Toward Precision Cosmology with the Galaxy Bispectrum

We are currently in the era of precision cosmology with the large-scale structure. Ongoing and future galaxy surveys, such as \textit{Euclid}, DESI, Roman Space Telescope, LSST, SPHEREx, and others, will cover an unprecedented volume of the sky, making the full exploitation of cosmological information crucial. One particularly useful class of observables for studying galaxy clustering is the three-dimensional, Fourier-space summary statistics of the galaxy distribution. In the case of a Gaussian distribution, all statistical properties are encoded in its power spectrum. However, non-Gaussianities, generated either by non-linear gravitational interactions or present in the initial conditions provided by inflation, lead to non-vanishing 3-point functions. Consequently, the study of its Fourier transform, known as the bispectrum, provides complementary information to the power spectrum, especially regarding non-linear evolution and the dynamics of inflation. My Ph.D. project is devoted to the development of various aspects of the galaxy bispectrum multipoles analysis, with a specific focus on addressing finite-volume effects to ensure a robust comparison with observable quantities. Notably, we developed an efficient formulation for bispectrum-window convolution using a two-dimensional Hankel transform, and introduced a modeling approach for handling wide-angle effects in the galaxy bispectrum. Accurate treatment of these finite-volume effects is crucial for unbiased cosmological parameter inference using bispectrum multipoles in future large-volume surveys.