Cosmological information from field-level analysis in redshift space

The field-level analysis of galaxy clustering with a forward model based on the Effective Field Theory of Large Scale structure provides cosmological measurements at optimal statistical precision which are simultaneously robust with respect to theoretical uncertainties regarding galaxy formation. Yet, the quantitative gains of field-level analysis in the perturbative regime over the current state-of-the-art, set by the combination of power- and bispectrum, are not obvious, and they depend on analysis choices, the cosmological model, and the observed galaxy population. We therefore quantify the precision improvement from field-level analysis over power- and bispectrum from redshift-space snapshots that closely resemble the DESI LRG sample. Our mock data are created with the LEFTfield forward model, which we also use for the subsequent field-level analysis and for a Fisher forecast of the power- and bispectrum precision. We find significant improvements from the field-level analysis over the power- and bispectrum for a Λ CDM cosmology; in particular the primordial fluctuation amplitude can be measured twice as precisely. Precision gains at the field-level are even more pronounced for extended cosmologies with a more flexible dependence between power spectrum shape and structure growth; they reach up to a factor of three in the primordial amplitude and a factor of two in parameters that capture deviations from Λ CDM. Our results highlight the potential of field-level analysis for future discoveries. Realizing this potential will require substantial developments on the modeling of observations and observational systematics as well as on the numerical inference techniques.