Modelling and estimation of the anisotropic galaxy 3-point correlation function.

The galaxy 3-point correlation function (3PCF) is a powerful tool for breaking degeneracies between cosmological and nuisance parameters and, thus, constraining the nature of Dark Energy. To this end, we present a routine that enables modelling the statistical anisotropies induced by redshift-space distortions on 3PCF. This approach, based on the 2D-FFTLog algorithm, allows us to numerically determine the tripolar spherical harmonics expansion of the 3PCF starting from its Fourier space analogue, the bispectrum. In addition, we implement for the first time the anisotropic Slepian-Eisenstein estimator, which enables measuring the redshift-space galaxy 3PCF in $\mathcal{O}(N^2)$ time, with $N$ number of galaxies. As a reliability test on both estimator and theoretical approach, we perform a likelihood analysis on a suite of 298 Minerva dark matter halo catalogs, finding non-biased estimates for the main cosmological parameters. This result, hence, opens up the possibility of performing a fully anisotropic joint 2 and 3PCF analysis, that would allow us to constrain the evolution history of the Universe with unprecedented precision.