An effective field theory approach to the study of cosmological blue isocurvature perturbations in large scale structure data

The standard cosmological model successfully explains the large-scale structure of the Universe under the assumption of purely adiabatic primordial perturbations. However, several well-motivated multi-field inflationary scenarios predict the presence of isocurvature perturbations, which remain only partially constrained by current observations. In particular, blue-tilted cold dark matter (CDM) isocurvature spectra can enhance power on small scales, making large-scale structure (LSS) surveys a promising probe of such non-standard initial conditions. In this thesis we investigate the impact of blue-tilted CDM isocurvature perturbations within the framework of the Effective Field Theory of Large Scale Structure (EFTofLSS), which provides a systematic description of non-linear gravitational evolution and galaxy bias on quasi-linear scales. We review the extension of the EFTofLSS formalism to mixed adiabatic–isocurvature initial conditions, emphasizing the modified ultraviolet behavior induced by large spectral indices and the associated renormalization procedure. Our original contribution develops along two directions. First, we analyze baryon–CDM relative perturbations generated by CDM isocurvature modes and implement their evolution using the CLASS Boltzmann solver, showing that they introduce additional bias operators in the galaxy power spectrum. Second, we extend the VDG redshift-space model to mixed initial conditions, demonstrating that its structure remains compatible with the effective framework, although the blue tilt enhances ultraviolet sensitivity in specific mapping contributions. These results show that baryon–CDM relative perturbations and redshift-space effects can be consistently incorporated within the EFTofLSS in the presence of blue-tilted isocurvature modes. Future LSS surveys will provide the opportunity to test these predictions and further constrain early-Universe physics.