Boosting galaxy clustering analyses with non-perturbative modelling of redshift-space distortions

Redshift-space distortions (RSD), caused by the peculiar velocities of galaxies, are a key modelling challenge in galaxy clustering analyses, limiting the scales from which cosmological information can be reliably extracted. Unlike dynamical or galaxy bias effects, RSD imprint features that are sensitive to non-linearities across all scales. Yet, no distinction between these effects is made by the state-of-the-art analytical approach - the effective field theory (EFT) - which applies the same perturbative expansion to each of them. This paper explores an alternative approach, where the non-perturbative nature of RSD is partially preserved, and compares its effectiveness against the EFT in analysing power spectrum and bispectrum multipoles from synthetic samples of luminous red galaxies, using the projected sensitivity of a Stage-IV galaxy survey. Our results demonstrate that this distinct treatment of RSD improves the robustness of model predictions for both statistics, extending the validity range of the EFT from approximately $0.2\,h\,\mathrm{Mpc}^{-1}$ to $0.35\,h\,\mathrm{Mpc}^{-1}$ for the one-loop power spectrum and from $0.1\,h\,\mathrm{Mpc}^{-1}$ to $0.14\,h\,\mathrm{Mpc}^{-1}$ for the tree-level bispectrum. This leads to a significant enhancement in the precision of cosmological parameter constraints, with uncertainties on the Hubble rate, matter density, and scalar amplitude of fluctuations reduced by $20$-$40\,\%$ for the power spectrum multipoles alone compared to the EFT, and by $25$-$50\,\%$ for joint analyses with the bispectrum. The RSD treatment proposed here may thus play a crucial role in maximising the scientific return of current and future galaxy surveys. To support this advancement, all models for the power spectrum and bispectrum used in this work are made available through an extended version of the Python package COMET.