Constraining Standard and Beyond-ΛCDM Cosmologies with the Large-Scale Structure: An Effective-Field-Theory Approach to Analytical and Numerical Modeling

The next generation of cosmological surveys---including Euclid, DESI, and the Rubin Observatory---will map the large-scale structure (LSS) of the Universe with unprecedented precision, offering the opportunity to test the standard cosmological model at sub-percent accuracy and to probe possible extensions beyond $\Lambda$CDM. Extracting reliable constraints on fundamental physics from this data requires theoretical models that are both analytically controllable and numerically efficient across the mildly nonlinear regime. The Effective Field Theory of Large-Scale Structure (EFTofLSS) offers a robust framework to achieve this objective. In this dissertation, we develop and apply EFTofLSS-based techniques to both standard and beyond-$\Lambda$CDM cosmologies, combining analytical modeling and numerical implementations to constrain the physics involved in structure formation. We begin by revisiting the perturbative modeling of the redshift-space galaxy power spectrum within $\Lambda$CDM. In this context, we introduce \textsc{CLASS-OneLoop}, a new module fully integrated into the Boltzmann code \textsc{CLASS}, which computes the one-loop galaxy power spectrum including nonlinear bias, stochastic and counterterm contributions, along with IR-resummation and Alcock–Paczynski effects. The code implements direct integration, FFTLog and SFTLog for fast evaluations of loop integrals and features a fast–slow parameter decomposition optimized for Monte Carlo sampling. We validate the model against \textsc{AbacusSummit} simulations and demonstrate its capability to recover fiducial cosmologies up to $k_{\rm max} = 0.3\,h\,{\rm Mpc}^{-1}$, while highlighting the biases induced by oversimplified models commonly used in forecasts. Continuing with beyond the standard model, we further explore the application of EFTofLSS to interacting dark matter (IDM) models coupled to neutrinos, which suppress small-scale clustering through early-time interactions. By comparing to $N$-body simulations, we confirm the validity of the EFTofLSS description for such non-standard cosmologies and perform forecasts for DESI-like spectroscopic surveys. Our analysis shows that, while conservative priors limit the constraining power on IDM parameters, an improved understanding of counter-terms and stochastic evolution with redshift could make these models observationally testable in the near future. At the level of primordial physics, we employ EFTofLSS-based redshift-space models for the joint analysis of the galaxy power spectrum and bispectrum to constrain primordial non-Gaussianity (PNG). Using Euclid-like mock catalogues derived from the \textsc{Abacus-PNG} simulations, we validate our one-loop $P_\ell$ and tree-level $B_\ell$ pipeline and demonstrate that the inclusion of the bispectrum significantly improves constraints on the amplitude of local-type PNG ($f_{\mathrm{NL}}$) while maintaining unbiased recovery of standard $\Lambda$CDM parameters. These results underline the importance of joint (power plus bispectrum) analyses in future surveys targeting physics during the period of inflation. Moreover, we extend the EFTofLSS formalism to theories introducing new physical scales that generate scale-dependent growth of structure. In particular, we study massive neutrinos and $f(R)$ gravity as examples of theories that depend on scale. We derive the one-loop galaxy power spectrum using a model-independent approach before applying it to the mentioned cases. We show how the presence of additional mass or interaction scales modifies the effective gravitational coupling and, therefore, the growth function, leaving observable imprints on the shape of the nonlinear galaxy power spectrum in redshift-space. Furthermore, we evaluate commonly used approximations and examine their accuracy within the context of Stage-IV galaxy surveys. Finally, we investigate the field-level formulation of the EFTofLSS by developing a recursive, Wilsonian renormalization approach to Eulerian Perturbation Theory (EPT). We introduce a consistent, order-by-order IR-resummation procedure to resum only large-scale bulk flows and built a unified numerical code to compute the EPT, Shifted EPT, and Lagrangian Perturbation Theory (LPT) forward models, the \textsc{Umbrella} framework. Using the \textsc{Quijote} simulation suite and the \textsc{Map2Map} emulator, we show that IR-resummed EPT achieves the accuracy of LPT at relevant scales while having improved UV properties and more Gaussian residuals, demonstrating its potential as a field-level forward model for cosmological inference. In summary, this thesis extends the EFTofLSS framework to a broader class of cosmological scenarios. We have shown how it can be effectively used to obtain robust theoretical predictions and connect them with both numerical simulations and actual observational analyses in today's era of precision cosmology.