when we combine SN with the measurements of the ratio between the comoving distance to the last scattering surface and the SDSS+2dfGRS BAO distance scale (S_{k}/D_{v}) we obtain, at 95.4% confidence level, z_{t}=0.84+{0.17}-{0.13} and \tau =0.51-{0.17}+{0.23} for (S_{k}/D_{v}+Gold182), and z_{t}=0.88-{0.10}+{0.12} and \tau =0.35-{0.10}+{0.12} for (S_{k}/D_{v} + SNLS), assuming q_i=0.5 and q_f=-1. We also analyze the general case, q_f\in(-\infty,0) finding the constraints that the combined tests (S_{k}/D_{v} + SNLS) impose on the present value of the deceleration parameter (q_0).Comment: 7 pages, 3 figures. Replaced to match the published versio