Field-level modeling of halo and galaxy alignments

We develop an effective field theory (EFT) of intrinsic alignments at the level of spin-2 field fluctuations of large-scale structure tracers, such as the shapes of galaxies and dark matter halos. Our perturbative model includes the non-linear treatment of the Zel'dovich displacement, and contains all necessary shape operators through the third order. We apply our field-level model to the full 3D distribution of galaxy shapes, whose sky projections are a known contaminant of cosmic shear measurements. Our field-level EFT model achieves a better description of the helicity fields of dark matter halo shapes than the standard non-linear alignment (NLA) and tidal torquing + tidal alignment (TATT) models in the literature, as evidenced by improved correlations with the simulations' initial conditions. We perform precision measurements of field-level bias parameters by means of a generalized least-squares problem, for which we derive an optimal estimator and analytic covariance matrices. We measure the full set of linear, quadratic, and cubic shape bias coefficients as a function of halo mass in the Quijote N-body simulations. We then study the intrinsic alignments of galaxies in the FLAMINGO hydrodynamical simulation, focusing on observationally relevant samples: spirals, ellipticals, luminous red galaxies (LRG) and emission-line galaxies (ELG). We detect linear and nonlinear alignment coefficients at high significance for LRG, spiral and elliptical galaxies. We also find evidence for non-zero density-weighted tidal bias coefficient of the simulated ELG. This work supports the notion that EFT-based models of alignments will be paramount in optimally extracting constraints from future shape correlations, and lays the foundation for the development of simulation-based priors for future galaxy shape samples.