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\nIn the first part of this thesis\, we study the generation of CDM uncorrelated blue-tilted isocurvature perturbations for the axion s when the axionic sector is far out of equilibrium during inflation t hrough an initial Peccei-Quinn symmetry breaking field displacement. W e investigate two distinct models\, where these fluctuations originate from the dynamical evolution of the radial field through the quadrati c and quartic components of the effective potentials. In the quadratic case\, we find that there exist parametric regions with a strong reso nant spectral behavior that leads to rich isocurvature spectral shapes . A consequence of this nonlinearity-driven resonance is the chaotic n ature of the map that links the underlying Lagrangian parameters to th e isocurvature amplitudes. In the quartic scenario\, we propose a nove l method to generate the blue-tilted spectrum over a large range of sc ales by utilizing the classical conformal limit.

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\nIn the s econd part of the thesis\, we present a Fisher forecast for the Euclid and MegaMapper experiments in their ability to detect blue isocurvatu re perturbations. We construct the theoretical predictions in the EFTo fLSS and bias formalisms and report optimistic results highlighting th e potential for detecting the CDM blue isocurvature amplitude in forth coming surveys. URL:https://www.physics.wisc.edu/events/?id=8744 END:VEVENT END:VCALENDAR