Transverse BAO scale measurement at $z_{\rm eff} = 1.725$ with the SDSS quasars catalog

TL;DR

This work measures the transverse BAO scale in a thin redshift shell of SDSS DR16 quasars at $z_{ m eff}=1.725$, obtaining $ heta_{ m BAO}=1.928^\circ \,igpm\,0.094^\circ$ with a robust $3\sigma$ detection. By fitting a flexible polynomial-plus-Gaussian model to the two-point angular correlation function within $z\in[1.72,1.73]$, and using an analytic covariance based on Planck $C_ ext{l}$, the authors derive $D_A/r_d = 10.906 \pm 0.532$ at $z_{ m eff}=1.725$. The analysis confirms that projection effects are negligible in this thin shell and that the measurement agrees with Planck and DESI cosmologies within uncertainties. When combined with other transverse BAO measurements, this high-redshift data point provides an independent constraint on the expansion history and offers a valuable test for dark energy models, with future surveys expected to substantially improve precision.

Abstract

Studying the SDSS-DR16 quasar catalog, we detect a baryon acoustic oscillation (BAO) signal in the two-point angular correlation function with a statistical significance of $3σ$, at an effective redshift of $z_{\rm eff}=1.725$. Using a simple parameterization-comprising a polynomial plus a Gaussian function-we measure the transverse BAO scale as $θ_{\rm BAO}=1.928^{\circ}\pm0.094^{\circ}$. This measurement is obtained from a narrow redshift shell, $z \in [1.72, 1.73]$ (i.e., $Δz=0.01$), thin enough that projection-effect corrections are negligible, making it only weakly dependent on the assumed fiducial cosmology. The only assumption adopted is isotropy in the computation of the correlation function, further ensuring that the result depends only weakly on specific cosmological-model hypotheses. We also investigate possible systematics that could affect the detection or significance of the BAO signal and find them to be subdominant or implausible. When combined with other transverse BAO measurements from the literature, our result shows good concordance-within the $1σ$ confidence level-with the cosmological parameter values reported by the Planck and DESI collaborations. This new measurement of the transverse BAO scale, obtained from the SDSS quasar sample with minimal cosmological-model assumptions, provides an additional independent constraint for updated statistical studies aimed at probing the nature of dark energy.

Figures (5)

• Figure 1: 2-point angular correlation function for the quasar subsample in the redshift interval $z \in [1.72,1.73]$. The BAO signal is detected with $\mathrm{SNR} = 2.33$. Error bars represent shot noise. The red dashed vertical line indicates the BAO scale predicted by the flat $\Lambda$CDM model with Planck parameters, plotted assuming an error of $1\%$ for visualization.
• Figure 2: The difference between the error from the theoretical covariance matrix and the shot-noise.
• Figure 3: Marginalized posterior distributions of the parameters of equation (\ref{['eq:ajuste']}), obtained through the MCMC analysis of the SDSS quasar sample in the redshift interval $z \in [1.72,1.73]$.
• Figure 4: Best-fit of equation (\ref{['eq:ajuste']}). The error bars were obtained by calculating the square root of the diagonal of the theoretical covariance matrix, displayed in equation (\ref{['eq:cov_matrix']}). The measurement of $\theta_{\rm BAO}$ is then used to obtain distance $D_A/r_d = 10.906 \pm 0.532$ at $z_{\rm eff} = 1.725$.
• Figure 5: Statistical best-fit analysis for studying the consistency of our measurement as compared with other $\theta_{\text{BAO}}$ measurements in the literature. The best-fit parameter values $(\Omega_m,hr_d)$ of the $\Lambda$CDM model that produce the red line are displayed in Table \ref{['table-results']}.