First full-shape joint analysis of the two- and three-point correlation functions on real data: $\Lambda$CDM cosmological constraints from BOSS DR12

Abstract

The three-point correlation function (3PCF) encodes cosmological information beyond the two-point correlation function (2PCF), yet a full-shape joint analysis in redshift space using real data has so far been lacking. We present the first full-shape cosmological constraints from a joint analysis of 2PCF and 3PCF in redshift space, using BOSS DR12 data, extending to real data, including Alcock--Paczy\'nski and redsfhit space distortions, the full-shape configuration-space framework validated in real space for the first time by Euclid Collaboration: Guidi et al (2026). We model both statistics adopting the velocity difference generating function (VDG) framework, incorporating non-perturbative Fingers-of-God damping, a complete Eulerian galaxy bias expansion, and infrared resummation. Fast and accurate theoretical predictions are obtained using dedicated emulators, which enable a full-shape likelihood analysis of the 3PCF and its combination with the 2PCF, varying the cosmological parameters $10^9 A_s, \omega_{\rm cdm}$ and $h$, while the baryon fraction density $\omega_{b}$ is fixed to its fiducial value. The covariance matrix is estimated from 2048 MultiDark-Patchy mocks, and an optimal data-vector compression ensures a stable covariance inversion. The perturbative model is validated against goodness-of-fit tests across different scales, and provides a good description of the joint data vector down to $r_{\rm min}^{\rm 3PCF} \sim 60\,h^{-1}{\rm Mpc}$. We find that the joint 2PCF+3PCF analysis yields significant improvements over the 2PCF-only baseline, with gains of approximately 29\%, 10\%, and 24\% on $\sigma(h)$, $\sigma(\omega_{\rm cdm})$, and $\sigma(A_s)$, respectively. The improvements mainly arise from the additional BAO cosmological information encoded in the 3PCF triangle configurations.