Towards Optimal Extraction of Cosmological Information from the Large Scale Structure

Forthcoming galaxy redshift surveys such as DESI and Euclid demand analysis pipelines that translate statistical precision on non-linear scales into robust cosmological inference. This thesis advances two complementary directions toward near-optimal information extraction from large-scale structure. First, it develops and evaluates wavelet scattering transforms (WST) as compact, interpretable summaries that capture non-Gaussian information beyond the power spectrum. Using the public Quijote and QuijotePNG simulations, Fisher forecasts are produced for standard cosmological parameters and the amplitudes of primordial non-Gaussianity (local, equilateral, orthogonal), and are benchmarked against power-spectrum-only and joint power–bispectrum analyses. With a controlled kmax filtering and transparent hyperparameter choices, WST is shown to outperform the power spectrum and to be competitive with state-of-the-art non-Gaussian summaries while being interpretable. Second, the thesis formulates a renormalized perturbative forward model for field-level inference based on the bootstrap approach to large-scale structure dynamics. By making the ultraviolet cutoff explicit and using a Wilsonian approach to take into account the inevitable discretization effects induced by a finite grid, the framework yields “bootstrap” coefficients which are independent on grid size effects, and identifies the higher-derivative operators required for unbiased recovery of these coefficients at fifth (and third) perturbative order. The results clarify how theoretical control at finite resolution enables principled field-level likelihoods and prepares the ground for realistic extensions. The final chapter outlines ongoing steps toward survey observables: incorporation of redshift-space distortions within the renormalized bootstrap framework and full marginalization over initial conditions with efficient high-dimensional samplers. Together, task-specific compression and controlled forward modeling provide a coherent path to stringent tests of fundamental physics with next-generation data.