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High-redshift transverse BAO measurements with the SDSS quasar catalog

This study analyzes the SDSS-DR16 quasar catalog to detect transverse BAO signals in two high-redshift shells ( $1.5 \leq z \leq 2.0$ ), providing new angular diameter distance measurements that bridge an observational gap and yield cosmological parameters consistent with Planck and DESI constraints.

Original authors: Felipe Avila, Armando Bernui, Miguel A. Sabogal, Rafael C. Nunes

Published 2026-08-03

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CC BY 4.0

Original authors: Felipe Avila, Armando Bernui, Miguel A. Sabogal, Rafael C. Nunes

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, expanding balloon being blown up by an invisible force. If you were to paint a pattern of dots on that balloon before it started inflating, those dots would drift apart as the balloon grew. But here's the twist: those dots wouldn't just drift randomly. Because of how the universe worked in its very first moments, the dots would have a "favorite" distance between them, like a cosmic ruler stamped into the fabric of space itself. This favorite distance is called the Baryon Acoustic Oscillation (BAO). Think of it as the echo of a giant sound wave from the Big Bang that froze in place, leaving a specific spacing between galaxies that we can still measure today.

Why do we care about this cosmic ruler? Because it helps us measure how fast the universe is stretching. If we know how big the ruler should be, and we measure how big it looks to us from Earth, we can figure out how much the universe has expanded since that light left the galaxies. This is crucial because there's a mysterious force called dark energy that is pushing the universe apart, and scientists are trying to understand if this force is constant or if it's changing over time. To do this, they need to measure the universe at different times in its history, like checking the speedometer of a car at different points on a long road trip.

Now, let's zoom in on a new road trip report from a team of astronomers who decided to look at a very specific, tricky part of that journey: the "high-redshift" zone. In astronomy, "redshift" is like a time machine; the higher the number, the further back in time we are looking. While we have good maps for the "nearby" universe and some for the very distant past, there was a huge, foggy gap in the middle, specifically between redshifts of 1.5 and 2.0. It was like trying to drive from New York to Los Angeles but having no map for the entire state of Colorado.

The team, led by Felipe Avila and colleagues, decided to fill in that gap using a massive catalog of quasars. Quasars are like the universe's brightest lighthouses—super-bright cores of distant galaxies powered by black holes. The problem is, they are rare and scattered, making them hard to use for precise measurements. It's a bit like trying to measure the distance between cities by counting how many lighthouses you see in a specific patch of sky; if the lighthouses are too far apart, your measurement gets "fuzzy."

To solve this, the researchers used a clever trick called tomography. Imagine slicing a loaf of bread into incredibly thin slices. Instead of looking at the whole loaf (which would blur the details), they sliced the universe into 50 very thin, separate layers of time, each representing a tiny slice of the redshift interval. By looking at these thin slices one by one, they could sharpen the image and stop the "fuzziness" caused by looking at things that are slightly in front of or behind each other.

They scanned these 50 slices looking for that cosmic ruler pattern. After crunching the numbers with a sophisticated statistical toolkit, they found the pattern! They spotted the acoustic peak—the signature of that frozen sound wave—in two specific, unconnected slices of time: one centered at a redshift of 1.725 and another at 1.775.

The results were statistically significant, meaning the odds of this being a random fluke were very low. For the slice at 1.725, they found the pattern with a confidence of 3.4 sigma (which is like saying, "We are 99.9% sure this is real"). For the slice at 1.775, the confidence was 3.0 sigma. They measured the angle of this pattern to be 1.911° ± 0.062° and 1.727° ± 0.081° respectively.

Using these measurements, they calculated the size of the universe at those times. They found that the angular diameter distance (a way of measuring how big things look) was 11.00 ± 0.36 times the sound horizon scale at the first redshift, and 11.96 ± 0.56 times that scale at the second.

When the team plugged these new, high-redshift data points into the existing maps of the universe, they found that everything fit together beautifully. Their new measurements bridged the gap perfectly and agreed with the predictions from other major studies, like those from the Planck satellite and the DESI collaboration. They didn't find any weird contradictions or evidence that the rules of the universe are breaking down in this time period. Instead, their work confirms that the standard model of cosmology (the flat-ΛCDM model) holds up even in this unexplored territory.

In short, these astronomers successfully used a thin-slice technique to find the cosmic ruler in a part of the universe that was previously too foggy to see. They didn't just find a needle in a haystack; they found two needles in two different haystacks, proving that the cosmic map is consistent and reliable all the way back to when the universe was much younger. This success suggests that using quasars as cosmic tracers is a powerful tool for future studies, especially if we want to understand if the mysterious dark energy is changing its mind as the universe expands.

Technical Summary: High-redshift transverse BAO measurements with the SDSS quasar catalog

Problem Statement
Baryon Acoustic Oscillations (BAO) serve as a standard ruler for measuring cosmic distances and probing the nature of dark energy. While transverse BAO measurements are robust geometric probes with minimal dependence on fiducial cosmological models, they face significant challenges in the redshift range $1.5 \leq z \leq 2.0$ . Existing literature contains a notable observational gap in this regime, with measurements previously concentrated at lower redshifts ( $z \lesssim 0.63$ ) or higher redshifts ( $z \approx 2.225$ ). Furthermore, detecting the transverse BAO signal in quasar catalogs is difficult due to the low number density of quasars, which leads to high shot noise. Additionally, analyzing data in finite redshift shells introduces projection effects that can smear the signal and shift the measured acoustic peak toward smaller angular scales, typically requiring corrections based on a fiducial cosmology.

Methodology
The authors analyzed the SDSS-DR16 (eBOSS) quasar catalog, which contains 343,708 quasars in the redshift range $0.8 < z < 2.2$ . To address the challenges of projection smearing and low signal-to-noise, the study employed the following methodological framework:

Fine Tomographic Analysis: The survey was divided into 50 thin, disjoint redshift shells with a width of $\Delta z = 0.01$ . This narrow binning strategy was chosen to suppress line-of-sight projection smearing, effectively isolating the transverse BAO feature and minimizing the need for fiducial-model-dependent shift corrections.
Statistical Estimation: The two-point angular correlation function (2PACF), $\omega(\theta)$ , was calculated using the Landy-Szalay estimator. The analysis utilized a full analytical Gaussian covariance matrix that self-consistently couples Poisson shot noise with cosmological clustering terms ( $C_\ell$ ), rather than relying solely on shot-noise estimates. This approach accounts for the survey mask and the linear bias of quasars, which was modeled using a redshift-dependent parameterization.
Parameterization and Fitting: The BAO signal was extracted by fitting the 2PACF with a model combining a second-degree polynomial (to model the broadband continuum) and a Gaussian peak. A dimensionless shift parameter, $\alpha$ , was introduced such that the measured scale $\theta_{FIT} = \alpha \theta_{th}^{BAO}$ . This allows for a direct quantification of the deviation from the fiducial cosmology.
Data Selection: A blind MCMC search was conducted across the 50 shells in the interval $1.50 \leq z \leq 2.00$ . Four shells showed local statistical significance $\geq 3\sigma$ . However, to ensure robustness and independence, the authors selected only two non-overlapping shells ( $z_{eff} = 1.725$ and $z_{eff} = 1.775$ ) that exhibited exceptional goodness-of-fit values ( $\chi^2_\nu \approx 1$ ) and uncorrelated measurements.

Key Contributions and Results
The primary contribution of this work is the detection of statistically significant transverse BAO signals in the previously unexplored redshift interval $1.5 \leq z \leq 2.0$ . The specific results are:

Detection of Acoustic Peaks: Two robust, uncorrelated detections were identified:
- At $z_{eff} = 1.725$ : $\theta_{BAO} = 1.911^\circ \pm 0.062^\circ$ with a statistical significance of $3.4\sigma$ .
- At $z_{eff} = 1.775$ : $\theta_{BAO} = 1.727^\circ \pm 0.081^\circ$ with a statistical significance of $3.0\sigma$ .
Distance Constraints: Using the geometric relationship between the angular scale and the sound horizon ( $r_d$ $r_{d}$ ), the authors derived scaled angular diameter distances:
- $D_A/r_d = 11.00 \pm 0.36$ at $z_{eff} = 1.725$ .
- $D_A/r_d = 11.96 \pm 0.56$ at $z_{eff} = 1.775$ .
Cosmological Parameter Estimation: These two new data points were incorporated into a compilation of existing transverse BAO measurements (14 from [33], 1 from [30], and 1 from [13]), totaling 18 measurements. A flat- $\Lambda$ $Λ$ CDM parameter estimation was performed, yielding:
- Matter density: $\Omega_{m,0} = 0.41 \pm 0.06$ .
- Scaled sound horizon: $h r_d = 99.3 \pm 2.0$ Mpc.

Significance and Claims
The paper claims that these measurements successfully bridge a significant observational gap in the high-redshift universe. The results are reported to be highly consistent with constraints from the Planck and DESI collaborations, reinforcing the validity of the standard $\Lambda$ CDM model in this redshift regime.

The authors emphasize that the use of thin redshift shells ( $\Delta z = 0.01$ ) combined with a full analytical covariance matrix allows for model-independent transverse BAO measurements that are free from projection effects. This demonstrates the potential of quasar tomographic surveys to provide competitive constraints on the dark sector and the expansion history of the Universe. The work suggests that such surveys can effectively probe dynamical dark energy and test for potential dark sector interactions, provided that future large-scale structure surveys (such as DESI, Euclid, and LSST) continue to expand the available data. The authors note that their updated measurements refine earlier preliminary results but remain statistically equivalent, ensuring that broader Bayesian analyses remain robust.

Technical Summary: High-redshift transverse BAO measurements with the SDSS quasar catalog

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