First Detection of the Baryon Acoustic Oscillation (BAO) Feature in the 3-Point Correlation Function of DESI DR1 Luminous Red Galaxies

TL;DR

This work achieves the first detection of the BAO feature in the DESI DR1 3PCF for Luminous Red Galaxies by modeling the redshift-space bispectrum with a tree-level PT template and transforming it to configuration space using FFTLog. The analysis yields BAO significances of about 8.1–8.5 sigma and measures the distance scale D_V(z=0.68)/r_d with 1.1–1.7% precision, in good agreement with DESI DR1 2PCF BAO results and Planck 2018 cosmology. Systematics are assessed with Abacus altMTL mocks, indicating a small 0.6% offset in the BAO scale and confirming consistency between data and mocks. This demonstrates the 3PCF’s potential to probe the expansion history and paves the way for joint DESI 2PCF+3PCF analyses using efficient FFTLog-based modeling.

Abstract

We present the first detection of the 3-Point Correlation Function (3PCF) Baryon Acoustic Oscillation (BAO) signal from the DESI Data Release 1 (DR1) sample of Luminous Red Galaxies (LRGs), which contains over 2.1 million galaxies. Our analysis is based on a tree-level redshift-space bispectrum template, which is then transformed to position space using the Fast Fourier Transform on Logarithmic scales (FFTLog) algorithm. We detect the BAO feature with a significance of approximately $8.1σ$ using the EZmock covariance matrix and $8.5σ$ using the analytical covariance matrix, for the full LRG redshift range ($0.4<z<1.1$), denoted as the $z_{\rm full}$ sample. We use the Abacus altMTL mocks, the most precise DESI DR1 mock catalogs currently available, to validate our model. We find that our model fits the mocks well, with a small offset of $0.6\%$ in the recovered BAO scale, which we treat as a systematic error due to modeling. We measure the angle-averaged distance, $D_{\rm V}(z = 0.68)/r_{\rm d} = 15.88 \pm 0.27$ ($1.72\%$ precision) when using the covariance matrix estimated from EZmocks and $D_{\rm V}(z = 0.68)/r_{\rm d} = 15.72 \pm 0.18$ ($1.12\%$ precision) when using the analytical Gaussian covariance matrix. Our results show excellent agreement with the DESI DR1 2PCF BAO measurements as well. We also explore several other ways to estimate the error and find between $1.7$--$2.2\%$ precision on the BAO scale from the EZmock covariance matrix and between $1.1$--$1.5\%$ precision from the analytical covariance matrix. This work represents the first detection of the BAO feature in the DESI 3PCF, establishing its ability to probe the expansion history of the Universe with future DESI 3PCF measurements.

Figures (7)

• Figure 1: Left: The top panel shows the wiggle power spectrum (red) and the no-wiggle power spectrum (blue), while the bottom panel displays their ratio. Right: We present the odd and even harmonics of the Fast Sine Transform (FST) of the power spectrum class_ptHamann_2010. Even harmonics are shown in blue (solid for the wiggle spectrum and dashed for the no-wiggle spectrum), and odd harmonics are shown in red using the same line style convention. The horizontal axis corresponds to the FST index, not to physical radial distances. We observe that the BAO bump spans FST indices from approximately 140 to 200 for our fiducial cosmology. We have verified that this range is roughly consistent across other similar cosmologies. To separate them on the plot from the even harmonics, we have multiplied the odd harmonics by 1.4. Overall, these wiggle and no-wiggle power spectrum models are used to estimate the BAO detection significance. In this plot we used $z = 0.68$, as it is the effective redshift of the $z_{\mathrm{full}}$ LRG sample (as further described in the §\ref{['sec:DESIsample']}).
• Figure 2: We compare the 3PCF multipoles up to $\ell = 5$ obtained from the wiggle power spectrum (left columns in each group of panels), which contains the BAO signal, and from the no-wiggle power spectrum (middle columns), which has the BAO feature removed. The right columns show the difference between the two. Each panel is also multiplied by the damping factor $\mathcal{D}_{\mathrm{visualization}}$, as defined in \ref{['eq:ddamp']}. Also, the $\ell = 0$ and $\ell = 1$ panels are multiplied by five for better visualization. As seen in the comparison, the BAO feature appears clearly around the characteristic scale $r_{\mathrm{d}} = 100\per\hHubble\Mpc$. In addition to this main scale, we observe enhanced signal when $|r_1 \pm r_2| = r_{\mathrm{d}}$, corresponding to configurations sensitive to the BAO geometry. The same features around $|r_1 \pm r_2| = r_{\mathrm{d}}$ are also seen in other works such as SE_Full3PCF_BAOChellino:2025dbiLeonard:2024xvy. The presence of these features in the 3PCF will enable us to estimate the BAO detection significance using the DESI DR1 data in the following sections. This plot is at $z = 0.68$, the effective redshift of the $z_{\mathrm{full}}$ LRG sample (as explained further in §\ref{['sec:DESIsample']}).
• Figure 3: The $\chi^2$ values from fitting the 3PCF template to the DESI DR1 data using the wiggle (solid red) and no-wiggle (dashed blue) models are shown for the NGC and SGC of the $z_{\mathrm{full}}$ sample. The difference between the $\chi^2$ of the wiggle and no-wiggle when using the analytical covariance matrix yields a $\sim$$7.0\sigma$ detection significance from the NGC and $\sim$$5.0\sigma$ detection significance from the SGC. When combining the detection significances in quadrature, we obtain a total significance of approximately $8.5\sigma$. Using the covariance matrix estimated from EZmocks, the total detection significance is $8.1\sigma$. The parameter $\alpha$ is included in the analysis to account for the difference between the fiducial cosmology and the true cosmology. The vertical gray dashed lines indicate the location of $\alpha_{\mathrm{min}}$, which corresponds to the minimum of $\chi^2_{\mathrm{w}}$ for the wiggle model. The last panel is obtained by summing the $\chi^2$ values from NGC and SGC for the wiggle and no-wiggle models separately.
• Figure 4: Left: Probability Distribution Function (PDF) of $\alpha_{\mathrm{min}}$, which is the value of $\alpha$ at which the $\chi^2$ of the wiggle model is minimized. The blue, red, and green histograms correspond to the distribution of $\alpha_{\mathrm{min}}$ obtained respectively from the NGC, SGC, and NGC+SGC of the Abacus altMTL mocks. The solid black vertical line represents the value from the data. The legends denote the means of the histograms as well as the uncertainty on the means, which is the standard deviation of the PDF divided by the square root of the number of mocks. This panel shows that the estimate of $\alpha_{\mathrm{min}}$ from the data is completely consistent with the mocks. We also note that the (stat.) errors given in the legends are the uncertainty of the mean, not the standard deviation of the Gaussian. Right: PDF of the precision on the BAO scale, denoted as $\Delta \alpha$. We measure $\Delta \alpha$ for each mock, similarly to the data, by minimizing $\chi^2_{\mathrm{w}}$ and then finding the $1\sigma$ width of $\alpha$. As in the left panel, the blue, red, and green histograms correspond repectively to the NGC, SGC, and NGC+SGC of the Abacus altMTL mocks, while the solid black vertical line is for the data. We note that, since the NGC constrains the BAO scale with higher precision, it drives the precision of the combined measurement. The data appear to give slightly worse precision on the BAO scale than the NGC+SGC of the mocks (green). We see that the statistical error on $\alpha$ is completely consistent with the mocks.
• Figure 5: We measured $\alpha$ using several different methods in this work and summarize the results in this figure. The plot shows that all measurements are consistent with one another and also agree with the Planck 2018 cosmology Planck:2018vyg at the $2\sigma$ level. The standard method, discussed in §\ref{['sec:BAO detection Sig.']}, constitutes the main result of this work. The bootstrapping, mock scatter, and marginalization methods are presented in Appendices §\ref{['sec:Bootstrap']}, §\ref{['sec:MocksMethods']}, and §\ref{['sec:MargMethod']}, respectively. The bootstrapping method is entirely data-driven and does not depend on the choice of covariance matrix for estimating error bars; therefore, we represent it with a single black error bar. Similarly, the error bars from the mock scatter method are independent of the covariance matrix. This plot demonstrates that the estimation of both the BAO scale and its precision is consistent across different methods.