Imprints of Dynamical Dark Energy Models on Observables of the Large Scale Structures: from CMB to Lensing Spectra

Understanding the nature of dark energy is one of the central challenges in modern cosmology. This invisible and exotic component, thought to be responsible for the observed late-time accelerated expansion of the universe, dominates the cosmic energy budget. Yet, its physical origin remains elusive. Among the proposed explanations is the possibility that dark energy arises from a fundamental dynamical scalar field not included in the Standard Model of particle physics, which drives the late-time acceleration. Such models were introduced over two decades ago following the discovery of cosmic acceleration, but only recently have observations of large-scale structures reached the sensitivity required to probe their dynamics. There is now broad consensus that combining Cosmic Microwave Background (CMB) data from Planck with measurements of the late-time clustering of matter offers a powerful means to constrain the evolution of the dark energy component, and to distinguish the standard Cosmological Constant scenario from more exotic physics. In this context, this thesis investigates the imprints of dynamical dark energy models—particularly those featuring non-trivial time evolution such as the Kink parameterization—on a range of cosmological observables. A central component of this research is the numerical implementation of dynamical dark energy models within the CLASS Boltzmann code; with subsequent Bayesian parameter estimation performed using the Cobaya MCMC framework. Through a comparative analysis of model predictions against CMB and large-scale structure datasets, this study aims to determine the observational viability of non-standard dark energy scenarios.