The statistics of large-scale structure in our Universe can discriminate between different scenarios for the origin of primordial density perturbations. Primordial non-Gaussianity can lead to a scale-dependent bias in the density of collapsed halos relative to the underlying matter density.

The galaxy power spectrum already provides constraints on local-type primordial non-Gaussianity complementary to those from the Comic Microwave Background, while the bispectrum contains additional shape information and has the potential to outperform CMB constraints in future.

In this talk, I will review the bias model for the halo density contrast in the presence of local-type primordial non-Gaussianity, based on a double expansion in terms of the local linear matter density contrast and the local gravitational potential in Lagrangian coordinates. This is known as the bivariate model.

The halo bispectrum predicted by the model will be presented, including the non-local features that arise when the spherical collapse approximation is dropped. Then, the model will be applied for the first time to estimate the large-scale galaxy bispectrum in redshift space.

To conclude, I estimate constraints on local-type primordial non-Gaussianity that could be expected from the bispectrum of large-scale structure.