A STUDY OF MARKED POWER SPECTRA INCLUDING THE MATTER TIDAL FIELD

Upcoming galaxy surveys such as Euclid will map the Large-Scale Structure (LSS) of the Universe with unprecedented precision and the main challenge is to extract as much cosmological information as possible from these new datasets. The galaxy power spectrum is the standard statistics used in LSS analyses, but non linear gravitational evolution transfers cosmological information into higher-order correlators, which are expensive to measure and model. Marked statistics offer a compelling alternative: by non linearly weighting the density field before computing its power spectrum, marked statistics can recover part of the higher-order information while retaining the simplicity of a two-point correlation function. Existing implementations, however, rely solely on marks constructed from the local density field, which does not capture the anisotropic geometry of the environment. This information is instead encoded in the matter tidal tensor. For this reason, this thesis extends the marked power spectrum formalism to a mark constructed from the matter tidal field, recovering the tidal marked power spectrum at one-loop order for both dark matter and biased tracers in real space within the Effective Field Theory of the Large-Scale Structure, complemented by a dedicated numerical implementation. Our Fisher forecast analysis shows that combining the standard power spectrum with the proposed tidal marked power spectrum substantially tightens cosmological constraints on the physical cold dark matter density parameter \omega_{cdm}, on the dimensionless Hubble parameter h and on the scalar spectral index n_s, which are the most robust results of this study, by factors 1.7, 1.7 and 2 respectively. The quadratic and tidal bias parameters b_2 and b_{\mathcal{G}_2}, generally well constrained with the inclusion of the galaxy bispectrum, are also measured with substantially higher precision, improving by up to a factor 3.2 and 2.7 respectively. Finally, the scalar amplitude of primordial fluctuations A_s and the linear bias b_1 show a remarkable improvement, driven by the breaking of the A_s-b_1 degeneracy present in real space. These results confirm the effectiveness of the tidal mark in recovering higher-order cosmological information, providing a new tool towards the broader goal of maximizing the scientific return of next-generation galaxy surveys.