The intrinsic alignment (IA) of galaxy shapes probes the underlying gravitational tidal field, thus offering cosmological information complementary to galaxy clustering. In this paper, we perform a Fisher forecast to assess the benefit of IA in improving cosmological parameter constraints, for the first time, leveraging the full-shape (FS) information of IA statistics. Our forecast is based on Subaru Prime Focus Spectrograph-like and Euclid-like surveys as examples of deep and wide galaxy surveys, respectively. We explore various cosmological models, with the most comprehensive one simultaneously including dynamical dark energy, curvature, massive neutrinos, and modified gravity (MG). We find that adding FS IA information significantly tightens cosmological constraints relative to the FS clustering-only cases, particularly for dynamical dark energy and nonflat-MG models. For a deep galaxy survey, the figure of merit for the dark energy equation of state parameters is improved by at least more than 40% in all dynamical dark energy models investigated. For nonflat-MG models, parameter constraints are tightened by 6%–28%, except for the dark matter density and spectral index parameters. For a wide galaxy survey, improvements with IA become milder, although its joint constraints are tighter than those from the deep survey. Our findings highlight the efficacy of the galaxy IA as a complementary cosmological probe to galaxy clustering.

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• Cosmological parameters
• Cosmology
• Dark energy
• Dark matter
• Gravitation
• Large scale structure of the Universe