Enabling cosmological analysis at BAO scale with a new matter anisotropic three-point correlation function emulator

Due to the large amount of data that the Stage IV galaxy surveys will bring, as well as the inherent limitations of the two-point statistics, higher-order statistics are needed to address the current issues in cosmology. A new model has been developed that enables us to obtain the anisotropic matter three-point correlation function (3PCF). It decomposes the redshift space 3PCF into multipoles, thus enabling the analysis of isotropic and anisotropic components with respect to the line of sight. In this work, we analyzed the Signal-to-noise ratio (SNR) in each multipole of the 3PCF, concluding that the highest signal lies in the isotropic multipoles. In each multipole, the highest SNR is in the isosceles and squeezed triangle configurations. Moreover, we studied a new BAO detectability metric, which allowed us to find triangle configurations with the highest BAO feature signal. Every multipole has BAO features within them, and the highest signal is in the isosceles and squeezed triangle configurations. Additionally, an emulator was developed for the anisotropic 3PCF at redshift zero for the cosmological parameters: matter density parameter, dimensionless Hubble parameter, and scalar amplitude of matter density fluctuations. It is over ten million times faster than numerical calculation, while maintaining competitive accuracy. Finally, the Fisher forecasts were calculated for a volume representative of a Stage IV spectroscopic survey with the same cosmological parameters mentioned before. We discovered that the isotropic multipoles have significantly higher constraining power than the anisotropic multipoles. Nevertheless, combining the isotropic and anisotropic multipoles resulted in 40% higher constraining power compared to the isotropic component alone. However, if the common modeling limit of 40 Mpc h^-1 for the triangle sides is applied, it is reduced to only 8% increase. Thus, it is crucial to include the small scales in future modeling and survey analysis.