Toward an independent reconstruction of the expansion history of the Universe

A cosmological-model independent reconstruction of the expansion history of the Universe can help to shed light on the dark sector and the current cosmological tensions. I will discuss past, present, and future efforts to constrain the Hubble parameter H(z) using two optimal astrophysical probes: cosmic chronometers and gravitational waves. The differential aging of massive and passive galaxies can be used to obtain direct measurements of the Hubble parameter without any cosmological assumptions. However, robust dt estimates require deep spectroscopy to break internal degeneracies between stellar population parameters (e.g., age and chemical content). I present a recent analysis of the stellar ages, [Z/H], and [α/Fe] of 140 cosmic chronometers at z~0.7 from the LEGA-C survey using an optimized set of Lick indices (arXiv:2106.14894). From the age-z relation of this population, a new measurement of H(z) is derived, assessing in detail its robustness and dependence on systematic effects (arXiv:2110.04304). Finally, I will discuss the prospects for gravitational wave cosmology in the context of future surveys and third-generation detectors.