Understanding how we went from the primordial density perturbations in the early Universe to the vast interconnected network of filaments, nodes, and voids we observe nowadays, is another major target of modern galaxy surveys. Measurements of galaxy clustering can constrain the growth rate of cosmic structure and shed light on the nature of gravity on cosmological scales.
On large scales, the galaxy distribution can be modeled within the context of cosmological perturbation theory, which describes the observed galaxy field as small density perturbations in an otherwise homogeneous, expanding background. This description of the Universe is accurate of very large scales, under the so-called linear regime, where the density fluctuations can be considered perturbative. However, in small scales, non-linear gravitational motions govern the evolution of structure, and the perturbative treatment no longer provides an accurate description of the galaxy field. Even though a significant fraction of the cosmological information from galaxy surveys is expected to be encoded in this non-linear regime, this portion of the data is usually discarded from the main cosmological analysis due to the difficulty of modeling galaxy clustering and weak lensing on these small scales.
Another consequence of the non-linear evolution on small scales is that the distribution of density fluctuations becomes non-Gaussian. The power spectrum, which is essentially a measure of the variance of the density field, is therefore no longer able to fully characterize the density field, in the same way as the variance is not enough to fully describe a probability distribution that departs from Gaussianity. Higher-order statistics (beyond two-point) are required in order to extract all cosmological information on small scales.
In this project, we will combine measurements from cosmological N-body simulations, which provide accurate estimations of galaxy clustering down to very small scales, with machine-learning algorithms, including neural networks and attention-based methods, building theoretical models of various clustering statistics, including the galaxy power spectrum and beyond-two-point statistics, and extracting cosmological information from the non-linear regime. We will apply our models to large observational datasets from the Dark Energy Spectroscopic Instrument.
