Probing the expansion history of the universe through cosmic time

This Thesis explores cosmic time as a new avenue to constrain the expansion history of the Universe, an alternative to traditional luminosity or distance approaches. Two complementary methods are studied and improved: cosmic clocks and cosmic chronometers. The cosmic clocks approach exploits the absolute ages of the most long-lived structures, providing a lower bound to the age of the Universe and an upper limit to the Hubble constant, H0. The cosmic chronometers method relies on a differential approach: measuring the ageing in redshift of massive and passively evolving galaxies yields a direct, nearly model-independent measurement of the Hubble parameter H(z). In the first part, we apply the cosmic clocks approach using different tracers. We begin with old Milky Way (MW) stars, deriving ages through Bayesian isochrone fitting combined with Gaia DR3 data. We then analyse MW globular clusters (GCs), benchmarking full spectral synthesis methods against classical isochrone fitting, a crucial step toward deriving ages from integrated spectra of distant, unresolved populations. Finally, we investigate the feasibility of using lensed GCs, now detectable with JWST, as cosmic time tracers at higher redshifts. In the second part, we apply the cosmic chronometers method in two redshift regimes. At z~1.25, we develop a more robust full spectrum fitting implementation, exploring the main sources of systematics. At z~0.5, we extend the analysis to galaxy clusters, evaluating the method's potential in this environment and opening the possibility for multi-probe analyses. We also present forecasts for forthcoming large-scale spectroscopic surveys, expected to achieve percent-level precision. A fundamental strength of this work is that all age determinations are fully independent of any cosmological model. This allows us to provide new constraints on the age of the Universe and H0, along with new H(z) measurements, paving the way toward a time-based reconstruction of the cosmic expansion history.