Timing the Expansion of the Universe: Improving the Cosmic Chronometers method with Full Spectral Fitting

Modern cosmology has demonstrated that, to uncover the nature of the Universe and shed light on its dark components, it is essential to go beyond standard cosmological probes. This need has become even more pressing due to recent tensions in the measurements of cosmological parameters obtained through different observational techniques. Progress in the field, therefore, requires the development of independent and complementary methods capable of offering robust constraints on the expansion history of the Universe. This thesis focuses on the cosmic chronometers (CC) method, an innovative technique designed to directly measure the Hubble parameter by estimating the differential age evolution of the most massive, passively evolving galaxies as a function of redshift. The primary goal is to establish a more robust and reliable framework for deriving differential ages using full spectral fitting (FSF), and to provide, for the first time, a comprehensive assessment of the systematic uncertainties affecting the FSF approach. The analysis is based on a carefully selected sample of CC from the SDSS BOSS survey in the redshift range 0.15 < z < 0.5, exploiting both the high signal-to-noise ratio of the spectroscopic data and the available photometry. Extensive validation tests are performed to derive accurate and robust galaxy age estimates, which are then used to constrain the differential ages. A key component of this work is the development of a modified version of the Bagpipes code, used for the FSF. This extended version introduces the possibility to vary the choice of stellar population synthesis models, initial mass functions, and stellar libraries, enabling a systematic exploration of model-dependent uncertainties. This analysis leads to a new, robust determination of the Hubble parameter: H(z = 0.34) = 79.3+16.8−13.0 (stat + syst) km/s/Mpc, opening a new avenue for CC as a cosmological probe.